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C-NRLF 



B 2b2 7MT 



LIBRARY 

OF THE 

Jniversity of California. 

Received %yUy^^ • ^^9 9 • 

tccession No.^ y ^"M^ • Cla^s No, 



are now ready. 

In the PRIMER the vowel sounds are presented in an easy 
and natural manner, being in every case exemplified by real 
words rather than by arbitrary syllables, and arranged m rhymmg 
groups. The lessons are composed of sentences woven mto 
narratives, and hieroglyphic lessons have been introduced for 
the purpose of making the work of revisal more varied and 
interesting. 

In the FIRST STANDARD the narrative form has been pre- 
served throughout, and the lessons, while inciidentally supplying 
considerable information, are mainly intended to enable the child 
to overcome the mechanical difficulties of reading. They have 
therefore been made as light and attractive as possible; many 
elliptical, and, as a new feature, several alliterative and hiero- 
glyphic, lessons have been constructed. Easy lessons are also 
given in Script for the reading and writing of Manuscript. 

In the SECOND STANDARD a variety of interesting matter 
has been simplified by the syllabification of difficult words and 
the grouping together of common affixes. A novel feature is 
the introduction of lessons on the Tenses of Verbs. Useful 
information is imparted on common objects and animals, with 
lessons inculcating duty and honour. In Dictation a large pro- 
portion of the matter is shown in Script ; while the Exercises 



Oliver and Boyd's New Code Olass-Books. 

appended to these, direct increased attention to the subjects 
presented, and furnish plenty of school- work. 

In the THIRD STANDARD, as the child will now have 
acquired considerable fluency in easy reading, a varied selection 
has been made from authors that have long been favourites with 
the young. In the Dictation all the difficulties in spelling 
monosyllables and easy dissyllables have been anticipated, and 
the Exercises, which are partly in Script, have been constructed 
so as to foster the habit of observing words and their distinctions. 



11. GEOGRAPHY. 

Three little works have been prepared by INIr W. Lawsox, 
F.Il.G.S., St Mark's College, Chelsea; Author of " Geography 
of the British Empire," etc. 

1. The GEOGRAPHICAL PRIMER will be found adapted to 
the requirements of Standard IV. The meaning of a Map is 
clearly explained ; an outline is given of the Chief Divisions of 
the World ; while the numerous facts have been selected and 
arranged to suit the age of the pupils. 

2. The GEOGRAPHY OF ENGLAND meets the requirements 
of Standard V., and is intended to succeed the " Geographical 
Primer." The style and su!)ject are a little in advance, and 
there is some attempt to show the dependence of one part of the 
geography upon another. A Chapter on the principal Railways 
will be found to meet the increasing desire for information on 
this subject. 

3. ELEMENTS OF PHYSICAL GEOGRAPHY. This work 
has been written as a " Specific Subject," with special reference 
to the New Code. The language and illustrations are simple, and 
suited to the capacity of pupils of from ten to fourteen years of age. 



III. ARITHMETIC. 

This subject has been undertaken by Mr Alex. Teotter, 
Teacher of Mathematics, etc., Edinburgh ; Author of " Arith- 
metic for Advanced Classes," etc. 

Part I. embraces Standards 1 and 2. 

„ II. „ „ 3 and 4. 

Part III. [in preparation) will embrace Standards 5 and 6. 

[Continued at end of Book. 



LESSONS 

IN 

ARITHMETIC 

FOR 
WITH 

TABLES OF MONEY, WEIGHTS, AND MEASURES, 

ACCORDINO TO THE IMPERIAL STANDARDS. 

By JAMES TROTTER, 

LATE OP THE SCOTTISH NAVAL AND MILITARY ACADEMY, 

Author of "A Complete System of Arithmetic," etc. 




EDINBURGH: 

OLIVER AND BOYD, TWEEDDALE COURT. 

LONDON : SIMPKIN, MARSHALL. AND CO. 



Price 6d., or 8d. cloth. Advanced Arithmetic, in Continuation of this 

Work, 6d., or 8d. cloth. Also, strongly bound together in 

leather. Is. 3d. Answers to both Works, 6d. each. 

1872. 



vt 



T7 



SCHOOL-BOOKS BY JAMES TROTTER, 

LATE OF TUB SCOTTISH NATAL ANI> MILITARY ACADEMY. 

LESSONS in ARITHMETIC for Junior Classes. 6d. 
A CoMPLBTB System of ARITHMETIC, Theoretical and Practical. 3s. 
Teotteb's Edition oi MUTTON'S BOOK-KEEPING. 2s. 
A Complete System of MENSURATION, by Ingram & Trotter. 2*. 
Ingram and Trotter's EUCLID; containing the Elements of Plan© 
Geometry and Trigonometry Is. 6d. 

Ingram's Concise System of MATHEMATICS. Revised by Mi 
Trotter. 4s. 6d. 

Trotter's LOGARITHMS and PRACTICAL MATHEMATICS. 3a. 

Ingram and Tbotteb's Elements of ALGEBRA. 38. 



PRINTED BY OLIVER AND BOYD, EDINBURGH. 



ADVERTISEMENT TO THE ENLARGED EDITION. 



The following little Work was originally composed for the 
use of the Author's Junior Classes. It was afterwards 
submitted to the public, in the hope that it would be 
found worthy of an introduction to Public Schools and 
Academies, and that, from the number and variety of the 
Exercises, it might prove a useful auxiliary to Governesses 
and Families. 

This hope having been fully realized, the present Edition 
has been subjected to a careful revision, and enlarged by 
the introduction of simple illustrations of the various rules 
and of a considerable number of Practical Exercises ; at the 
end of the work also, are given Exercises on that system of 
Decimal Coinage which, in course of time, is most likely 
to be adopted in this country. 

These additions have been made by the Author's son, Mr 
Trotter, Teacher of Mathematics, &c., who has recently pre- 
pared a Continuation of this Work for Advanced Classes. 



MULTIPLICATION TABLE. 



2 times 


4 times 


6 times 


8 times 


10 times 


12 times 


2 are 4 


2 are 8 


2 are 12 


2arel6 


2 are 20 


2 are 24 


3 ... 6 


3 ... 12 


3 ... 18 


3 ... 24 


3 ... 30 


3 ... 36 


4 ... 8 


4 ... 16 


4 ... 24 


4 ... 32 


4 ... 40 


4 ... 48 


5 ... 10 


5 ... 20 


5 ... 30 


5 ... 40 


5 ... 50 


5 ... 60 


6 ... 12 


6 ... 24 


6 ... 36 


6 ... 48 


6 ... 60 


6 ... 72 


7 ... 14 


7 ... 28 


7 ... 42 


7 ... 56 


7 ... 70 


7 ... 84 


8 ... 16 


8 ... 32 


8 ... 48 


8 ... 64 


8 ... 80 


8 ... 96 


9 ... 18 


9 ... 36 


9 ... 54 


9 ... 72 


9 ... 90 


9 ... 108 


10 ... 20 


10 ... 40 


10 ... 60 


10 ... 80 


10 ... 100 


10 ... 120 


11 ... 22 


11 ... 44 


11 ... 66 


11 ... 88 


11 ... 110 


11 ... 132 


12 ... 24 


12 ... 48 


12 ... 72 


12 ... 96 


12 ... 120 


12 ... 144 


3 times 


5 times 


7 times 


9 times 


11 times 


20 times 


2 are 6 


2 are 10 


2 are 14 


2 are 18 


2 are 22 


2 are 40 


3... 9 


3 ... 15 


3 ... 21 


3... 27 


3 ... 33 


3 ... 60 


4 ... 12 


4 ... 20 


4 ... 28 


4... 36 


4 ... 44 


4 ... 80 


5 ... 15 


5 ... 25 


5 ... 35 


5... 45 


5 ... 55 


5 ... 100 


6 ... 18 


6 ... 30 


6 ... 42 


6... 54 


6 ... 66 


6 ... 120 


7 ... 21 


7 ... 35 


7 ... 49 


7 ... 63 


7 ... 77 


7 ... 140 


8 ... 24 


8 ... 40 


8 ...56 


8... 72 


8 ... 88 


8 ... 160 


9 ... 27 


9 ... 45 


9 ... 63 


9... 81 


9 ... 99 


9 ... 180 


10 ... 30 


10 ... 50 


10 ... 70 


10... 90 


10 ... 110 


10 ... 200 


11 ... 33 


11 ... 55 


11 ... 77 


11... 99 


11 ... 121 


11 ... 220 


12 ... 36 


12 ... 60 


12 ... 84 


12 ...108 


12 ... 132 


12 ... 240 



EXPLANATION OF ARITHMETICAL TERMS AND SIGNS. 



Number is either a unit, or consists of a collection of units ; 
being the name given to our conception of things considered 
as one or many. 

Abstract numbers. When we consider numbers in their 
general nature, without referring them to any particular 
subject, they are then called abstract; as, 3, 7, 10, &c. 

Concrete or applicate numbers. When we consider 
number not in its general nature, but as applied to certain 
})articular things, as, two pounds, three pence, &c., it is 
termed concrete or applicate. 

A WHOLE number cousists of one or more units. 

A FRACTION consists of one or more parts of unity. 

A mixed number consists of a whole number and a 
fraction. 

A COMPOUND number cousists of several applicate num- 
bers joined together in one expression ; as, £4, 6s. 8d. 

An even number is that which can be divided into two 
equal whole numbers. 

An odd number is that which cannot be divided into two 
equal whole numbers. 

A PRIME number is that which can only be divided by 
itself and unity, without a remainder; and numbers are 
said to be prime to each other when no number but unity 
will divide both without a remainder. 

A SQUARE NUMBER is the product of any number by 
itself. 

A CUBE NUMBER is the product of a number and its 
square. 

A COMPOSITE NUMBER is that produced by multiplying two 
or more numbers together; thus 28 = 4X7 is a composite 
number, and 4 and 7 are called its component parts. 

An ALIQUOT PART is a number which is contained in a 
greater an exact number of times ; thus 4 is an aliquot part 
of 16, but not of 17, as it is contained exactly 4 times in the 
former, and in the latter 4 times and 1 over. 

An integer is any whole number; as, a pound, a mile, 
&c., or, 1, 2, 4, 6, 9, &c. 

Minuend is the greater number in Subtraction. 

buBTRAHEND is the Icss number. 



4 ARITHMETICAL TERMS AND SIGNS. 

MuLHPLicAND in Multiplication is the number to be 
multiplied or repeated. 

Multiplier is the number by which we multiply, or 
which expresses how often the multiplicand is to be repeated. 

Product is the sum or result of the operation in Mul- 
tiplication. 

Factors. The multiplicand and multiplier are called 
factors of the product. 

Divisor in Division is the number by which we divide. 

Dividend is the number to be divided. 

Quotient is the number which shows how often 

the divisor is contained in the dividend, or the result of the 
operation. 

Denomination in applicate numbers is the name of the 
subject to which the number is applied; as, pounds, shil- 
lings, yards, miles, &c. 

Numerator is the upper number of a fraction, and shows 
how many parts of unity are expressed by the fraction. 

Denominator is the under number of a fraction, and 
shows into how many parts the unit is divided, 

A COMMON measure is any number that will divide two 
or more numbers without a remainder, and their greatest 
common measure is the greatest number that will do so 
thus 2 is a common measure of 12 and 18, and 6 is their 
greatest common measure. 

A COMMON multiple of two or more numbers is any 
number that contains each of them an exact number of 
times, and the least number that will do so is called their 
least COMMON MULTIPLE ; thus 48 is a common multiple of 
12, 6, and 4, and 12 is their least common multiple. 

= {equal to) denotes equality; thus 21s. = 1 guinea. 

-f- Cptiis) addition ; thus 6 4-4=10. 

— {minus) subtraction; thus 7 — 3= 4. 

X {multiplied hy) multiplication; thus 4X3 = 12. 

-7- {divided hy) division; thus 18 ~- 6= 3. 

: {is to) : : {as) are signs used in proportion to denote 
an equality of ratios; thus 4 : 6 : : 8 : 12 denote that the ratio 
of 8 to 12 is the same as that of 4 to 6, and is read, 4 is to 
6 as 8 is to 12. 

i represents & farthing ^ or the quarter of any thing. 

i a halfpenny, or the AaZ/of any thing. 

f three farthings, or three quarters of any thing. 



AEIIHMETiCAL TABLES. 



ADDITION AND SUBTRACTION TABLE. 





1 


2 
3 

4 
5 
6 
7 
8 
9 

11 


3 
4 

5 
6 
7 
8 
9 

10 
11 
12 


4 
5 
6 
7 
8 
9 


5 
6 

7 
8 
9 
10 


6 
7 
8 
9 

10 
11 
12 
13 
14 
15 


7 
8 
9 

10 
11 
l2 
13 
14 
l5 
16 


8 
9 

10 
11 
12 
13 
14 
15 
16 
17 


9 

10 
11 
12 
13 

11 
15 

15 

17 
18 


10 
11 
12 
13 
14 
15 
16 
17 

1! 
19 


11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
2l 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 


12 13 


14 
15 
16 
17 
18 
19 
20 

!i 
22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 


15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 


16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 


17:18 


19 


20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
37 
38 
59 
40 


1 

2 
3 
4 
5 


2 
3 
4 
5 
6 


13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 


14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

?1 
32 

33 


18|19 
19|20 
2021 
21j22 
2223 
23:24 
24 25 
25^26 
26 27 


20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
3l 
32 
33 
34 
35 
36 
37 
38 
39 


6 

7 
8 
9 


7 
8 
9 
10 


lOill 
1112 

12 13 

13 14 


10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 


11 
12 
13 
14 
15 
16 

11 

18 

19 
20 
21 


12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 


13 
14 
15 
16 
I7 
18 
19 
20 
21 
22 
23 


14 
l5 
16 
17 
18 
19 
20 
21 
22 
23 
24 


15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 


18 
19 
20 
21 
22 
23 
24 
25 
26 


17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 


18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 


19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 


20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 


27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
37 


28 
29 
30 
31 
32 
33 
34 
35 
36 
37 
38 



Note. Before commencing Arithmetic it is absolutely neces- 
sary that the pupil should commit to memory that part of the 
preceding table which is cut off by a double line. The remaining 
part should likewise be learned as soon as possible. The same 
remark applies to the Multiplication and Division Table on the 
next page, as well as to all the tables which follow. Indeed the 
earlier that a child begins to learn the Arithmetical Tables, the 
more lasting will the impression be upon the mind, and his pro- 
gress in Arithmetic afterwards will be easy and unobstructed. 



ARITHMETICAL TABLES. 



X) 


^ 


s 


§ 


o 


o 

CO 

o 

t 

o 

CT) 

"^ 

00 
00 


■o" 


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o 

00 

co" 

CO 

t 

CO 


o 

t 

o" 
o" 

CO 

t 


o 
CO 

CO 

05 

00 

cO~ 

t 
1 

co" 


o 

CO 

00 

CO 
CO 

CO 

C5 

t 

oo" 

CO 
CO" 


CO 

CO 


i 


o 

00 

CO 




CO 

CO 


CO 


i 


8 


§ 




CO 
CO 

cr> 

CO 

CO 
(N 

CO 
o 

CO 

oc 

(N 


00 
§! 


CO 

c^ 

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c^ 

00 
CD 

CO 

1 

CO 


OS 
00 

l> 

o 


CO 
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CO" 
CO 


CO 

kO 

t 


CO 

CO 

CO 

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05 

t 

CO 


CO 


CO 

CO 


i 


o 

00 
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2 




CO 

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CO 

CO 

CO 

CO 
o 
CO 

00 


o 

CO 


OC' 
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CO 


CO 

CO 


CO 

CO 
CO 
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l> 

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t 

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CO 

t 

CO 


00 

l> 

CO 

"<# 

CO 




Ci 
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o 

00 
Oi 

Ci 


CO 

CO 
oo" 

CO 

t 

co~ 

o 


05 
X; 

£L 

CO 

CO 

To 

1 

CO 


CD 

00 
00 

CO 
o 
CO 

to 
CO 

-^ 




o 
'f 

CO 

CO 
CO 


CO 

CO 
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CO 




CO 
CO 

FT 


o 

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CO 


o 

CO 

05 
tH 


t 

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s 




— ( 

o 

X) 




CO 


^ 

^ 
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s 


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00 


s 


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o 


o 
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00 
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05 

cd" 


00 

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co" 

t 


CD 
CO 

2 

00 

co~ 

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t 

To 

CO 


00 

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05 

o 

05 

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CO 

xO 

co" 

CO 


o 
o 

CO 

t 

CO 


CO 

o 

C5 

X 






CO 
CO 




00 
00 


C5 


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CO 


2 


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00 
CO 




CD 

CO 

CO 

CO 


2 


00 


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g 


1 


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05 
05 

00 
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05 

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05 


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t 

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00 




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CO 


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05 


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GO 

o 


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05 


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00 


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00 


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c 


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00 
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CO 
CO 


00 

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tH 

05 


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CO 
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*>* 

CO 

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00 
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05 


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CO 


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CD 


r> 


00 


CJ5 


o 


^ 


CO 


CO 


05 


o 

CO 





Note. In using the preceding table for a Division one, we 
take the numbers in the left-hand column out of the numbers in 
the same horizontal line, and the number of times each is con- 
tained will be found either in the top or bottom line. 



ARITHMETICAL TABLES. 



STERLING MONEY. 

4 farthings qi's. =■ 1 penny d. 
12 pence =: 1 shilling 5. 

5 shillings =. 1 crown cr. 

20sMm„gs ={Lrrefg^''£ 
21 shillings = 1 guinea G. 



TROY WEIGHT. 
24 grains ^r.= 1 penny weiglit (fitf^ 
20 dwt. = 1 ounce oz. 

12 ounces = 1 pound lb. 

Gold, Silver, and Jewels, are weighed 
by Troy Weight. 



APOTHECARIES' WEIGHT.* 
20 grains gr. = 1 scruple ^ 
3 scruples = 1 dram ^ 

8 drams = 1 ounce 5 

12 ounces = 1 pound lb. 

Used only for medical prescriptions. 

AVOIRDUPOIS WEIGHT. 
16 drams cZr.^i 1 ounce oz. 

16 ounces = 1 pound lb. 

28 pounds = 1 quarter qr. 

4 quarters = 1 hundred wt. cvA. 
20 hund wt.= 1 ton T. 

112 lbs. = 1 cwt. 

7000 grains = 1 lb. avoird. 

14 lb. = 1 stone 

This table is used for all articles, except 
Gold, Silver, and Jewels. 



LINEAL MEASURE. 



12 lines li. 

12 inches 

3 feet 
5i yards 

40 poles 

8 furlongs 

reO yards 



= 1 inch 171. 

= 1 foot ft. 

=. 1 yard i/d. 

= 1 pole po. 
= 1 furlong fur. 

= 1 mile ml. 
= 1 mile 



2 yds. or 6 feet = 1 fathom 
2 i feet = a military pace 

4 inches = 1 hand 

1 1 foot = 1 cubit 

22" yds. or 66 ft. = 1 chain; and as 
the chain contains 100 links, 
each link is = 7*92 inches, 
and 80 chains = 1 mile. 



CLOTH MEASURE. 

2} inches = 1 nail nl. 

4 nails = 1 quarter qr. 

4 quarters = 1 yard yd. 

8 quarters = 1 Flemish ell Fl. e. 

5 quarters = 1 English ell En. «. 

6 quarters =: 1 French ell Fr. e. 
37 inches = 1 Scotch ell Sc. e. 



GEOGRAPHICAL MEASURE. 
6076 feet nearly = 1 geo. mile 
3 miles = 1 league le. 

20 leagues = 1 degree dpg. or" 
360 degrees =. the earth's cir- 
cumference 



SQUARE, OR LAND MEASURE. 

144 square inches = 1 square foot 
9 sq. feet = 1 square yard 

30 J sq. yards ^ 1 pole or perck 
40 perches = 1 rood ro. 
4 roods =1 acre ac. 

640 acres = 1 sq. mile 

36 sq. yards = 1 rood of building 
100 sq. feet =1 square of flooring 

10 sq. chains, or ) ^ 

100,000 sq. links | — -^ acie 

CUBIC, OR SOLID MEASURE. 
1728 cubic inches = 1 cubic foot 
27 cubic feet = 1 cubic yard 

40 cubic feet of) 

rough, or 50 of V= 1 load lo. 

hewn timber J 
42 cubic feet = 1 ton shipping 

6 cubic feet = 1 barrel bulk 



MEASURE OF CAPACITY. 
2 pints pt. = 1 quart qt. 

4 quarts = 1 gallon 

2 gallons = 1 peck 

4 pecks = 1 bushel 

8 bushels = 1 quarter 



pk. 
bu. 
qr. 



ANGULAR MEASURE. 
60 seconds " =1 minute ' 
60 minutes = 1 degree ** 

30 degrees = 1 sign 5. 

12 signs = 1 circle cira. 



• In the British Pharmacopoeia (1864), the 
whue the lb. avoir, of 7000 grains, and the oz. 1 



. Troy of 4f10 prains has been abolished, 
»oir. of 437^ grains, have been adopted. 



ARITHMETICAL TABLES. 



APOTHECARIES' 
FLUID MEASURE * 

60 minims min. = 1 drachm Jl. drm. 

8 drachms = 1 ounce /f. oz. 
20 ounces = 1 pint O. 

8 pints = 1 gallon C. 



HAY AND STRAW WEIGHT. 

36 lbs. avoir. = 1 truss of straw 
56 lbs. = 1 truss of old hay 

60 lbs. = 1 truss of new hay 

36 trusses = 1 load 

Hay sold befween the begirning of June 
and the end of August, of that gear's 
growth, is reckoned new. 



TIME. 

60 seconds sec. = 1 minute mi. 
60 minutes = 1 hour ho. 

24 hours =. 1 day da. 

7 days = 1 week we. 

4 weeks = 1 co. month mo. 

365 days, or 52 ] 

weeks and 1 >-= 1 co. year t/e. 
day j 

365J days = 1 Julian year 

366 days = 1 leap year 

The year is divided into 12 cal 
endar months, viz. : 



QUARTERLY TERMS. 

In England. 
Lady-day, March 25. 

Midsummer, June 24. 

Michaelmas, September 29. 

Christmas, December 25. 

In Scotland. 
Candlemas, February 2. 

Whitsunday, May 15. 

Lammas, August 1. 

Martinmas, November 11. 

FLOUR & BREAD WEIGHT. 
A peck-loaf = 17 lb. 6 oz. avoird. 
A half-peck do. = 8 11 — 

A quarter-loaf = 4 5J — - 

A peck of flour is 14-44 lb,, or 
14J lbs. nearly, and a bushel 57J lbs. 
very nearly. Five bushels make a 
sack, which ought to weigh 288-8 
lbs. avoirdupois. 

The number of days in each month may be easily remembered from 
the following lines : 

Thirty days hath September, 
April, June, and November; 
All the rest have thirty-one, 
Excepting February alone, 
Which hath but 28 days clear, 
And 29 in each leap year. 

365 days 5 hours 48 min. 50 sec. = 1 solar or tropical year. 



January 31 days. 
February 28 — 
March 31 — 
April 30 — 
May 31 — 

June 30 — 



July 31 days. 
August 31 — 
Septem.30 — 
October 31 — 
Novem. 30 — 
Decern. 31 — 



MISCELLANEOUS TABLE. 



24 sheets 

20 quires 

10 reams 

12 articles 

20 articles 

12 dozen 

12 gross 

120 articles 

500 bricks 

1000 tiles 



: 1 quire of paper 

: 1 ream 

: 1 bale 

: 1 dozen 

: 1 score 

: 1 gross 

r 1 great gross 

= 1 great hundred 

: 1 load 

= 1 load 



500 herrings = 

500 red do. = 

10(X) sprats = 

60 herrings = 

100 lbs. avoir.: 

56 lbs. = 

64 lbs. = 

256 lbs. = 

112 lbs. r 

19i cwt. = 



: 1 barrel 

: 1 cade 

: 1 cade 

:1 keg 

: 1 bari. gunpowder 

: 1 firkin of butter 

: 1 firkin of soap 

: 1 baiTel of soap 

: 1 barrel of raisins 

: 1 foddftr of lead 



♦ AocordiiMi to the British Pharmacopoeia (18C4>. 



ARITHMETICAL TABLES. 



Farthings. 


Pence. 


qrs 


d. 


d. s. d. 


4= 


= 1 


12=1 


6. 


.. 1; 


13.. .1 1 


6. 


.. It 


14.. .1 2 


7. 


.. 1: 


15.. .1 3 


8. 


.. 2 


16.. .1 4 


9. 


.. 2J 


17.. .1 5 


10. 


.. 2% 


18.. .1 6 


11. 


.. 2| 


19.. .1 7 


12. 


.. 3 


20.. .1 8 


13. 


.. 3i 


21.. .1 9 


14. 


. 3$ 


22.. .1 10 


15. 


. 3| 


23.. .1 11 


IG. 
17. 
18. 
19. 


. 4 


24... 2 
25.. .2 1 
26.. .2 2 
27.. .2 3 


20. 
21. 


. 5 
. 5i 


28.. .2 4 
29.. .2 5 


22. 


. 5 J 


30.. .2 6 


23. 


. 61 


31.. .2 7 


24. 


. 6 


32.. .2 8 


25. 


. 6J 


33.. .2 9 


26. 


. ^ 


34.. .2 10 


27. 


• 4 


35.. .2 11 


28. 


. 7 


36.. .3 


29. 


• 7} 


37.. .3 1 


30. 


• 7} 


38.. .3 2 


31. 


• n 


39.. .3 3 


82. 


. 8 


40... 3 4 


33. 


• 8i 


41.. .3 5 


34.. 


. 8} 


42.. .3 6 


35.. 


• n 


43.. .3 7 


36.. 


. 9 


44.. .3 8 


37.. 


• H 


45... 3 9 


38.. 


. 9f 


46.. .3 10 


39.. 


• n 


47. ..3 11 


40.. 


.10 


48... 4 


41. 


•lOi 


49.. .4 1 


42. 


•lOJ 


50... 4 2 


43. 


.io| 


51. ..4 3 


44 


.11 


52... 4 4 


45. 


.llj 


53... 4 5 


46. 


.11} 


54... 4 6 


47. 


.lll 


55.. .4 7 


48. 


.12 


56.. .4 8 



MONEY TABLE. 



d. s. 
57=4 
58.. .4 
59.. .4 
60... 5 
61.. .5 
62.. .5 
63..,5 
64.. .5 
65.. .5 
66.. .5 
67.. .5 
68.. .5 
69.. .5 
70.. .5 
71.. .5 
72.. .6 
73... 6 
74.. .6 
75.. .6 
76.. .6 
77.. .6 
78.. .6 
79.. .6 
80... 6 
81.. .6 
82.. .6 
83... 6 
84.. .7 
85.. .7 
86.. .7 
87.. .7 
88.. .7 
89.. .7 
90.. .7 
91.. .7 
92.. .7 
93... 7 
94... 7 
95.. .7 
96.. .8 
97.. .8 
98.. 8 
99... 8 
100.. .8 
101.. .8 





Shillings. 1 


. d. 


sk. 


£ s. 


9 


20= 


=1 


10 


21. 


..1 1 


11 


22. 


..1 2 





23. 


..1 3 


1 


24. 


..1 4 


2 


25. 


..1 5 


3 


26. 


..1 6 


4 


27. 


..1 7 


5 


28. 


..1 8 


6 


29. 


..1 9 


7 


30. 


..110 


8 


31. 


..1 11 


9 


32. 


..1 12 


10 


33. 


..1 13 


11 


34. 


.1 14 





35. 


..1 15 


1 


36. 


.116 


2 


37. 


.1 17 


3 


38. 


.1 18 


4 


39. 


.1 19 


5 


40. 


.2 


6 


41. 


.2 1 


7 


42. 


.2 2 


8 


43. 


.2 3 


9 


44. 


.2 4 


10 


45. 


.2 5 


11 


46. 


.2 6 





47. 


.2 7 


1 


48. 


.2 8 


2 


49. 


.2 9 


3 


50. 


.2 10 


4 


51. 


.2 11 


5 


52. 


.2 12 


6 


53. 


.2 13 


7 


54.. 


.2 14 


8 


55. 


.2 15 


9 


56. 


.2 16 


10 


57. 


.2 17 


11 


58. 


.2 18 





59. 


.2 19 


1 


60. 


.3 


2 


61. 


.3 1 


3 


62. 


.3 2 


4 


63. 


.3 3 


5 


64. 


.3 4 



sh. 

65= 

66. 

67. 

68. 

69. 

70. 

71. 

72. 

73. 

74. 

75. 

76. 

77. 

78. 

79. 

80. 

81. 

82. 

83. 

84. 

85., 

86., 

87., 

88., 

89., 

90., 

91., 

92.. 

93.. 

94.. 

95.. 

96.. 

97.. 

98.. 

99.. 
100.. 
101.. 
102.. 
103.. 
104.. 
105.. 
106.. 
107.. 
108.. 
109., 



£ 
=3 
.3 
.3 

..3 
,.3 9 
.3 10 
,.3 11 
.3 12 
,.3 13 
.3 14 
.3 15 
.3 16 
.3 17 
.3 18 
.3 19 
.4 
.4 1 



.4 
.4 
.4 
.4 
.4 
.4 
.4 
4 

.4 10 
.4 11 
.4 12 
.4 13 
.4 14 
.4 15 
.4 16 
.4 17 
.4 18 
.4 19 
.5 



10 



ARITHMETICAL TABLES. 



NUMERATION TABLE. 

Units 9 

Tens 98 

Hundreds 987 

Thousands 9; 876 

Tens of Thousands 98; 765 

Hundreds of Thousands 987 ; 654 

Millions 9 ; 876 ; 643 

Tens of Millions 98; 765; 432 

Hundreds of Millions 987 : 654 ; 321 

Billions 9; 876; 543; 210 

Tens of Billions 98; 765; 432; 109 

Hundreds of Billions 987; 654; 321; 098 

Trillions 9; 876; 543; 210; 987 



EOMAN NOTATION. 

The Eomans used the following letters only for numbers, viz. 
I one, V five, X ten, L fifty, C a hundred, D or Iq five hundred, 
and M or CI^ a thousand. 

Any letter followed by another of equal or less value denoted 
the sum of their separate values ; thus III three, LXXVl 
seventy-six. 

Any letter followed by another of greater value denoted the 
liflerence of their separate values ; thus XL forty, XC ninety. 

Every 3 annexed to Iq, and every C and 3 joined to CIq, 
increased the value ten times ; thus 1q3 five thousand, CCIq;;) 
ten thousand. 

A line drawn over a letter denoted that its simple value was 
increased a thousand times ; thus X ten thousand, XL forty 
thousand. 



1 


or 1 


XVII 


or 17 


II 


.. 2 


XVIII 


.. 18 


III 


.. 3 


XIX 


.. 19 


IV 


.. 4 


XX 


.. 20 


V 


.. 5 


XXI 


.. 21 


VI 


.. 6 


XXII 


.. 22 


VII 


.. 7 


XXIII 


.. 23 


VIII 


.. 8 


XXIV 


.. 24 


IX 


.. 9 


XXV 


.. 25 


X 


.. 10 


XXVI 


.. 26 


XI 


.. 11 


XXVII 


.. 27 


XII 


.. 12 


XXVIII 


.. 28 


XIII 


.. 13 


XXIX 


.. 29 


XIV 


.. 14 


XXX 


.. 30 


XV 


.. 15 


XL 


.. 40 


XVI 


.. 16 


L 


.. 50 



LX or 


60 


LXX 


70 


LXXX 


80 


XC 


90 


C 


100 


CI, &c. 


101 


CC, &c. 


200 


CCCC or CD .. 


400 


lO or D 


500 


l0CorDC,&c. .. 


600 


loCCCC, DCCCC, 


or CM 900 


CIo or M 


1000 


CIoCorMC,&c... 


1100 


MM or II, &c. .. 


2000 


loo 0^ ^» «^c. .. 


5000 


lODO or L, &c. .. 


50,000 



ARITHMETIC. 



Arithmetic, as a science, explains the propei'ties of num- 
bers, and as an art, the methods of computing by them. 

The fundamental rules are. Numeration, Notation, Ad- 
dition, Subtraction, Multiplication, and Division. 

The characters by which all numbers are expressed are, 
1, one or unit; 2, two; 3, three; 4, four; 5, Jive; 6, six, 
7, seven; 8, eight; 9, nine; 0, cipher or nought. 



NUMERATION 
Is the art of reading a number expressed in figures. 

Trillions. Billions. Millions. Thousands. Units. 

604; 450; 360; 412; 474. 

Read or write in words the following : 
24079 — Twenty-four thousand and seventy-nine. 
79_97_18— 24— 81— 67— 76— 35— 67— 26— 53— 91 — 19 
—48—101—208—84—110—802 — 111 — 109—119 — 125 — 
152—319—913—301—310—4617—4107—4170—28410— 
20814—5106—74125—47010—2097431—501746-730087— 
1730086—9704010—21070—20202020—5170409 — 2017101 
— 74107 — 1074010 — 29654301 — 102030401 — 157301074 
—748017018—547207542—63710073001—54872193543270. 



NOTATION 
Is the art of expressing any given number in figures. 

Express in fig^ires the following : 
Five thousand and sixty-four — 5064. 
Seventy-four — ninety-six — one hundred and one — one 
hundi-ed and ten — one hundred and eleven — two hundred 
and eight — one hundred and eighteen — one hundred and 
thirty-one — one hundred and thirteen — seven hundred and 
eight — nine hundred and eighty — two thousand, three hun- 
dred and twenty-one — nine thousand and seven — twenty- 
one thousand and ten — one hundred and fifty thousand 
and five — six millions, forty thousand and thirty — eighty- 
niue millions, one hundred and forty thousand and twenty- 
six — seven hundred billions, ten millions, eleven thousand, 
one hundred and one — four hundred and one millions, seventy 
thousand and seventeen — eight trillions, twenty billions, 
sixty-nine millions, four thousand and sixty-three. 

B 



12 



SIMPLE ADDITION 
Is the method of finding a number equal to several num- 
bers taken togetlier. The number found is called the 
sum or amount. 







EXERCISES ON THE ADDITION TABLE. 






1. 2. 


3. 4. 5. 6. 7. 8. 9. 10. 11. 


12. 


13. 




2 


3 


4 


5 


6 


7 


8 


9 


4 


5 


6 


7 




2 


3 


4 


5 


6 


7 


8 


9 


3 


4 


5 


6 




2 


3 


4 


5 


6 


7 


8 


9 


2 


3 


4 


5 




2 


3 


4 


5 


6 


7 


8 


9 


1 


2 


3 


4 




2 


3 


4 


5 


6 


7 


8 


9 


4 


1 


2 


3 




2 


3 


4 


5 


6 


7 


8 


9 


2 


5 


1 


2 




2 


3 


4 


5 


6 


7 


8 


9 


3 


2 


5 


7 


7 


14 


21 


28 


35 


42 


49 


56 


63 


19 


22 


26 


34 



14. 


15. 


16. 


17. 


18. 


19. 


20. 


21. 


22. 


23. 


24. 


25. 


26. 


27. 


28. 


7 


6 


9 


5 


4 


9 


7 


7 


6 


3 


6 


2 


6 


2 


4 


3 


3 


5 


2 


2 


1 


3 


4 


4 


4 


2 


1 


7 


3 


5 


9 


8 


4 


1 


7 


2 


8 


8 


8 


5 


7 


2 


8 


4 


6 


6 


4 


3 


4 


1 


4 


1 


2 


7 


9 


3 


3 


9 


5 


7 


5 


2 


6 


8 


6 


6 


5 


1 


3 


6 


1 


4 


1 


6 


8 


4 


1 


2 


3 


8 


7 


4 


1 


5 


8 


2 


6 


2 


7 


9 


2 


6 


1 


7 


5 


5 


2 


3 


4 


7 


2 


1 


3 


8 


2 


8 


8 


8 


9 


9 


8 


6 


3 


2 


3 


3 


2 


4 


9 


4 


4 


4 


7 


6 


3 


3 


9 


4 


1 


4 


4 


3 


5 


1 


5 


7 


5 


3 


8 


2 


6 


7 


2 


1 


5 


4 


4 


6 


2 


6 


1 


2 


6 


2 


7 


4 


3 


1 


2 


6 


2 


5 


7 


3 


7 



29. 


30. 


31. 


32. 


33. 


34. 


35. 


36. 


37. 


38. 


39. 


40. 


41. 


42. 


43. 


7 


4 


7 


8 


1 


7 


4 


7 


9 


9 


6 


3 


5 


7 


9 


2 


2 


9 


7 


9 


2 


2 


9 


7 


2 


7 


8 


2 


2 


5 


6 


3 


6 


6 


6 


1 


9 


6 


5 


8 


4 


1 


1 


9 


4 


1 


1 


5 


2 


3 


8 


9 


3 


6 


6 


8 


7 


4 


8 


6 


8 


8 


4 


1 


4 


4 


8 


8 


3 


8 


2 


4 


7 


5 


7 


3 


7 


2 


3 


8 


2 


7 


7 


8 


4 


4 


2 


9 


3 


2 


9 


5 


1 


8 


7 


1 


5 


2 


7 


2 


8 


6 


8 


1 


1 


5 


4 


3 


4 


2 


3 


6 


9 


4 


2 


2 


9 


3 


4 


3 


6 


2 


9 


6 


1 


8 


7 


8 


5 


8 


6 


8 


6 


7 


5 


4 


1 


5 


2 


6 


2 


8 


4 


8 


7 


5 


3 


9 


2 


7 


5 


3 


2 


1 


1 


1 


5 


6 


3 


4 


1 


7 


4 


3 


9 


3 


8 


1 


8 


8 


6 


4 


3 


7 


6 


2 


9 


8 


9 


6 



SIMPLE ADDITION. 



13 



Example. Add together 847, 478, 19, and 951. Ans. 229 
Solution. Arrange the numbers as in the margin ; 
adding the units' or right-hand column, 1 and 9 are 
10 and 8 are 18 and 7 are 25 ; write down 5 and carry 
2 to the second column : 2 and 5 are 7 and 1 are 8 
and 7 are 15 and 4 are 19 ; write down 9 and carry 
1 to the third column : 1 and 9 are 10 and 4 are 14 
and 8 are 22 ; write down 22, and the answer is 2295. 

The work may be checked by adding the columns down^ 
wards. 



847 

478 

19 

951 

2295 



1. 


2. 


3. 


4. 


5. 


6. 


7. 


8. 


9. 


10. 


234 


754 


869 


649 


214 


314 


987 


374 


215 


118 


982 


475 


698 


495 


421 


431 


879 


743 


152 


181 


342 


638 


986 


218 


638 


209 


798 


437 


521 


811 


758 


863 


213 


821 


863 


920 


654 


865 


634 


214 


875 


921 


542 


637 


759 


516 


465 


685 


463 


579 


426 


192 


121 


736 


975 


651 


546 


856 


346 


798 



11. 


12. 


13. 


14. 


15. 


16. 


17. 


18. 


7486 


2146 


4816 


5411 


2222 


8888 


5555 


4848 


4867 


6412 


6184 


2196 


3333 


9999 


6666 


5959 


2194 


1093 


7298 


3482 


4444 


nil 


7777 


6767 


1942 


3901 


8735 


9876 


5555 


2222 


8888 


7676 


7368 


2473 


4567 


3846 


^m^ 


3333 


9999 


9595 


3687 . 


3742 


8912 


2198 


7771 


4444 


1111 


8484 



19. 


20. 


21. 


22. 


23. 


24. 


25. 


26. 


1234 


7921 


4869 


1276 


1874 


2764 


4872 


6729 


6678 


1297 


5728 


2761 


7481 


6427 


3481 


6278 


9012 


3808 


6372 


3849 


2310 


3818 


5834 


6483 


3456 


8076 


7184 


4598 


1046 


2984 


6287 


7321 


7890 


6487 


8296 


6623 


9875 


4629 


7821 


1234 


1234 


7923 


9543 


6312 


6793 


9273 


1234 


6678 



27. 


28. 


29. 


30. 


31. 


32. 


33. 


34. 


9847 


2146 


4121 


1214 


2009 


.9817 


9002 


7189 


6438 


6148 


1246 


6421 


9002 


1789 


2009 


9871 


5279 


6437 


3459 


9543 


4716 


2138 


6174 


8312 


7346 


2977 


9528 


8259 


6174 


4817 


4716 


7184 


8978 


3888 


6473 


3746 


8136 


7864 


6318 


4687 


6438 


8436 


8987 


7898 


2198 


3189 


8912 


9813 



14 



SIMPLE ADDITION. 



35. 


36. 


37. 


38. 


39. 


40. 


41. 


8729 


4816 


7286 


9112 


9876 


5469 


5726 


7298 


3729 


3465 


2968 


2187 


3874 


6275 


4165 


5412 


2187 


4627 


4632 


5286 


3874 


2189 


8046 


7129 


3729 


2893 


9684 


9873 


3145 


4208 


1408 


8463 


3984 


5836 


3521 


8729 


9807 


1076 


2198 


5726 


2194 


1234 



42. 

8768 
7543 
2189 
9138 

4672 
8279 



43. 


44. 


45. 


46. 


47. 


48. 


49. 


50. 


7284 


4869 


2790 


4286 


5216 


2149 


1876 


2168 


4563 


4964 


4623 


6384 


2615 


9186 


3848 


8614 


3629 


5208 


2347 


2198 


3842 


3456 


2193 


2196 


9245 


2080 


5867 


5486 


2876 


7289 


1984 


5483 


5483 


1897 


3867 


2173 


3184 


9738 


4876 


3146 


2196 


7986 


9218 


4817 


7296 


4865 


3842 


8965 



51. 


52. 


53. 


54. 


55. 


56. 


57. 


58. 


9726 


6295 


4872 


2138 


4965 


9876 


3097 


2974 


8643 


4368 


2198 


5483 


3846 


6298 


9808 


9084 


5273 


7348 


8169 


9654 


3876 


6786 


4097 


9840 


2736 


2763 


2367 


3672 


6723 


7236 


1876 


9489 


1894 


9653 


6539 


4875 


9864 


2198 


8965 


1284 


9867 


2198 


4963 


2186 


4372 


7234 


8629 


5814 


3095 


1986 


9631 


8472 


3729 


2139 


6243 


8145 



59. 


60. 


61. 


62. 


63. 


64. 


65. 


66. 


7486 


2981 


7298 


2184 


4763 


4863 


3456 


9871 


2193 


1892 


8917 


4218 


8769 


6348 


7890 


2179 


4728 


3720 


2347 


5763 


2986 


2176 


1234 


5046 


2089 


4175 


5486 


3698 


4863 


8472 


5678 


6804 


9082 


5176 


3847 


7296 


3648 


2784 


9012 


8470 


4754 


2347 


9176 


4738 


2198 


5168 


3456 


1986 


7538 


6129 


7153 


7219 


1927 


3615 


7891 


3459 



67. 


63. 


69. 


70. 


71. 


72. 


73. 


74. 


1874 


2112 


7411 


2119 


86 


834 


2174 


2487 


7486 


331 


1721 


9112 


186 


4747 


4187 


87 


8291 


2897 


862 


7486 


5681 


6363 


83 


7428 


9182 


987 


48 


3849 


2196 


5995 


3189 


83 


3748 


729 


5496 


486 


987 


559 


5 


4876 


1876 


8297 


7486 


42 


91 


87 


1765 


42 


741 


54 


59 


3798 


8746 


63 


6789 


9899 


3496 


7289 


876 


7983 


3904 


7298 


49 


114 



SIMPLE ADDITION. 



15 



75. 


76. 


77. 


78. 


79. 


80. 


87469 


18734 


89846 


19876 


98846 


11421 


84697 


81423 


72844 


28674 


21174 


21896 


33442 


47884 


51168 


54869 


38965 


69847 


21756 


58337 


27489 


96843 


56897 


38176 


67498 


21486 


98472 


21876 


21984 


47897 


39846 


68742 


21224 


48638 


51478 


38189 


27485 


89638 


18769 


88768 


31894 


49898 


58744 


48621 


97652 


21777 


98499 


98974 



81. 


82. 


83. 


84. 


85. 


86. 


74985 


71279 


84120 


98797 


98724 


34563 


12345 


48694 


21796 


38468 


84786 


78908 


67890 


38848 


69845 


21896 


86749 


42809 


90876 


97120 


38471 


54868 


87498 


90786 


65217 


17208 


18769 


98976 


98863 


36094 


71489 


80967 


48684 


48698 


97377 


27158 


38594 


74689 


18769 


38489 


98776 


38646 


48684 


98467 


38478 


89765 


19864 


64583 



87. 


88. 


89. 


90. 


91. 


92. 


47216 


90804 


49899 


48899 


87748 


47189 


86143 


79048 


98765 


37744 


51123 


98765 


31487 


21886 


34775 


44768 


17648 


38486 


21879 


66477 


21984 


89443 


48679 


34896 


39842 


38896 


56348 


34886 


15015 


69847 


23876 


59769 


84237 


29876 


27987 


97849 


54875 


27998 


73486 


54869 


92764 


38488 


16846 


54889 


54997 


12345 


89898 


21776- 



93. 


94. 


95. 


96. 


97. 


98. 


94863 


42174 


8989 


49864 


97867 


8765 


8639 


7148 


98798 


644 


1008 


219 


86394 


837 


654 


6449 


976 


38480 


7563 


1896 


94568 


21786 


54890 


10846 


75638 


61784 


28 


38486 


12789 


8973 


6387 


4721 


2875 


9876 


76 


87997 


29846 


12 


38486 


54868 


38147 


738 


4875 


38469 


94783 


987 


21898 


84778 



99. 7368+ 8451+5184+6372+ 3147+1763 + 2189. 

100. 5436+ 2195+7964+6830+ 8347+5146+ 798. 

101. 73847+85487+3486+5763+84695+3146+ 495. 

b2 



16 



SIMPLE ADDITION. 



102. 


103. 


104. 


105. 


106. 


714816 


187621 


876548 


971028 


918765 


148617 


317849 


721473 


876980 


187659 


548389 


948647 


374869 


487694 


876591 


821864 


218698 


968768 


527389 


243876 


217784 


384869 


486842 


938765 


438762 


548987 


198768 


172986 


387659 


387624 


987786 


2147-29 


348697 


647548 


876554 


489754 


987486 


374898 


475486 


554433 


457986 


579864 


548694 


754864 


765432 



107. 


108. 


109. 


110. 


111. 


314579 


869457 


304756 


274816 


908076 


145793 


694578 


475630 


748163 


807069 


457931 


945786 


756309 


481634 


760908 


579314 


457869 


563098 


816345 


219374 


894632 


578694 


630987 


123456 


475432 


946328 


786945 


789063 


234567 


173849 


463284 


123456 


890637 


345678 


948386 


632846 


789012 


637890 


876543 


872198 


328466 


345678 


378906 


765432 


749865 


778998 


901234 


906378 


654321 


384976 



112. 


113. 


114. 


115. 


116. 


548637 


493128 


795846 


497864 


998776 


486378 


931284 


598467 


864794 


887769 


863789 


312849 


218694 


468479 


776698 


637890 


128493 


580308 


684947 


433821 


749087 


740086 


984678 


218624 


388466 


490876 


409648 


394867 


374186 


218968 


471874 


218408 


973842 


987384 


478149 


548643 


184820 


298765 


219864 


941798 


896847 


123456 


458738 


718698 


217486 


376849 


654321 


219986 


398748 


989999 


729287 


987489 


487219 


216847 


874865 



117.47563+74298+98254+214865+652193+381964 
+300892+476983+396847+734682. 

118. 2 14736 + 637240 + 509984 +998447 + 219863 + 
863214+792186+197235+748692+897628. 

119. 742869+38475+8476+317286 + 863217 + 9846 
+72354+748693+7486+95476+4721864. 





SIMPLE ADDITION. 


17 


120. 


121. 


122. 


123. 


124. 


786904 


5744 


217846 


849784 


216 


72189 


186473 


3868 


84 


47386 


2891 


862 


9 


7698 


472 


749863 


7648 


778466 


377669 


8 


2847 


97448 


47 


4886 


67489 


47283 


189654 


3848 


847334 


738789 


898647 


347219 


543896 


27 


48 


98 


386 


8965 


7846 


2748 


749 


4 


47 


987654 


64 


7864 


786473 


889764 


87654 


736 


987654 


876 


74869 


78 


876489 



125. 7486 + 7489 + 9846 + 3748 + 5634+7486+ 9847 
+5329+4675+3869+9873+8469+4683. 

126. 5276+8943+9486+3114+98760+3456+72894 
+729+89657+3846+47836+7584+48765. 

127. 74486+311472+68476+38169+744869 + 1870 
+542138+216746+9876+521869+31468. 

128.7486957+75312984+9104763+7238641+521437 
+43879654+9876+34819+9896543+47869847. 

129. The population of London, in 1851, was 2,362,236 ; 
of Dublin, 258,369 ; of Edinburgh and Leith, 191,221 ; 
of Glasgow, 329,097; of Liverpool, 375,955; of Bir- 
mingham, 232,841 ; of Manchester, 316,213 ; of Bristol, 
137,328 ; and of Leeds, 172,270 : required the amount of 
the whole. 

130. Bought a house for £3150 ; what should it be 
sold for to gain £275? 

131. The number of wrecks and collisions on or near 
the coasts of the United Kingdom in 1852 was 1015 ; in 
1853, 832; in 1854, 987; in 1855, 1141; and in 1856, 
1153 : find the whole number during these five years. 

132. The total number of British Cavalry who joined 
the Allied Army in the Crimean Campaign, was 4819 ; 
Artillery, 7032 ; Sappers and Miners, 403 ; and Infantry, 
43,726 : how many men joined in all? 

133. In 1856, the passengers conveyed by Kail in 
Scotland were. First Class, 1,664,005; Second Class. 
1,952,240; Third Class, 9,476,226; Mixed, 4767: find 
the total number. 

c 



18 SIMPLE ADDITION. 

134. In the same year the receipts were, First Class. 
£232,130; Second Class,£171,588; Third Class,£436,564; 
Mixed, £14,892 : required the whole sum. 

135. Find the sum of twenty- seven thousand, eight 
hundred and forty-nine — thirty-eight thousand, live 
hundred and forty-six — eight thousand and nine — twelve 
thousand, nine hundred and sixty-three — five thousand 
and forty — five hundred and seventy-eight thousand and 
forty-six — nineteen thousand and sixty — twenty-seven 
thousand, eight hundred and forty-seven. 

136. A merchant has £1275 in the bank ; his goods are 
worth £2760 ; his household furniture, £565 ; and debts 
owing to him, £674 : how much is he worth ? 

137. What quantity of tea was consumed in the 
United Kingdom in 1856, England having consumed 
47,986,635 lbs. ; Scotland, 6,583,233 lbs. ; and Ireland, 
8,708,344 lbs. ? 

138. In 1856, the Emigrants to Canada consisted of 
5555 English; 3872 Scotch ; 4357 Irish ; 3136 Prussians , 
2806 Norwegians; 1249 Germans; 823 Belgians; 260 
Swiss, and 381 Italians, French, &c. ; find the whole 
number. 

139. Two travellers start from the same place and 
travel in opposite directions, the one travels 75 miles 
the first day, 63 the second, and 45 the third ; while the 
other travels 65 miles the first day, 180 the second, and 
378 the third : how far distant will they then be from 
each other ? 

140. In 1856, the quantity of cofi*ee consumed in Eng- 
land was 33,019,884 lb. ; in Scotland, 1,197,6851b. ; and 
in Ireland, 778,385 lb. : what quantity was consumed in 
the United Kingdom ? 

141. In 1856, the tonnage of registered ships in the 
British Empire was in England, 3,461,031 tons ; in 
Scotland, 592,974 ; in Ireland, 250,455 ; in Jersey, Man, 
&c., 62,496 ; and in the Colonies, 949,780 tons : find 
the amount of tonnage. 

142. A merchant owes to A £597, to B £694, to C 
£748, to D £899, to E £1045, and to F £1303 j how 
much does he owe in all? 



19 



SIMPLE SUBTRACTION 
Is the method of taking a less number from a greater. 

The greater number is called the minuend^ the less, 
the subtrahendj and the number found, the remainder or 
difference. 



Ex. 



From 7986734 
Take 2463212 
Diflf. 5523522 



Ex. 607482678 minuend. 

5140346 subtrahend. 
602342332 remainder. 



217486973489 
105342341056 



46798765483 
23214342352 



85179684729 
23123461304 



600796857439 
342526125 



10008694758 
3242745 



85069857497 
3042354443 



Ans. 9890771. 



Ex. From 10574363 take 683592. 

Sol. 2 from 3 leaves 1, write 
down 1 ; 9 from 6 we cannot, but 9 
from ten leayes 1 and 6 are 7 ; write 
down 7 ; having borrowed ten, carry 
one to 5 is 6 from 3 we cannot, but 
6 from ten leaves 4 and 3 are 7 ; 
write down 7 and carry one to 3 is 4 from 4, &c. 

The work may be checked by adding the lower nurnber 
and remainder together, or by subtracting the remainder from 
the upper number. 



From 

Take 

Difference 

Proof 

Proof 



10574363 

683592 

9890771 

10574363 
683692 



217634821643 90000000000 
124368412781 47654321809 


47386743841 
31728698748 


10. 11. 12. 

987214638475 1 47869386481 63112141763 
298765428969 j 18976248656 32197648763 


13. 14. 15. 

804765786935 30241704862 47214127004 
276548674876 18702930409 21807163047 


16. 17. 18. 

172876548734 20468754874 53748688714 
89658714968 9876547185 31765948976 



20 



SIMPLE SUBTRACTION. 



374869040735 
9876524698 


10074021004 21047386943 
734861047 987654897 


22. 23. 24. 

734869548647 20417386984 15473846731 
27486009829 1763047098 7348209872 


25. 

111473869875 
9174869989 


26. 27. 

21765483642 1 60000472986 
9176254961 | 73864786 


28. 29. 30. 

300712684734 10203040506 60708090104 
987000487 1020304050 6070809017 


31. 32. 33. 

10000473698 1 34072986410 20172345604 
784629 1 29738047306 1073647298 


70047216384 17047386473 40100721647 
1976006548 8721738462 1700876109 


87. 38. 39. 

21734007201 21738400078 40072173867 
9172073167 4764873091 74169081 


40. 41. 42. 

100002402503 600043216753 100000643289 
76543209 67429768 854989 



43. From 

44. From 

45. From 

46. From 

47. From 

48. From 

49. From 

50. From 

51. Take 

52. Take 

53. Take 

54. Take 

55. Take 



748163486 take 79106474 and 549876. 
2104738400 take 219846736 and 2173844. 
2174863 take 478654+312842+176348. 
548629+748634take318467+21986+73894 
2198641+200473take54876+78698+9846. 



8047- 
5278- 
9873- 



7048+5734 take 2174+3846- 



■8497. 



9176+8796 take 8976+7421+1121. 

•7894+2198 take 4987+8746+1471. 
2173+4173+9876from 78469+2174+8459. 
74867382176983 from 4879684721674974. 
58217384698746 from 5763847218698481. 
91047384687690 from 9476347869485203. 
20734076948763 from 9846738479894210. 



SIMPLE SUBTRACTION. 21 

56. The battle of Waterloo was fought in 1815, and 
the battle of the Alma in 1854 ; how many years elapsed 
between them ? 

57. A merchant owed £2476, but has paid £1587 ; 
how much does he still owe ? 

58. A man born in 1775, died in 1858; what was his age? 

59. Napoleon I. born in 1769, died in 1821 ; what was 
his age ? 

60. A man was 98 years old in 1858 ; when was he born ? 

61. Americawas discovered in 1492; howlongis it since? 

62. A piece of cloth contained 1074 yards ; 274 yards 
were sold to one person and 123 yards to another ; how 
many yards remained ? 

63. From Edinburgh to York by rail is 209 miles, and 
to London 413 miles ; how far distant is York from 
London ? 

64. A ship sails from London to Sydney, a distance of 
13,640 miles ; after sailing 7684 miles, how far has she 
still to sail ? 

65. What number added to 354896 will make 432678? 

66. The sum of two numbers is 4789246, and the less 
is 849758 ; what is the greater ? 

67. Howlong is it since the invention of printing in 1430? 

68. In 1856, the number of Post-office Orders issued 
in the United Kingdom was 6,178,982 ; the number 
issued in England and Ireland was 5,693,459 : how many 
were issued in Scotland ? 

69. The receipts from passengers and goods by rail 
in Scotland amounted to £2,319,217 in 1856, and from 
goods alone £1,464,041 ; find the receipts from passen- 
gers alone. 

70. How long is it since the invention of gunpowder in 
1400? 

71. B was born when A was 27 years old ; what age is 
A when B is 51, and how old is B when A is 76 ? 

72. A merchant owed to A £7486, but has paid him 
£4736; to B, £5746, but has paid him £3721; to C, 
£10,844, but has paid him £7483 ; to D, £5748, but has 
paid him £4106 ; to E, £5120, but has paid him £3980; 
and to F, £11,111, but has paid him £9879 ; how much 
does he owe to each, and how much in all ? 



22 



SIMPLE MULTIPLICATION 

Is a short method of finding the sum of any given num- 
ber when repeated as many times as there are units in 
another given number. 

The number to be repeated is called the multiplicand^ 
the other number, the multiplier^ and the result is called 
the product. 

The two given numbers are also called factors of the 
product. 

Case L When multiplier does not exceed 12. 

Ex. Multiply 5974587 by 8. Ans. 47796696. 

Sol. 8 times 7 are 56, write Multiplicand 5974587 

down 6 and carry 5 ; 8 times 8 Multiplier 8 

are 64 and 5 are 69, write down Product 47796696 

9 and carry 6 ; 8 times 5 are 40 = 
and 6 are 46, &c. 

1. 384607592176 X 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. 

2. 597260875486 X 2, 4, 6, 8, 10, 12, 11, 9, 7, 5, 3. 

These Exercises may all be checked by Addition. 

Case II. When the multiplier is found in the table. 
Ex. Multiply 74867384 by 14. Ans. 1048143376. 
74867384 X 14 = 2 X 7 

Ex. Mult. 748673 by 20 
20 



149734768 prod, by 2 
7 



1048143376 prod, by 14 



14973460 



1. 748674869 

2. 530472937 

3. 374216487 

4. 796548737 

5. 975318642 

6. 759386154 

7. 649587596 

8. 927635849 

9. 123456789 
10. 987654321 



X16, 
X15, 
X22, 

X33, 
X25, 

X35, 
X36, 
X48, 
X55, 
X64, 



18, 24. 
21, 32. 
30, 28. 
42, 45. 
36, 49. 
27, 44. 
40, 42. 
54, 56. 
60, 63. 
m, 70. 



11.219703842 
12.504382796 
13. 846593742 
14. 142857142 
15.846153846 
16. 952380952 
17.543207159 
18.791364857 
19. 517369428 
20. 629752837 



X72, 77, 81. 
X84, 88, 90. 
X96, 99,110. 
X96, 81, 63. 
X80, 96, 77. 
X 81,121,144. 
X 99,132,121. 
X 84,110,100. 
X56, 54,132. 
X 45,121, 81. 



SIMPLE MULTIPLICATION. 



'23 



Case III. When the multiplier is not found in the 
table, and does not exceed 156, or 12 X 12 + 12. 



Ex. 74238476X26=5X6+1 

5 

371192380= 5 times 
5 



1855961900 = 25 >^ 
74238476= 1 " 



Ex. 67584937X38=6X6+2 

6 

405509622 = 6 times 
6 



2433057732 = 36 »* 
135169874 = 2 ,' 
2568227606 = 38 times 



1930200376 = 26 times 

1. 674295386 X 17, 23, 26, 29, 31, 34, 37, 43, 46. 

2. 965830295 X 38, 47, 62, 58, 62, 68, 74, 79, 83. 

3. 534869738 X 39, 59, 69, 75, 87, 93, 103, 105, 115. 

4. 275963849 X 19, 38, 47, 59, 74, 87, 95, 137, 149. 
Case IV. When the multiplier exceeds 156. 



Ex. 3210421765X235 
235 

16052108825= 5 times 
9631265296 = 30 « 
6420843530 =200 « 
754449114775=235 times 



1. 74863847 X 

2. 43958172 X 
8. 79586216 X 

4. 31596857 X 

5. 74951084 X 

6. 16847593 X 

7. 39416809 X 

8. 20537958 X 

9. 53104009 X 

10. 69073854 X 

11. 90768300 X 

12. 71765184 X 



364, 729. 
513, 624. 
734, 856. 
807, 965. 
760, 398. 
976, 304. 
854, 930. 
216, 648. 
729, 356. 
457, 390. 
278, 936. 
548, 690. 



25. 51948673X7040908. 

26. 94076803X4667890. 

27. 72584692X1234667. 

1. My income is £29 per week ; what is it per annum ? 

2. 87 parishes are each assessed £37 ; what is the whole 
assessment ? 



Ex. 48769486X407500 
407500 
24384743000 
341386402 
195077944 
19873565545000 

13. 5976843 X 2798, 6005. 

14. 3179648 X 4035, 3907. 

15. 5271809 X 4576, 7689. 

16. 6485937 X 3090, 7406. 

17. 7268369 X 6480, 4729. 

18. 5184736X2751, 6043. 

19. 4958674X1234, 6678. 

20. 6396274X9560, 8009. 

21. 7261587X8154, 6700. 

22. 8430957 X 8900, 3007. 

23. 9376864X7461, 6893. 

24. 1069769 X 9876, 4500. 

28. 40769864 X 70049000. 

29. 36947582 X 84000960. 

30. 52749683 X 90004396. 



24 SIMPLE MULTIPLICATION. 

3. How many sheaves are in a field containing 327G 
Bhocks, each 12 sheaves ? 

4. How many miles does a ship sail in 17 days at the 
rate of 169 miles a-day ? 

5. How many hours are there in a year ? 

6. How often does the seconds hand of a watch re- 
volve in a day and in a year ? 

7. A railway train travels at the rate of 35 miles an 
hour ; how many miles does it travel in 56 hours ? 

8. A ship's cargo consists of 435 boxes, each contain- 
ing 598 apples ; find the number of apples. 

9. How many letters are there in a volume of 436 
pages, each page 39 lines, and each line 52 letters ? 

10. Sound moves at the rate of 1142 feet in a second; 
how many feet will it move in 75 seconds ? 

11. A peal of thunder is heard 35 seconds after seeing 
the flash of lightning ; how far distant is the cloud ? 

12. A train consists of 13 carriages having each 3 com- 
partments, each containing 12 seats ; how many passen- 
gers would find seats ? 

13. What is the value of an estate, containing 7564 
acres at £56 per acre ? 

14. A ship's crew of 375 men is provisioned for 115 
days, now each man is to receive 16 ounces a-day; how 
many ounces have they in all ? 

15. A ship after sailing 37 hours at the rate of 7 miles 
an hour, encounters a storm, which drives her back 
during 7 hours at the rate of 12 miles an hour ; she then 
sails at her original rate during 5 hours ; how many miles 
will she now be upon her voyage ? 

16. How many shots does a fleet of 3 ships of 72 guns 
each, 5 of 91 and 7 of 42, fire in 93 rounds ? 

17. How many soldiers are there in 12 regiments of 
9 companies each, and each company consisting of 95 
men? 

18. How much powder does a sixteen gun-battery of 
18 pounders expend in 18 hours, if each gun is discharged 
22 times iji an hour, the charge for an 18 pounder being 
6 lbs. ? 



25 



Divisor. Dividend. 

7)47286492 
6755213^ 

7 



Quot. 



SIMPLE DIVISION 

Is the method of finding how often one number is con- 
tained in another. 

The number we divide by is called the divhor, the num- 
ber to be divided, the dividend^ and the result, the quotienU 

Case I. When the divisor does not exceed 12. 

Ex. Divide 47286492 by 7. 

Sol. 7 is not contained in 4, but 
7 in 47 is 6 and 5 over; place 5 
before 2, then 7 in 52 is 7 and 3 
over ; 7 in 38 is 5 and 3 over, &c. 

The work is proved by multiply- 
ing the quotient by the divisor and 
adding in the remainder, 

1. 7298763408 ~ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. 

2. 5487219876 — 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. 

3. 9846798764 -^ 12, 6, 2, 3, 11, 9, 10, 8, 5, 4, 7. 

Case II. When the divisor is found in the table. 
Ex. Divide 74263849 by 14. 
2 )74263849 ^14=2X7 
7 )37131924 — 1 quot. by 2 
5304560— 4 ... 14 



47286492 Proof. 



20 



4X2+1=8+1=9 rem. 

1. 34867896-M5, 16, 18. 13. 47654876- 

2. 48678963-^20, 21, 24. 14. 76548764 ■ 

3. 86789634-^-25, 27, 28. 15. 98765432 - 

4. 21750486-H30, 32, 33. 16. 23457219 - 

5. 30975219-^35, 36, 40. 17. 34807280- 

6. 93048765-r42, 44, 45. 18. 48702083 - 

7. 12345678-^48, 50, 54. 19. 54621487 - 

8. 23456789-^56, 60, 63. 20. 18765486- 

9. 34567890-^64, 66, 70. 21. 33144777 - 

10. 51146784-^72, 77, 80. 22. 11847654- 

11. 38712967-1-81, 84, 88. 23. 28048694 ■ 

12. 76921783+90, 96, 99. 24. 78648769 • 



Ex. 275473 - 

2,0) 27547,3 

13773^§ Quot. 



100,108,110. 
120, 121, 132. 
144, 121, 108. 

72, 81, 50. 

54, 96, 44. 
108, 88, 77. 
132, 81, 56. 
144, 54, 48. 
121, 36, 32. 
120, 64, ^Q. 
110, 72, 42. 
108, 99, 35. 
c2 



26 SIMPLE DIVISION. 

Case III. When the divisor is not contained in the table. 



Ex. Divide 48769847 by 7486. 

Divisor. Dividend. 
7486)48769847( 
7486 X 6 = 44916 



Ans. 6514f 043, 

Quotient. 
6ol4f£|? 
7486 Divisor. 





38538 


... X5 = 


37430 




11084 


... Xl = 


7486 




35987 


... X4 = 


29944 


Kemainder. 


6043 



39084 
52112 
26056 
45598 

6043 Rem. 
48769847 Dividend. 



1.77486694- 
2.54809678- 
3.48096785- 
4.57486786- 
5.38492136- 
6.48675846- 
7.21486483- 
8.54862187- 
9.48765486- 
10.30846298- 
11.74869548- 
12.34112118- 
13.21476548- 
14.58643876- 
15.79864879- 
16.54867384- 
17.79847684- 
18.54867486- 



■23, 31, 43. 
■26, 37, 47. 
•29, 39, 51. 
•17, 19, 13. 
•52, 53, 57. 
■61, 75, 69. 
•73, 74, 78. 
•79, 82, 83. 
■85, 86, 87. 
■89, 91, 95. 
■97, 92, 98. 
■93, 74, 94. 
■784, 842. 
•542, 876. 
■325, 498. 
■173, 156. 
•139, 147. 
•163, 184. 



73846548 
65482173 
87460094 
86754800 4- 
38476700 -^ 
48216784 -^ 

25. 7384698700 

26. 4869873846 

27. 7298740000 

28. 3216504000 

29. 2190874860 

30. 5486384766 

31. 4768754867 

32. 7321987645 

33. 5419738473 

34. 2176548698 

35. 1876487693 

36. 3175486987 



217, 298. 
248, 263. 
376, 483. 
800, 900.' 
600, 390. 
740, 500. 
- 17640. 

- 47687. 

- 87000. 

- 36500. 
- 17000. 
-37480. , 
- 176487. 

- 279864. 

- 548637. 

- 248765. 

- 764869. 

- 987654. 



1. A product is 4822150080, and one of the factors 704 ; 
what is the other? 

2. My yearly income is £364 ; what is that per week ? 

3. Great Britain and Ireland contain a population of 
27,675,780, and their surface is 121,385 square miles; how 
many inhabitants is that on an average to the square mile? 

4. France contains a population of 35,700,000, at the 
rate of 175 to the square mile ; how many square miles 
is the surface of France ? 



SIMPLE DIVISION. 27 

ft. If a floor 40 feet long require 1280 stones, each a 
foot square, to pave it; what is its length? 

6. The number of letters in a volume containing 746 
pages is 1,846,350 ; how many letters are in a page? 

7. An assessment for the poor of £5616 is raised from 
48 parishes ; how much is levied from each parish ? 

8. If a pigeon fly at the rate of 56 miles an hour, what 
time would it take between Edinburgh and the Cape of 
Good Hope, a distance of 5544 miles ? 

9. Divide £6725 equally among 25 men. 

10. In how many days will a ship accomplish a voy- 
age of 4473 miles, sailing 213 miles in a day? 

11. How many loaves, each weighing 69 ounces, can 
be made from 16,491 ounces of flour? 

12. The circumference of a wheel is 13 feet ; how 
often does it revolve on a road 68,640 feet long ? 

13. A tax of £7791 is to be levied from 53 parishes; 
how much must each pay ? 

14. Divide 343 oranges equally among 7 boys. 

15. How many carriages, each containing 36 passen- 
gers, would be required to convey 648 persons ? 

16. A gentleman's income is £6205 per annum ; how 
much is it per day ? 

17. One man alone can build a wall in 378 hours ; in 
how many hours would 7 men do the same ? 

18. 7 regiments, consisting of 716 men each, are to be 
reduced into 4 others of equal strength ; how many men 
will be in each new regiment ? 

19. How often can 375 be subtracted from 744375? 

20. 15,855 ounces of beef are divided among 755 sol- 
diers ; what is the weight of each man's ration ? 

21. How many dozens of wine are in 64 pipes, each 
containing 756 bottles ? 

22. A product is 2632938, and one of the factors 246 ; 
what is the other factor ? 

23. A ship sails 5712 miles in 28 days ; how many 
miles is this on an average per day ? 

24. The circumference of the Earth is 25,000 miles 
nearly ; how long would a person take to travel this dis- 
tance at the rate of 40 miles per hour ? 



28 



SUPPLEMENT TO MULTIPLICATION AND DIVISION. 

I. When the multiplier 
contains a fraction. 
Ex. 6487536 X 8f 



5 )19462608 = 3 times. 
38925213- = I times. 
51900288" = 8 times. 
557928091 Product. 



1.7486948X 
2.5721987X 
3.7121846X 
4. 5987648 X 
5.3842198X 
6. 4876529 X 
7.7214867X 
8.4962184X 
9. 4763148 X 
10.2147634X 
11.9847693X 
12.6478796X 
13. 5463784 X 
14. 8754964 X 
15. 8075084 X 



41 



63, 8i. 



_, 71,10^. 
41, n, 6|. 

84,121,2^. 

37A, 46^. 

65^1,304^. 
113^\,312if 
416^V 549if 
1791, 484^'^. 

44U, 574j. 

41 1, 59 A- 

84A, 93,\. 
108ii,275A. 



II. When the divisor con- 
tains a fraction. 
Ex. 487654-^-31 
30 487654 

_5 5 

16 f 2)2438270= prod, by 5 
(8 )1219135 

1523911 Quotient. 



l.4765847-^- 
2.5862190-^ 
3. 4948645-^ 
4. 5482169-:- 
5.7928465^ 
6. 5786478-f- 
7.87486736^ 
8. 57638469. 
9.78621475- 
10. 86275846- 
11.51840963- 
12.78219865- 
13.21973465 
14.34758694 
15.97986089 



Q 3 K 6 m 3 



As Q6 
"T25 ^85 



. - 12i. 
13i, 14f, 155. 
244|. 
18J. 
56i^ 
94i«. 



104,11 



-^ 17 



631 



84i 



— 71 6 

^58^^, 644H. 
^ 251^,5124^. 



-^7364 3674^. 



EXERCISES ON THE PRECEDING RULES. 

1. In 1856, the number of seamen registered in Eng- 
land was 156,913; in Scotland, 29,987; in Ireland, 13,403; 
in Jersey, Man, &c. 5424 ; and in the Colonies, 62,032 : 
lind the whole number. 

2. In 1851, the population of the South-eastern 
Counties of Scotland was : Linlithgow, 30,590 ; Edin- 
burgh, 259,493 ; Haddington, 36,363 ; Berwick 36,165; 
Peebles, 10,804 ; and Selkirk, 9802 : find the sum. 

3. In 1856, the number of births registered in Scot- 
land was 52,301 males and 49,447 females ; and the 
number of deaths was 29,417 males and 29,039 females : 
find the excess of births over deaths in that year. 



EXERCISES. 29 

4. How many passengers are in a train consisting ot 
4 first class carriages, each containing 18 persons ; 3 
second class containing 30 each, and 2 third class con- 
taining 40 each ? 

5. In 1856, the number of marriages in the 33 coun- 
ties of Scotland was 20,487 ; what was the average 
number in each ? 

6. The British Army at the battle of the Alma was 
composed as follows : — Light Division, 5454 men; 1st 
Division, 4711; 2d, 4222 ; 3d, 3794; 4th, 4419 ; Cavalry, 
1100; Artillery, 2700; Sappers and Miners, 400; how 
many men were engaged in all ? 

7. At the same battle, the loss of the British amounted 
to 2196 killed and wounded; how many effective men 
remained ? 

8. How many yards are in 15 pieces of cloth, each 
containing 56 yards ? 

9. Mercury's distance from the Sun is 36,793,000 miles, 
Mars' distance is 108,031,000 miles greater than Mer- 
cury's, and Neptune's is 2,710,114,000 miles greater than 
Mars' ; find the distances of Mars and Neptune from the 
Sun. 

10. In 1856, the number of Post-ofiice Orders issued 
in Ireland was 461,723; the number in Scotland was 
23,800 more than in Ireland, and the number in England 
exceeded that in Scotland and Ireland together by 
4,284,490 : how many were issued in Scotland, in Eng- 
land, and in the United Kingdom ? 

11. How many times is Mount Blanc, 15,732 feet in 
height, higher than Arthur Seat, which is 820 feet high ? 

12. At the battle of the Alma, the Fusilier Guards 
lost 11 officers and 170 non-commissioned officers and 
men killed and wounded ; the Grenadiers, 3 officers and 
126 men ; and the Coldstreams, 3 officers and 27 men : 
at Inkerman, the Fusiliers lost 9 officers and 169 men ; 
the Grenadiers, 9 officers and 223 men ; and the Cold- 
streams, 13 officers and 178 men. How many of the 
Guards fell at Inkerman more than at Alma? 

13. A pear-tree one year produced 14,861 pears, aver- 
aging 11 to the pound ; how many lbs. were produced? 

^4- In how many days will a boy read through the 

D 



30 EXERCISES. 

Bible, which contains 31,173 verses, if he reads 39 verses 
daily? 

15. How often does the hammer of a clock strike in a 
day and in a year y 

16. One female can cut out 300 gross of blanks for steel 
pens in a day ; how many will she cut out in a year of 
313 days? 

17. A steel pen manufactory sends out 180,000,000 
pens yearly ; how many boxes, each containing a gross 
or 12 dozen, would they fill ? 

18. A gentleman has 3 farms containing 675 acres ; 
the first and second together contain 490 acres; and 
the second and third 425 acres . how many acres are in 
each farm ? 

19. The gallant Sir John Moore fell at the battle of 
Corunna in 1809, at the age of 48 ; in what year was he 
born? 

20. The Sun's diameter is 882,000 miles ; how many 
times is it greater than the Earth's diameter, which is 
7920 miles ? 

21. Divide 1584d. among 3 girls and 5 boys, giving 
each girl twice the number which a boy gets. 

Sol. Since each girl gets 2 boys' shares, 3 girls have 
2X3 = 6 boys' shares ; the number of boys' shares is 
therefore 6 + 5 = 11. Hence each boy gets 1584 4- 11 = 
144d., and each girl 144 X 2 = 288d. 

22. How much grain will a farm of IG fields, each 29 
acres, produce, if one acre produces 9 quarters of grain ? 

23. A gentleman gave £484 to two charities, and to 
one he left 3 times as much as to the other ; what did 
he leave to each ? 

24. Several volumes contain 10,192 pages ; in how 
many days would a person read the whole, reading 4 
hours a day and 7 pages an hour ? 

25. In a church there are 12 windows ; in the lower 
sash there are 12 panes and in the upper 18 ; how many 
panes of glass are there in all ? 

26. A gentleman has 4 farms, containing 240, 375, 408, 
and 425 acres respectively, and he wishes to divide them 
into as many others of equal size ; how many acres will 
there be in each farm ? 



EXERCISES. 31 

27. In one class there are 150 boys, in another 145, 
in a third 140, in a fourth 135, and in a fifth 130; how 
many are there on an average in each ? 

28. The sum of two numbers is 2779, and their difi'erence 
is 293 ; what are the numbers ? 

Sol. 2779 2779 

Add 293 Subtract 293 

2 ) 3072 2 ) 2486 

1536 is the greater. 1243 is the less. 

29. At an election, the successful candidate had a ma- 
jority of 84 votes out of 572 votes ; how many had each 
of the two candidates ? 

80. The loss of the French and Sardinians at the battle 
of the Tchernaya or of Traktir Bridge, amounted to 
1792 men killed and wounded; the French loss was 
1292 more than the Sardinian : what was the loss of each? 

31. Divide 204 apples among 4 girls and 5 boys, giving 
each girl 3 times as many as a boy. 

32. Galileo died in 1642, and Newton in 1725; how 
long is it since each of these events, and how many years 
elapsed between them ? 

33. A gentleman dying, left £45,000 ; to his widow he 
bequeathed ^ of his estate, and the remainder was to be 
equally divided among his 4 children ; how much did he 
leave to each ? 

34. A ship at sea fires a gun, the report of which is 
heard 12| seconds after seeing the flash ; how far distant 
is the ship, sound moving at the rate of 1142 feet per 
second? 

35. Two casks of wine contain together 151 gallons, 
and one contains 31 gallons more than the other; how 
many gallons does each contain ? 

36. What number being divided by 337 gives 9472 for 
the quotient, and 108 for the remainder ? 

37. Divide £416 among 6 men and 8 women, giving 
each man 4 times as much as a woman. 

38. Two brothers being asked their ages, said that the 
sum of their ages was 63, and that the difference of their 
ages was 9 ; find their ages. 



Ex.Red.l9718farth.to£. 
4 )19718 Farth. 
12 ) 4929 ^ Pence. 
2,0) 41,0s. 9|d. 



£20, 10s. 9§d. 



32 



COMPOUND NUMBERS 

I. STERLING MONEY. 

REDUCTION 

Is the method of bringing numbers from one denomina- 
tion to another without altering their value. 

To bring higher to lower denominations multiply. 

To bring lower to higher denominations divide. 

Ex. Red. £20, 10s. 9id. to farth 
Mult, by 20 and add 10s. 

410 Shillings. 
Mult, by 12 and add 9d. 
4929 Pence. 

Mult, by 4 and add 2f. 

19718 Farthings. 

1. Reduce£35, 17s. 4id.; £28,lls.ll|d.; £40, 10s. lOf d.; 
€200. 10s. 8fd.; £574, 19s. 11^.; £409, 17s. 4id. ; 
£147', 10s. lOid. ; and £105, 2s. 4id. to farthings. 

2. Reduce £470, 10s. O^d. ; £270, lis. 6d. ; £672, 18s. 
9^.; £486, 12s. l^d. ; 12s. 4id. ; 17s. S^d. ; lis. lid. 
£700, 10s. 2d. ; £21, 15s. S^d. to halfpence. 

3. Reduce £87, 19s. lO^d. ; £11, lis. lid. ; £50, 19s. 6d. 
£47, 15s. 9id. ; £400, 10s. O^d. ; £290, 16s. 4d. ; £403, 
lis. ll^d.; 16s. 8id. ; lis. S^d. ; 13s. 4^d. ; £43, 12s. 4d. 
and 15s. 8^d. to halfpence and farthings. 

4. Reduce 4786; 3040; 7098; 48769; 73846; 4098 
7214 ; and 38463 farthings to pence, shillings, and pounds 

5. Reduce 4876; 7487; 3562; 1749; 3689; 2177 
5848 ; 7216 ; 111111 ; 33333 halfpence to d. s. and £. 

6. Reduce 78469 ; 738467; 87698; 714086 farthings: 
48763; 21764; 50487; 140715 halfpence: 729374; 89214; 
47865; and 571640 pence to sovereigns. 

7. Reduce £2716, 2s. 2id. ; £4176, 12s. S^d. ; £3108, 
14s. 7id. ; £176, Os. 2id. ; £417, Os. O^d. ; £49, 17s. 6d. ; 
and £2010, 10s. 6|d. to halfpence and farthings. 

8. Reduce 41763 ; 58462 ; 71209 ; 17268 ; 38467 ; 
84762; 47219; and 876213 farthings to sovereigns. 



REDUCTION. 33 

Ex. Red. £2475 to crowns and guineas. 

2. £2475 X 20 



£2475 

20 

5 )49500 s. 
Ans. 9900 cr. 



f 3)49500 s. 
17 )16500 
Ans. 2357 gu. 3 s. 



9. Reduce £7485; £3876; £4921; £3817; and £3760 
to crowns and guineas. 

10. Reduce 17486; 887; 2130; 2491; 2168; and 
7430 guineas to pounds. 

Ex. Red. £21, 17s. 6d. to sixpences. Ans. 875 sixd. 
£21, 17 s. 6d. Proof. 

20 2 )875 sixd. 

437 s. 2,0)4Vs. 6d. 

2 (sixd. in Is.) £21, 17s. 6d . 

Ans. 875 sixd. c===; 

11. Reduce £121 ; £45, 7s. 6d. ; £56, 18s. 6d. ; £79, 
18s. ; £84, 5s. 6d. ; and £99, 19s. 6d. to sixpences. 

12. Reduce 448; 977; 2163; 3729; 4125; and 5763 
sixpences to shil. and pounds. 

13. How many half-crowns in £42, 7s. 6d. ; £54, 12s. 
6d. ; £67, 15s. ;"'and in £99, 17s. 6d. ? 

14. Reduce 528 ; 1254; 3453; 4869; 5871; and 7459 
half-crowns to pounds, &c. 

15. How many threepences are in £49, 7s. ; £54, 6s. 3d. ; 
£72, 19s. 6d. ; and in £84, 14s. 9d. ? 

16. Reduce 1748; 2153; 3785; 5142; 6897; and 7455 
threepences to shillings and pounds. 

17. How many florins are in £170 ; £144 ; 6743 far- 
things ; 1786 pence ; and in 436 shillings ? 

18. Reduce 43 guineas ; 77 gu. 8s. l^d, ; £37, 2s. 6d. ; 
93 gu. 2s. 4»d. ; 78 gu. 18s. 9|d. ; and 18s. 9|d. to farth. 

19. Find the sum of £18, 19s. 4^d.+5 crowns+17 half- 
crowns-f-234 florins-}-! 7 guineas, in farthings and pounds. 

20. How many pounds will a man save yearly, by lay- 
ing aside 5s. 9M. weekly ? 

21. How many penny stamps may be obtained for 
£49, 17s. 7d.? 



34 



COMPOUND ADDITION. 

Example. 
Sol. The sum of the farthings is 10 = £381 17 s. 6id. 
2^d., write down ^d. and carry 2 to the 148 12 9^ 

pence. The sum of the pence is 44 = 412 16 7| 

3s. 8d., write down 8d. and carry 3 to the 319 11 ll| 

shil. The sum of the units column of the 470 19 9f 

shil. is 28, write down 8s. and carry 2 to £1733 18 8^ 
the tens of the shil. : the sum is 7 ten shil. ===== 
pieces = £3 and 1 ten shil. piece, write down 1 and carry 
3 to the pounds. The sum of the pounds is £1733, and the 
whole answer is £1733, 18s. 8^d. — The results in Compound 
numbers may be checked as in Simple numbers. 



1. 


2. 


3. 


4. 


£ s. d. 


£ s. d. 


£ s. d. 


£ s. d. 


24 11 4 J 


31 17 lU 


27 15 1\ 


14 19 111 


16 18 9i 


13 14 lOi 


72 18 10 


12 16 Si 


61 10 2| 


42 16 9.f 


36 11 5i 


29 11 5A 


32 17 lU 


24 12 4i 


63 10 4^ 


18 18 8£ 


45 16 3i 


56 18 Hi 


41 17 lOi 


15 14 10 



96 11 41 


49 19 111 


68 16 Si 


15 14 9 


69 13 7i 


94 13 7 


86 15 51 


19 17 lOi 


12 16 10 


17 11 lU 


74 11 91 


91 19 6i 


14 18 n 


16 15 5i 


47 16 10 


51 14 lU 


29 15 6i 


18 18 Hi 


51 10 4i 


18 13 2\ 


31 17 111 


81 17 lOi 


15 8 111 


81 10 9| 



9. 


10. 


11. 


12. 


17 18 HI 


42 18 9i 


29 10 8^ 


14 12 Si 


16 13 7i 


36 17 2| 


34 8 11^ 


17 13 61. 


19 12 41 


34 16 3| 


76 7 7i 


98 19 2 


20 11 3| 


43 12 111 


82 11 10| 


84 10 6| 


31 17 Si 


45 19 101 


49 17 71 


18 11 111 


17 16 111 


53 11 4| 


63 13 91 


19 10 81 



13. 


14. 


15. 


16. 


45 17 SI 


40 21 


51 S 3| 


82 12 llf 


49 16 4| 


38 19 11 


64 19 111 


4M8 71 


38 18 71 


51 15 5| 


73 17 10^ 


72 16 9 


64 4 llf 


86 16 7 


84 16 91 


S8 11 4f 


39 17 6i 


13 14 101 


18 18 11| 


22 15 101 


83 11 4f 


89 19 6 


17 14 10| 


16 18 7i 





COMPOUND ADDITION. 


35 


17. 


18. 19. 


20. 


£ s. d. 


£ s. d. 


£ s. d. 


£ s. d. 


274 13 lOf 


426 16 4J 


410 10 lOf 


329 19 111 


476 12 8J 


246 13 3^ 


104 17 4f 


293 18 11 


567 11 4| 


642 17 8f 


816 11 \\\ 


932 17 6i 


658 13 Ik 


351 9 lU 


681 13 4 


456 16 10| 


549 18 7i 


513 12 Al 


168 12 lOJ 


564 13 3i 


721 16 111 


135 11 lU 


473 2 U 


645 17 6 


213 19 lOf 


497 18 101 


734 3 0^ 


897 13 4i 


132 15 7i 


974 19 9i 


347 11 111 


978 19 9^ 



21. 


22. 


23. 


24. 


476 11 llf 


847 13 6| 


984 17 m 


484 15 4| 


725 13 4i 


472 19 2i 


845 15 0| 


846 13 8| 


870 11 9| 


756 14 llf 


756 13 21- 


725 16 10^ 


708 17 lOi 


793 18 5A 


384 11 5i 


857 11 Ak 


534 16 3i 


904 15 81 


479 18 lOi 


583 3 9i 


729 19 111 


405 12 lOi 


721 19 111 


879 16 8| 


297 18 4| 


762 16 81 


562 13 8i 


405 17 Ik 


972 15 3| 


636 17 9^ 


629 16 9i 


896 19 111 



25. 


26. 


27. 


28. 


325 14 71 


420 12 7J 


508 19 71 


874 13 6 


256 15 81 


500 13 8^ 


850 11 2 


847 16 8i 


719 11 61 


721 16 6| 


793 16 71 


856 17 101 


971 13 lOi 


217 18 lU 


918 13 41 


865 11 21 


47*2 16 8i 


172 16 4| 


981 17 10 


832 18 6 


749 18 111 


901 17 21 


974 18 Q^ 


823 7 4| 


426 19 9^ 


847 19 111 


953 12 111 


748 16 3 


273 17 10^ 


487 15 lOi 


947 13 3^ 


784 17 4| 



29. 


30. 


31. 


32. 


219 13 111 


549 16 2 J 


Ill 11 111 


204 8 0| 


192 16 5^ 


495 17 10 


222 17 10^ 


420 -3 n\ 


921 17 4 


954 11 2| 


363 18 2| 


569 18 21 


476 13 &l 


867 18 31 


746 12 91 


931 13 11 


764 18 lOi 


678 19 3i 


805 13 7| 


139 15 4| 


647 11 11 


786 12 9 


508 19 61 


721 4 8^ 


513 17 101 


954 13 81 


741 10 41 


801 12 7 


315 19 8^ 


987 16 10 


417 11 U 


971 19 101 



33. £473, 18s. 10|d.+£972, lis. 4id.+£987, 19s. llid. 
+£852, 17s. 9id. + £112, 15s. 61d. + £521, 14s. 8|d. -f 
£846, 13s. 7|d. + £613, 12s. 9^d. + £716, 17s. ll|d. 



36 



COMPOUND ADDITION. 



34. 


35. 


36. 


37. 


£ s. d. 


£ s. d. 


£ s. d. 


£ 8. d. 


540 13 llf 


321 17 8i 


463 18 9 


897 11 81 


419 19 9 


123 16 3i 


364 19 lOi 


879 12 71 


914 13 41 


231 15 4i 


643 11 2i 


798 13 4| 


411 12 2 


213 18 11 


634 17 10 


789 16 llf 


114 8 6| 


312 16 8J 


346 18 9i 


978 4 2 


701 13 4 


132 11 2i 


436 12 71 


987 11 4| 


158 17 llf 


474 13 6 


183 16 8 


363 15 71 


815 16 8 


744 11 3f 


831 15 41 


633 18 9f 



38. 


39. 


40. 


41. 


948 12 71 


574 11 lOf 


530 11 4f 


876 11 llf 


489 13 61 


457 16 41 


504 17 111 


768 19 lOl 


894 19 91 


739 19 9 


876 19 91 


687 14 41 


276 15 41 


395 11 10| 


743 12 lOf 


527 13 8 


568 17 llf 


953 14 41 


549 13 61 


498 19 llf 


729 19 9 


476 15 11| 


985 19 llf 


409 17 lOf 


276 11 111 


729 13 8i 


859 18 10| 


490 17 101 


467 13 41 


297 16 41 


764 13 81 


385 13 4f 



42. 


43. 


44. 


45. 


210 11 5i 


741 18 11 


116 17 41 


901 18 71 


101 13 61 


387 16 5f 


161 13 5f 


910 13 41 


354 16 21 


862 10 101 


600 17 21 


864 12 111 


726 15 111 


629 17 61 


560 13 81 


648 17 6f 


367 18 10| 


748 15 5f 


74 11 3f 


899 11 11 


481 19 111 


796 17 llf 


9 8 6 


988 15 7^ 


816 15 81 


869 19 10 


408 12 llf 


749 18 llf 


964 17 lOf 


176 17 8f 


780 16 91 


548 17 61 


489 19 111 


298 11 41 


473 18 111 


721 16 21 


984 12 61 


476 10 6f 


729 16 71 


387 19 9i 



571 18 llf 

80 16 101 

780 13 31 

807 12 111 

709 11 41 

89 13 61 

10 16 71 

840 15 llf 

742 18 91 

476 13 4- 



47. 

48 19 41 

480 13 61 

408 15 91 

72 11 41 

568 17 111 

367 13 2f 

673 18 81 

469 12 lOf 

576 19 8f 

864 13 4j 



61 

7: 



48. 

500 11 llf 
499 9 " 

72 18 
308 15 

38 12 
380 11 
596 12 

65 13 
962 18 



298 14 llf 



If 



49. 

344 18 101 
436 19 111 

87 13 " 
728 12 
864 11 111 

86 13 41 
987 12 

49 14 
986 17 
806 4 



91 
61 
2i 



COMPOUND ADDITION. 37 

50. A owes to B £743, lis. 6id., to C £325, 4s. 8|d., 
to D £750, 19s. lOfd., to E £113, lis. lljd., to F £1041, 
13s. 8fd., to G £89, 16s. 8d., to H £1430, 153. ll|d., and 
to I £740, 16s. lOd. ; how much does he owe in all ? 

51. A paid to B £675, 13s. 7id., to C £298, 16s. lOid., 
to D £749, 13s. 7id., to E £97, 18s. 6|d., to F £987, 13k. 
Hid., to a £75, 13s. 8|d., to H £1279, 17s. 4fd., and 
to I £684, 13s. ll^d. ; how much did he pay in all? 

52. A person collected in January £744, lis. 8fd., in 
February £896, 17s. lO^d., in March £472, 17s. 4id., in 
April £583, 16s. llfd., in May £739, 17s. 6fd., in June 
£1096, 13s. 8id., in July £578, 12s. 8^d., in August 
£1374, 18s. 5jd.,in September £458, lis. llid.,in October 
£735, 13s. 4id., in November £2179, 16s. 4id., and in 
December £532, lis. Ijd. ; how much did he collect? 

53. I received from A £736, 15s. lid., from B £874, 
13s. 8fd., from C £879, 17s. lOid., from D £84, Us. 2|d., 
from E £98, 17s. lOfd., from F £921, 16s. llid., from 
G £1093, 10s. 4^d., and from H £729, 8s. lid. ; how 
much did I receive in all ? 

54. A owes me £274, lis. lOid., B £89, 13s. 7d., C 
£74, lis. lid., D £96, 18s. 9^d., E £65, lis. 2id., F 
£418, 4s. 6fd., G £173, 13s. 4id., H £748, 17s. 6fd., 
K £847, 13s. 4id., and I have in the bank £7486, 17s. 
ll|d. ; how much am I worth? 

55. A housekeeper's account was, for beef, &c., £4, 
2s. 7id. ; tea and coffee, 21s. 3d. ; sugar, 17s. 7|d. ; 
potatoes, 5s. 6|d. ; butter, lis. l^d.', fruit, 21s. 3^d. ; 
and bread, 43s. 7d. ; find the amount. 

56. A corn merchant laid out on wheat, £597, lis. 6^d. ; 
on barley, £409, 17s. 4|d. ; and on oats, £347, 9s. llfd. : 
what should he sell the whole for to gain £79, 18s. 11 ^d. ? 

57. A gentleman left to his widow, £7692, 17s. 4id. ; 
to each of his two sons, £3000, 17s. 6d. ; to each of his 
four daughters, £2559, 18s. 7^d. ; and to his other rela- 
tives, £4975, 8s. 4id. : how much was this in all? 

58. A gentleman owes his tailor, £23, 14s. 8^d. ; his 
bootmaker, £14, 7s. 3jd. ; his grocer, £48, 17s. 7|d. ; 
his baker, £35, 16s. 8^d. ; his house-rent is £115, 17s. 
6d. : how much must he draw from the bank to pay 
these sums ? 



38 



COMPOUND SUBTRACTION 

Ex. From £429 17s. Sjd. 
Take 145 12 3i 
Diff. 



£284 5 5^ 



Ex. From £501 15s. 6^d. 
Take 250 4 Gj 
Diff. 



£251 11 Oi 



1. 


2. 


3. 


4. 


£ ». d. 


£ 5. d. 


£ s. d. 


£ 5. d. 


146 12 7i 


247 16 lOf 


375 15 6i 


508 6 7| 


73 5 2^ 


184 5 3^ 


183 10 4^ 


348 3 7i 



Ex.From£742,15s.8id.take£653,17s.9id.Ans.£88,17s.l0|d. 



From £742 15s. S^d. 
Take 653 17 9| 
Diff. £88 17 lo| 



Sol. 2f. from If. we cannot, but 2f. 

from 4f. (or Id.) is 2f. and If. is |d.; 

write down |d., and carry 1 to 9d. is 

lOd. from 8d. we cannot, but lOd. from 

12d. (or Is.) is 2d. and 8d. are lOd. ; write do^Am lOd., and 

carry 1 to 17s. is 18s. from 15s. we cannot, but 18s. from 20s. 

(or £1) is 28. and 15s. are 17s. ; write down 17s., and carry 



1 to £653 


is £654 from £742 are £88 ; write down £88. 






5. 






6. 






7. 






8. 




427 


13 


4i 


450 


10 


44 


296 


16 


34 


609 


13 


64 


298 


16 


lOi 


276 


13 


B| 


109 


11 


114 


379 


14 


7f 




9. 






10. 






11. 






12. 




825 11 


6 


742 


17 


84 


408 


18 


10 


504 


16 


74 


296 


13 


6i 


486 


13 


94 


298 


19 


9| 


329 


16 


8f 




13. 






14. 






15. 






16. 




742 


13 


84 


200 








804 10 


14 


476 


17 


7f 


427 


12 


n 


99 


12 


04 


721 


13 


6 


298 


17 


11 




17. 






18. 






19. 






20. 




547 


10 





976 


15 


4 


705 





44 


325 


6 


04 


238 


11 


Of 


762 


18 


K 


396 17 


2^ 


298 


13 


04 




21. 






22. 






28. 






24. 




610 


17 


3| 


542 


16 


04 


726 


17 


104 


789 


11 


5| 


496 


16 


lU 


486 


16 


04 


498 


17 


11 


499 


11 


74 




25. 






26. 






27. 






28. 




271 


13 


0^ 


542 


16 


04 


980 15 


6 


832 


17 


64 


148 


17 


0| 


347 


19 


111 


890 


15 


6| 


328 


18 


7f 




29. 






30. 






31. 






32. 




532 16 


7 


424 


19 


10 


173 


16 


14 


410 


12 


44 


325 


11 


9| 


248 


19 


104 


99 


17 


Of 


147 


13 


74 



COMPOUND SUBTKACTION. 



39 



83. 


34. 


35. 


3a. 


£ s. d. 


£ s. d. 


£ s, d. 


£ s. d. 


901 18 0| 


386 16 4 


409 11 H 


251 13 4^ 


496 18 U 


293 17 2| 


359 11 6 


151 17 9| 



109 13 10 
96 13 lOi 


38. 

499 17 3i 
399 17 61 


39. 

256 11 2i 
193 4 7i 


40. 

704 14 4 
407 14 9i 





41. 






42. 






43. 






44. 




275 


12 


^ 


326 


9 


3 


533 


4 


0^ 


214 


17 


11 


186 


11 


7i 


263 


18 


H 


353 


7 


6f 


142 


17 


iH 





45. 






46. 






47. 






48. 




973 





2^ 


841 


1 


0^ 


711 


5 


2 


817 








739 


3 


If 


418 


1 


n 


117 


5 


lU 


718 





03 



49. £748, 13s. 6id.— £589, 15s. 8|cl. 

50. £721, 15s. 8d. —£629, 13s. lUd. 

51. £721, 17s. 6|d.+£853, 13s. l|d.— £684, 13s. 6id. 
+£789, 17s. lid. 

52. £987, 2s. lid.+£305, 2s. Hid.— £896, 12s. 8id 
+£296, 17s. 9id. 

53. A merchant bought goods for £578, 15s. 6^d., and 
sold them for £642, 8s. 7Jd. ; what did he gain ? 

54. Borrowed 500 guineas and paid £125, 17s. 4id. at 
one time and £298, 14s. 5id. at another ; what is still 
due? 

55. The receipts of a railway one year amounted to 
£48,984, 17s. 8id. ; and the year followmg to £50,492, 
2s. 3d. ; find the increase. 

56. A housekeeper went to market with £5 ; she paid 
for beef 17s. 6id. ; mutton, 12s. 7id. ; fish, 7s. ^^L.', 
tea, 6s. 5d. ; coffee, 2s. 3^d. ; sugar, 7s. l^d. ; vegetables, 
7s. 3|d. and sundries, 4s. l|d. ; with what sum did she 
return ? 

57. A owed to B £748, 16s. 7id., but has paid £398, 
17s. 6^d. ; to C £1000, but has paid £899, 17s. 4id. ; to 
D £470, lis. 4id., but has paid £381, 13s. 4£d. ; to E 
£721, 18s. 7|d., but has paid £643, lis. 9id. ; to F £896, 
13s. 2id., but has paid £799, 17s. l|d. ; how much does 
he still owe to each and in all? 

58. A merchant has in cash £7328, 17s. 11 Jd., goods 
worth £12,748, 16s. lOd., furniture £574, 18s. lljd. ; 



40 COMPOUND SUBTRACTION 

A owes him £112, 17s. 6id., B £327, 18s. 7Ad., C £486 
13s. 8|d., D £89, 16s. lO^d. and E £136, 18s. 8id. ; at 
the same time he owes to F £574, 18s. 11 ^d., to G £324, 
lis. 7|d., to H £723, 18s. 6d., to I £327, 17s. 4|d., and 
to K £587, 10s. 3fd. : how much is he worth? 

59. A gentleman's yearly income is £500, his household 
expenses £294, 13s. 7:|d., rent £54, 13s. 6d., taxes £20, 
lis. 8id., servants' wages £25, 17s. lid., tradesmen's ac- 
counts £52, lis. 7fd., and incidental expenses £24, 17s. 
ll^d. ; how much does he save yearly? 

60. Three ponies cost £35, 15s. 6d ; the first and second 
cost £26, 10s. 4d. and the second and third £30, 3s. 9d. ; 
find the price of each. 

61. A, B, and C contributed £109, 18s. l^d. to a 
charity ; A and B contributed £61, 3s. 3^d. and A's 
contribution was £21, 10s. lO^d. less than C's: how 
much did each contribute? 

62. A bankrupt's debts amount to £19,728, 15s. 7jd. 
and his effects to £12,899, 17s. 8|d. ; how much is he de- 
ficient ? 

63. A gentleman dying left £17,584, 17s. 6d. ; to his 
widow he left £3756, l8s. 9d. ; to each of his three sons, 
£2573, 7s. 6d, ; to each of his two daughters, £2000, 
14s. 3d. ; and the remainder to his other relatives : how 
much was this ? 

64. A bankrupt owes to A, £329, 10s. 7^d. ; to B, 
£748, 17s. ll^d. ; to C, £876, 17s. lOjd. ; to D, £1783, 
17s. Hid.; to E, £578, 19s. 3|d. ; to F, £1047, 18s. 
6jd. ; and to Gr, £1270, 8s. 8^d. : at the same time he 
has in cash, £520, 17s. S^d. ; in bills, £325, 16s. lO^d. ; 
goods valued at £984, 17s. 6d. ; H owes him £44, 16s. 
7id.; I,£72,lls.7|d.; K, £84, 13s. 4id. ; and L, £105, 
17s. llfd. How much will his creditors lose by him? 

65. A tax of £975, 17s. lO^d. is raised from 5 towns ; 
the first town pays £190, 14s. 8^d. ; the second, £204, 
15s. 7|d.; the third, £199, 17s. 8f d. ; and the fourth, 
£219, 15s. 3id. : how much does the fifth town pay? 

66. A merchant laid out £756, 18s. 9^d. on wheat, bar- 
ley, and oats ; the sum laid out on wheat and barley was 
£437, 6s. 2d., and on barley and oats, £540, 12s. l^d. : 
how much was laid out on each ? 



41 



COMPOUND MULTIPLICATION. 
Case I. When the multiplier is not greater than 12. 

Ex. Multiply £8, 17s. 9id.by 9. Ans. £79, 19s. lUd. 

Sol. 9 times If. = 9f. or 2Jd. ; write down £8 17s. 9id, 
Jd., and carry 2d. 9 times 9d. are 81d. and 9 

2d. are 83d. or 6s. lid. ; write down lid., and £79 19 \i^ 
carry 6s. 9 times 7s. are 63s. and 6s. are = 

69s. ; write down 9s. and carry 6 9 times 1 are 9 and 6 
are 15 ten s. pieces = £7, 10s. ; write down 1 before 9s. and 
carry £7. 9 times £8 are £72 and £7 are £79. 

1. Multiply £27, 17s. 8jd.by2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. 

2. Multiply£36,15s.ll|d. by 7,5,2,9, 6,11,4,10, 8, 12,3. 

Case II. When the multiplier does not exceed 156. 

Ex. Multiply £3, 16s. 7id. by 16 and by 26. 

2. £3 16s. 7id.X26=5x5-f 1 



1. £3 16s. 7jd.Xl6 = 4X4 | 






_5 




4 


19 


3 


0| = 5 times. 


15 6 


5 = 4 times. 
4 


5 




95" 
3 


15 
16 


1 J = 25 // 


£61 5 


8 =16 times. 


7i= 1 '/ 




d. 


£99 


11 


8i = 26 times. 


£ 5. 


£ 


5. 


d. 


1.27 11 


4iX 14, 18, 20 


13.42 


18 


6iX 17, 23, 26 


2.31 17 


2|X 24, 27, 30 


14.36 


15 


lliX 29, 31, 34 


3.19 18 


6iX 32, 25, 36 


15.25 


13 


lOfX 38, 43, 39 


4.34 14 


lliX 42, 45, 48 


16.38 


11 


OiX 47, 59, 68 


5.28 19 


lOiX 49, 54, 65 


17.45 


12 


8IX 67, 69, 74 


6.74 13 


8|X 56, 60, 64 


18.56 


18 


6iX 75, 76, 79 


7.16 19 


lliX 63, 66, 72 


19.73 


16 


4|X 83, 87, 86 


8.35 


OfX 70, 77, 81 


20.84 


19 


llfX 89, 93, 98 


9.54 19 


OiX 80, 90, 96 


21.91 


13 


4iX 94,103,107 


10.47 13 


111X108,121,144 


22.94 


15 


2iXll5, 95,106 


11.45 15 


6|X110, 99,132 


23.96 


17 


81X117,127,139 


12.39 17 


10|X 84, 77, 81 


24.99 


19 


11|X148,126,137 



42 COMPOUND MULTIPLICATION. 

Case III. When the multiplier exceeds 156. 

Ex. Multiply £2, 13s. 4|d. by 536. Ans. £1431, Os. 2d 

£2 13s. 4|d.X6 = £16 Os. 4id.= 6 times. 
10 





26 13 11^ X3= 80 1 lOi = 30 times. 
10 

£266 19 7 X5= 1334 17 11 = 500 times. 

£1431 2 =536 times. 


1. 

2. 
3. 
4. 


£ s. d. 

5 18 11| X 583, 742 

6 5 2^X 879, 986 

3 13 4i X 1004, 2963 

4 17 9| X 3125, 7518 


£ *. d, 

5. 7 19 lOfX 7384, 6472 

6. 10 11 lliX 5809, 4365 

7. 13 16 8iX 9416,10738 

8. 16 17 101X27580,74087 



Find the price of, 

1. 27 cwt. of sugar at £3, 16s. 6d. per cwt. 

2. 38 tons of steel at £25, 17s. lid. per ton. 

3. 45 quarters of wheat at £3, 6s. 7^d. per quarter. 

4. 67 dozen Madeira at £6, 8s. llf d. per dozen. 

5. 53 gallons whisky at 12s. 2f d. per gallon. 

6. 86 acres of turnips at £17, 16s. 8d. per acre. 

7. 57 cwt. butter at £4, 5s. 8Jd. per cwt. 

8. 67 lbs. tea at 7s. ll^d. per lb. 

9. 58 acres of grass at £7, 8s. 7id. per acre. 

10. 75 cwt. Carolina rice at £2, 15s. 7^d. per cwt. 

11. 46 sugar loaves, each 17^ lbs., at ll^d. per lb. 

12. 17 boxes pimento, each 87 lbs. at lljd. per lb. 

13. 19 cwt. potashes at £1, 7s. llfd. per cwt. 

14. 116 cwt. tallow at £2, 10s. 7id. per cwt. 

15. 73 gallons rum at 18s. O^d. per gallon. 

16. 59 ounces of gold at £3, 17s. ll|d. per oz. 

17. 153 bushels malt at 7s. A^d. per bushel. 

18. The daily pay of a foot soldier is Is. Id. ; how 
much is this yearly ? 

19. A farm of 379 acres is rented at £3, lOs. 7^d. per 
acre ; how much is the whole rent ? 

20. A merchant bought 25 pieces of cloth, each con- 
taining 20 yards at £1, 2s. t^d. a-yard, and sold the 
whole for £612, 10s. ; what was his gain? 



COMPOUND MULTIPLICATION. 43 

21. If the weekly forage of a horse be 14s. 6^d. ; what 
sura will be required to keep a regiment of 750 horses 
for a year ? 

22. The rent of a house is £1, 10s. 6Jd. per week ; how 
much is that in the year ? 

23. How much will a farmer pay for cutting down his 
crop, if he employs 53 reapers for 3 weeks at 2s. llfd. 
each per day ? 

24. If an hospital contains 80 boys, and each on an 
average costs Is. 3^d. a-day for food and clothing; how 
much will each, and also the whole, cost in the year ? 

25. How much will a tax on property of £8746 yearly 
value amount to, at 2s. 2f d. per pound ? 

26. A clerk's salary is £2, 17s. 9d. a-week ; how much 
is it yearly ? 

27. Find the price of 7 pieces of cloth, each 45 yards, 
at £1, 2s. 7^d. per yard. 

2i». The pay of an Ensign in the Foot Guards is 5s. 6d. 
per day ; what is it yearly ? 

29. A bankrupt owes his creditors £4876, and pays 
them 8s. 6^d. per pound ; how much does he pay in all? 

30. How much does the pay of a regiment of 895 men 
amount to in a year, at the rate of Is. l^d. to each man 
per day ? 

31. Find the value of a lac of rupees, that is 100,000, 
at Is. llfd. each. 

32. How much will a farmer receive for a field of wheat 
containing 16 acres, if each acre produces 7^ quarters, 
and the price of wheat is £2, 16s. 7d. per quarter? 

33. A farmer has a field of potatoes containing 1000 
drills ; now if each drill produces 19 bushels, how much 
will he receive for each drill, and also for the whole, at 
the rate of 4s. 7Jd. per bushel ? 

84. A butcher purchases 4 oxen for 49 guineas, and 
sells the beef, which amounted to 165 stones, at 6s. llfd. 
per stone, and he gets besides £2, 3s. 5|d. for the hide, 
&c. of each ; what is his net gain ? 

35. The weekly receipts of a railway are £1768, 17s. 
8id. ; how much is this per annum ? 

36. Find the value of 17 tons of coal at 15s. 3d. per 
ton. 



44 



COMPOUND MULTIPLICATION. 



37. What should 7 chests of tea, each containing 74 lb., 
cost, at 3s. lOd. per lb. ? 

38. An hospital contains 165 boys, and each requires 
for food and clothing Is. 2Jd. a-day; the governor's 
salary is £368, 7s. 6d. yearly, and 4 teachers have each 
£182, 14s. 8d. yearly ; the porters' and servants' wages 
and board amount to £215, lis. 6d. per annum ; and the 
treasurer's salary amounts to £400 yearly : what is the 
annual income of the hospital, supposing the yearly sur- 
plus to be £597, 18s. 9d. ? 



COMPOUND DIVISION. 

Case I. When the divisor does not exceed 12. 
Ex. Divide £27, 13s. 7id. by 5. Ans. £5, 10s. SJd. 
Sol. 5 in £27 is 5 times and £2 
over; £2 



:40s. and 13s. are 53s. 5 
in 53s. is 10 times and 3s. over; 3s. 
= 36d. and 7d. are 43d. 5 in 43d. is 
8 times and 3d. over; 3d. = 12f. and 
If. are 13f. 5 in 13f. is 2 times and 3 over. 



5 )£27 13s. 7|d . 
£5 10 8i I 

5 

Proof £27 13 7i 



1. Divide £35, 17s. 8id. by 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. 

2. // 74 15 7i by 3, 5, 7, 9, 11, 2, 4, 6, 8, 10, 12. 

Case II. When the divisor is found in the table. 
Ex. Divide £30, lis. 8id. by 18. Ans. £1, 13s.ll|d.^\. 
2 )£30 lis. Sj d. -M8 = 2 X 9 
9)15 5 10^- 1 quot. by 2. 
£ 1 13 11 1- 1 " by 18. 
1X2 + 1 = 2 + 1=3 rem. 

£ s. d. 

9.612 16 3i-r 80, 84, 90 

10.714 13 10^+ 70,121,144 

11.896 11 2i+ 20, 42, 81 

12.968 17 9|-f- 88,108,132 

13.742 16 8i+ 63, 72, 81 

14.845 17 9^+120, 44, 56 

15.874 5 6f+ 36, 88,108 

16.997 19 1U-+121, 132, 144 



1. 374 16 

2. 456 18 



d. 



3.354 11 lOf+32,35,40 
4. 729 19 9i+30, 36, 44 
6.847 17 llf-f-45,48,49 

6. 783 11 9 ■ 

7. 874 14 10*- 

8. 956 15 4| 



16,21,25 
■24, 27, 28 



■54, 55, 56 
■60, 63, 64 
•50, 66, 72 



COMPOUND DIVISION. 



45 



Case III. When the divisor is not contained in the table. 
Ex. Divide £27, 13s. 7id. by 17. Ans. £l,12s.6id.-rV 
17)£27, 13s. lid. ( £1 12s. Gfd.^^'y 



17X1 = 



10 


6 10 


3=4 times. 


Mult, by 20 




4 


213 s. 


.26 1 


= 16 " 


17 X 1= 17 


1 12 


6i=l . 


43 




|Rem. 


17X2= 34 


£27 13 


7i Proof. 



Mult, by 
17X6 = 
Mult, by 
17X3 = 



£ s. 

476 13 

764 17 

1387 11 



17 
i 

r 

t: 
\' 

9 
12 
115 d. 
102 
13 
_4 
54 f. 
51 
3 rem. 



d. 



8^-7-13,19,23 
8i-rl7,26,29 
4i-^37, 46, 58 
4. 7480 16 lOi-f-67, 78, 89 
5.5387 14 11^47,58,69 
6. 6892 17 4i-^53, 57, 59 
7.9673 8 lU-^73,75,79 
a 2723 4 U-f-83,91,95 



£ s. 
9.9873 18 
10.3725 17 
11.4876 11 
12.5983 13 
13.6473 12 



571, 
219, 
432, 
729, 



843 
343 

563 

984 



d. 

llf-f- 
6 -^ 

41-^8463,1729 
14.7893 17 10i-^- 2748, 9740 
15.8739 16 11^^5490,6753 
16.9378 11 71-^4386,9897 
Case IV. To divide one sum of money by another. 
Ex. How often does £99, 8s. 5id. contain £1, lis. 6|d. 
£1, lis. 6|d. ) £99, 8s. 5Jd. 



20 
31s. 
12 
378 d. 

4 

1515 f. 



20 

1988 s. 
12 



23861 d. 
4 



)95445 f. (63 times. 
9090 

4545 

4545 



46 



COMPOUND DIVISION. 



£ 8. 


d. 


£ s. 


d. 


£ s. 


d. 


£ s. d. 


1. 113 12 


6 - 


- 2 10 


6 


9. 402 2 


- 


-4 3 9i 


2. 51 7 


3 - 


- 12 


2| 


10. 103 14 


0|- 


-0 18 4i 


3. 630 7 


8^ 


- 1 14 


6^ 


11. 308 15 


0- 


-2 7 6 


4. 248 17 


3^ 


-72 


2^ 


12.9093 12 


- 


-2 12 1\ 


5. 484 19 


4^ 


-13 17 


H 


13. 201 9 


9^- 


-3 9 5f 


6.2855 7 


o^ 


-27 14 


4 


14.4349 1 


n- 


-6 3 8| 


7. 2673 1 


6 - 


- 7 13 


n 


15.4539 8 


4 - 


-0 18 7i 


8.8866 


0^ 


- 1 5 


Oi 


16.4574 15 


3^- 


-2 11 2^ 



17. How many moidores, each 27s., are in £149, 17s. 
sterling ? 

18. How many francs, each 9|d., are equal to £9, 15s. ? 

19. How many books at 3s. 6d. are equal in value to 
868 at Is. 9d.? 

20. £lj 3s. 4d. was distributed among a number of 
boys, each received Is. 8d. ; how many were there? 

21. How many pounds Irish, each 21s. 8d., are equal 
to 1404 pounds Scotch, each Is. 8d. ? 

22. The railway fares of a certain number of passengers 
amounted to £26, 12s. 6d. ; the fare of each was 35s. 6d. : 
how many were there ? 



SUPPLEMENT TO COMPOUND MULTIPLICATION AND DIYISION. 



Ex. £4 17s. e^d. X 4g 

4| 

3)9 15 1 =2 times. 



3 5 
19 10 



Oii 
2 



£22 15 21 J = 4§ times. 



Ex. £27, 10s. lljd. -r4|. 
4| )£27 108.11id. 

5^ 5 

22 [2 )137 14 8^ =5 tunes. 
1 1 1)68 17 4'g -l \b_ 
£6 5 2^/22 





£ 5. d. 




£ 8. 


d. 




1. 


4 8 7iX 41, 


5f 


1. 270 18 


llf- 


- 4i, 5^ 


2. 


6 17 10| X 6^, 


H 


2. 384 13 


lOi- 


- 9i, 114 


8. 


7 14 IH X 7^, 


H 


3.487 11 


5^- 


" 9f, 10| 


4. 


8 19 7i X 8f, 


9f 


4. 592 13 


n- 


-llf, 13| 


6. 


9 12 1\ X 111, 


12t\ 


5. 756 17 


lu- 


-16i, 29^ 


6. 


12 14 7i X 16y% 


27A 


6. 847 11 


9^- 


-47|, 59i 


7. 


17 18 11|X 19f, 


26^ 


7. 967 11 


H- 


-84t?^,97t*, 


6. 


24 11 7^ X 46 ,V 


52^ 


8. 989 17 


lU- 


r8U\,89^\ 



COMPOUND DIVISION. 47 

1. Divide £746, lis. 6d. equally among 48 men. 

2. If 38 cwt. sugar cost £108, 16s. 8d. ; what is that per 
cwt.? 

3. If 32 quarters of wheat cost £110, lis. 6d. ; what is 
that per quarter ? 

4. A gentleman spends £960 a-year ; what is that a- 
week, and a-day ? 

5. A gentleman's income is £1000 ; what should his 
daily expenses be to save £340 a-year ? 

6. A labourer earns 15s. 7^d. per week, but he must 
save £12 a-year for house-rent and clothes; how much 
may he spend per week ? 

7. If 46i lbs. tea cost £18, 17s. 6id. ; what is that 
per lb. ? 

8. If27| gallons Cognacbrandycost £33, 17s. 6d.;what 
is that per gallon ? 

9. If 34 men gain £1360 in a year; what does each gain 
per week, and per day ? 

10. Divide £255, 17s. 6d. among 7 marines and 75 
sailors, giving each marine twice as much as a sailor. 

11. A farm of 156 acres is let for £375, 18s. 3d. ; what 
is that per acre ? 

12. A joint-stock company consists of 527 shares, and 
the capital is £500,000 ; what is the value of a share ? 

13. A merchant bought 6 pieces of cloth, each 56 yards, 
for £308, 12s. 6d., and sold it at 19s. llfd. per yard; 
how much did he gain upon the whole, and per yard ? 

14. How much cloth at 15s. 6i d. per yard can be bouglit 
for£95, lis. 7id.? 

15. How much wine at £2, 2s. 6d. per dozen can be 
purchased. for £297, 10s.? 

16. In £59, 17s., how many crowns, half-crowns, and 
florins, and of each an equal number? Ans. 126 of each. 

Sc*L. 1 crown = 60d. £59, 17s. 

1 h.-cr. = 30 _20 

1 florin =_24 1197 s. 

ll4d. )14364d . 

126 of each. 



17. How many guineas, half-gumeas, crowns and florins, 
and of each an equal number, are in £25, 6d. ? 



48 COMPOUND DIVISION. 

18. How many gallons of brandy can be bought for 
£625, 19s. 6d. at 36s. 6d. the gallon? 

19. The revenues of an hospital amount to £1807, 8s. 
yearly ; how many boys wiU it maintain, if each costs 
£18, 16s. 6^d. ? 

20. A gentleman distributed £19, 14s. 6d. among some 
poor people, giving each 10s. ll^d. ; how many poor 
were there ? 

21. Divide £73, 7s. 44 d. among 3 men, 5 women, and 
10 boys, giving each man twice a woman's share, and 
each woman 3 times a boy's share. 

22. If a man gains 2s. 6d. a-day, and spends Is. lO^d.; 
how many days must he labour to pay a debt of £11, 
7s. 6d. ? 

23. A farmer, who employed 49 reapers for 4 weeks to 
cut down his crop, paid them in aU £158, 12s. 9d. ; how 
much was that to each reaper, and what was the daily 
wages of each ? 

24. A merchant pays for gas £12, 17s. 6d. yearly, at the 
rate of 10s. per 1000 cubic feet; how many cubic feet does 
he consume in the year ? 

25. The wages of an equal number of men, women, 
and children amounted to £24, 7s. 6d. ; each man earned 
Is. 6d., each woman Is., and each child 9d. : how many 
were there of each ? 

26. A house and its furniture are worth £3750, 16s. 
8d., but the house is worth 7 times as much as the 
furniture ; what is the value of each ? 

27. If 1000 muskets are worth £3333, 6s. 8d. ; what 
is the price of each ? 

28. A corn merchant lays out £581, 17s. on equal 
quantities of wheat at 42s. per quarter, barley at 36s. 
6d. per quarter, and oats at 29s. 3d. per quarter ; what 
quantity of each did he buy ? 

29. How many gallons of ale at 3s. 6d. a-gallon should 
be exchanged for 75 gallons brandy at 38s. 6d. per 
gallon ? 

30. A person spends £8, 12s. 6d. weekly ; what must 
his daily income be that in 12 years he may lay by 
£312 r 



49 



BILLS OF PARCELS. 



Mr James Scott 

14 gallons malt aqua 
13 rum 

12 hollands 

9 brandy 

15 dozen port wine 
16 sherry 



Edinburgh, Jan. 2, 1858. 
Bought of William Oliver^ 

@ 15/6 £ 

.. 18/6 

.. 24/6 

.. 55/6 

.. 47/6 

.. 36/6 



Mr Andreio Turnhull 

Bought of John Smart & Co, 
27J yards superfine black cloth @ 21/8. ..£ 

17| blue do. .. 23/6... 

15| olive do. ..14/9... 

23» mixt do. ..17/10.. 

343 bl. cassimere .. 6/4i... 



3n 



.drab do. ..5/9^... 







£ 


Mr John Williamson 






Bought of J. & W, Allan, 


17 reams large thick post HP. 


. @41/7.... 


..£ 


23 small do. do. 


.. 32/9.... 




13 foolscap ruled 


.. 20/3.... 




16 coloured yellow 


.. 25/8i... 




18 do. green 


..24/111. 




21 marbled 


.. 19/11... 






£ 


Mr John Anderson 






Bought of William Tod, 


13j lbs. green tea 


@ 6/61.... 


..£ 


17^ hyson skin 


.. 5/3^... 




26 1 souchong 


.. 4/lU... 




191 pekoe 


.. 5/8^... 




27 raw sugar 


.. 6^... 




35 refined do. 


.. 8.... 






£ 



50 



BILLS OF PARCELS. 



Mr William Brown 

56 cwt. raw sugar 

29 boxes oranges 

5 lemons 

150 sugar loaves ea. IS^lbs 

52^ cwt. of molasses 

A chest of black tea, ST^lbs. 



Bouglit of Drysdale & Co. 

@ 50/8 £ 

.. 34/lU 

.. 19/4i 

.. 8|p.lb. 
.. 17/6 p. cwt. 
.. 4/3jp.lb... 



Mr George Thomson 

Bought of David Wright, 

54i yds. superfineBrussels carpet @4/10|..£ 

71 fine do. do. ..3/9 

67f superfine English do. .. 2/11 J.. 



294 



fine 



do. 



17^ floor-cloth 



15J.. 



V crumb-cloth 



do. 



■2/M 
. 5/71... 
. 8/9i... 



Mr David Simpson 

52 quarters wheat 

47 barley 

39 oats 

17 pease 

19 beans 

117 stones hay 



Bought of Richard Davidson, 

@46/6 £ 

.. 43/5., 
.. 27/8. 
.. 45/3. 
.. 46/8. 



9i.. 



Miss Murray 

14^ yds. pink sarcenet 

17f green silk 

25 printed calico 

23 J ..... Norwich crape 

19 gingham 

24| do. striped 

27| silk velvet 



Bought of Thomas Watson, 

@3/7i £ 

.. 4/2i 

.. l/2i 

.. 3/2i 

.. llf 

•• 10^ 

.. 14/8^ 



61 



II. WEIGHTS AND MEASTJKES. 

KEDUCTION. 

Ex. Eed. 8472 grs. to ib. 
f 4)8472 grs. 
(6)2118 



16 )2118 
2,0)35,3 dwt. 
12)17 oz. 13 dwt. 
lib. 5 oz. 13 dwt 



Ex. Red. 3 lb. 4 oz. 5 dwt. to gi'S. 
Mult. by 12 and add 4 oz. 

40 oz. 
Mult, by 20 and add 5 dwt. 

805 dwt 
Mult. by 24 

19320 grs. 

1. Reduce 27 lbs. ; 14 lbs. 10 oz. 13 dwts. ; 57 lbs. 8 oz. 
12 dwts. 16 grs. ; 82 lbs. 3 oz. 15 dwts. 20 grs. troy re- 
spectively to grains. 

2. Reduce 27653 dwts. ; 476890 grs. ; 478670 oz. ; 
72586 grs. ; 5147G0 dwts. ; and 738469 grs. to pounds. 

3. Reduce 29 lbs. 2 oz. 3 drs. 1 scr. 18 grs. ; 18 lbs. 
4drs, ; 461bs. 4oz. 2 scrs. ; and 205 lbs. 15 grs. to grains 
apothecaries' weight. 

4. Reduce 4968 drs. ; 72190 scrs. ; 618764 grs. ; 5489 
oz. ; 73864 drs. ; and 892164 grs. to pounds. 

5. Reduce 24 tons ; 6 tons, 3 cwt. 2 qrs. 14 lbs. 12 oz. 
12 drs. ; 15 cwt. 27 lbs. 14 drs. ; 27 lbs. 13 oz. 15 drs. to 
drams avoirdupois. 

6. Reduce 21704736 drs.; 41876 lbs.; 219864 oz. , 
518764 lbs. ; 21983 qrs. ; 714867846 drs. to tons. 

7. Reduce 3 fur. 34 po. 3 yds. 2 ft. ; 17 miles, 2 fur. 28 
po. 2 yds. 9 in. ; and 81 mis. 1 fur. 26 po. 3 yds. 2 ft. 6 in. 
to inches. 

8. Reduce 71846 yds. ; 4189628 inches ; 4596327 ft. ; 
8476 po. ; 51486973 in. ; and 7184896 ft. to miles. 

9. Reduce 4 yds. 2 qrs. 1 nl. ; 24 yds. 3 nls. ; 25 Eng. 
ells, 3 qrs. 2 nls. ; 53 Fie. ells, 2 qrs. 3 nls. ; 56 yds. 3 qrs. 
3 nls. to nails. 

10. Reduce41764 nls. ; 5174 qrs. ; 318769 inches ; 49864 
nls.; 217384 inches; and 8172144 nls. to yards and 
English ells. 

11. Reduce 27 ac. 3 ro. 16 per. ; 84 ac. 2 ro. 24 per. 28 
yds. ; 108 ac. 1 ro. 36 per. 25 yds. 5 ft. 84 in. to square 
inches. 



52 REDUCTION. 

12. Reducel47847684sq.inches; 218764yds.; 5189764 
ft. ; 31874 per. ; and 84726084 inches to acres. 

13. Reduce 48 cub. yds. ; 403 cub. yds. 21 ft. 908 in. , 
700 tons of ship. ; 672 loads of hewn timber ; and 876 
do. of rough, to cubic inches. 

14. Reduce 17486936 cu. in.; 784693 cu. ft.; 874869684 
cu. in. ; and 784627 cu. ft. to cubic yards and tons of 
shipping. 

15. Reduce 8 qrs. 3 bu. 2 pk. 1 ga. ; 208 qrs. 7 bu. 3 pk. 
1 ga. 3 qts. ; 409 bu. 2 pk. 1 ga. 3 qts. 1 pt. to pints. 

16. Reduce 7486984 pts. ; 87634 pks. ; 918764 gals. ; 
8176 bu. ; 514876 pts. ; and 784673 qts. to quarters. 

17. Reduce 208 galls. 3 qts. 1 pt. ; 476 galls. 2 qts. ; and 
749 galls. 1 qt. 1 pt. to pints. 

18. Reduce 74869 pints ; 586476 pints ; 3486 qts. ; and 
79040 pints to gallons. 

19. Reduce 42 signs 39° 36' ; 81^ 15° 49' 59'^ ; 208s 20° 
56' 28''; and 315^ 19° 34' 38'' to seconds. 

20. Reduce 718460"; 87654'; 374°; 8178640"; 71860'; 
7186940"; and 7184° to signs and circles. 

21. Reduce 36 co. ye. 219 da. 18ho. 15 min. 27 sec. ; 380 
CO. ye. 219 da. 23 ho. 29 min. 36 sec. ; and 7184 Julian 
years to seconds. 

22. Reduce 71847630 sec. ; 48196219 min. ; 81468 ho. ; 
31817640 sec. ; and 7187210 min. to com. and Jul. years. 

23. How long would it require to count 800 millions of 
sovereigns, at the rate of 120 in a minute? 

24. How many seconds have elapsed since the birth of 
Christ or in 1858 Jul. years? 

25. The distance of Jupiter from the sun is 494,513,000 
miles ; express this in feet. 

26. Saturn revolves round the sun in 10,756 days, 5 ho. 
16 m. 32 sec. ; how many seconds is this ? 

27. In Scotland there are 29,167 square miles j how 
many acres does it contain ? 

28. The polar axis of the Earth is 41,706,360 feet ; 
express this in miles, &c. 

29. Light travels at the rate of 192,000 miles per sec. ; 
in what time will it travel between the Sun and Saturn, 
the distance being 906,643,000 miles ? 



53 



COMPOUND ADDITION. 

TROY WEIGHT. 
2. 



lbs. 


oz. 


dwt. 


gr. 


lbs. 


oz. 


dwt. 


gr. 


lbs. 


oz. 


dwt. 


gr. 


27 


10 


11 


18 


31 


10 


19 


23 


67 


8 


13 


22 


36 


11 


16 


17 


53 


8 


17 


19 


76 


9 


18 


20 


41 


8 


18 


23 


35 


4 


15 


20 


18 


11 


15 


23 


34 


9 


10 


12 


20 


3 


4 


6 


81 


4 


12 


14 


26 


5 


8 


19 


25 


9 


16 


17 


15 


3 


13 


13 


37 


11 


16 


15 


48 


11 


19 


21 


56 


11 


4 


8 


47 


10 


18 


22 


84 


10 


16 


18 


9 


10 


8 


17 



APOTHECARIES' WEIGHT. 





4. 








5. 








6. 






lbs. 


oz. 


dr. 


Bcr. 


oz. 


dr. 


sc. 


gr- 


lbs. 


oz. 


dr. 


Bcr. 


18 


9 


4 


1 


11 


7 


2 


19 


56 


10 


7 


2 


17 


8 


7 


2 


10 


4 


1 


15 


84 


11 


5 


1 


26 


5 


4 





8 


3 


2 


18 


96 


10 


6 


2 


62 


11 


7 


2 


7 


5 


1 


17 


31 


8 


4 


1 


25 


10 


4 


1 


9 


4 


2 


15 


28 


9 


7 


2 


64 


11 


2 


2 


11 


6 


1 


18 


86 


11 


7 


2 



AVOIRDUPOIS WEIGHT. 





7 








8 








s 


. 




ton. 


cwt. 


qrs. 


lbs. 


cwt. 


qrs. 


lbs. 


oz. 


qrs. 


lbs. 


oz. 


dr. 


74 


18 


2 


25 


27 


2 


18 


14 


14 


14 


14 


14 


87 


16 


3 


27 


31 


3 


26 


15 


27 


26 


15 


15 


65 


13 


1 


20 


46 


1 


24 


13 


38 


22 


13 


12 


29 


11 





18 


49 


2 


27 


11 


47 


11 


12 


13 


94 


17 


3 


26 


37 





24 


12 


31 


18 


15 


11 


38 


14 


2 


19 


84 


3 


16 


10 


72 


27 


13 


15 


45 


19 


1 


27 


93 


1 


27 


15 


29 


22 


10 


4 



LINEAL MEASURE. 





10. 






11 








12. 






mis. 


fu. po. 


yds. 


fu. 


po. 


yds. 


ft. 


po. 


yds. 


ft. 


in. 


45 


3 27 


4 


17 


18 


2 


1 


39 


'2 


1 


7 


76 


7 39 


5 


25 


36 


1 


2 


45 


4 


2 


11 


64 


5 29 


3 


64 


31 


3 


1 


53 


3 


1 


10 


85 


6 34 


2 


45 


39 


5 


2 


32 


5 


2 


8 


58 


7 26 


4 


74 


26 


4 





25 


4 


2 


y 


69 


3 37 


2 


55 


34 


5 


2 


74 


5 


2 


11 


73 


5 33 


4 


79 


18 


1 


1 


43 


2 


1 


9 



54 



COMPOUND ADDITION. 



CLOTH MEASURE. 





13 








14 










15. 




yds. 


qrs. 


nls. 


in. 


En.ell 


qrs. 


nls. 


in. 


Fr.ell. 


qrs. 


nls. 


in. 


27 


3 


3 


2 


45 


3 


2 


1 


48 


5 


3 


2 


73 


1 





1 


36 


4 


3 


2 


76 


3 


2 





48 





2 





75 


2 


1 


1 


51 


4 


1 


1 


86 


2 


1 


1 


64 


4 


3 


2 


36 


5 


3 


2 


74 


2 


3 


2 


38 


4 


1 


2 


71 


4 


1 





39 


1 


2 





76 


3 


3 


1 


67 


1 





2 


76 


1 


3 


2 


69 


4 


2 


2 


84 


5 


3 


2 









SQUARE OR LAND MEASURE. 










16. 




17. 




u 


I 




ac. 


ro. 


pe. 


yds. 


ro. 


pe. yds. 


ft. 


pe. 


yds. 


ft. 


in. 


36 


3 


39 


30 


14 


27 18 


4 


27 


29 


8 


67 


45 


2 


33 


24 


25 


11 19 


8 


31 


30 


4 


96 


72 


3 


27 


29 


32 


17 21 


4 


27 


27 


1 


99 


85 


1 


36 


30 


36 


38 29 


7 


38 


11 


7 


84 


96 


3 


38 


27 


48 


28 26 


6 


29 


26 


3 


47 


71 


2 


31 


25 


86 


39 30 


8 


36 


30 


8 


98 


78 


3 


39 


30 


74 


36 28 


7 


39 


30 


8 


99 



MEASURE OF CAPACITY. 





19 








20 








21. 




qrs. 


bu. 


pe. 


Ra. 


bu. 


pe. 


ga. 


qt. 


pe. 


ga. qt. 


pt. 


56 


7 


3 




56 


2 


1 


2 


74 


1 3 




74 


6 


2 




39 


1 





3 


38 


1 2 




45 


3 


1 




47 


3 


1 


2 


84 


1 3 




63 


7 


3 




76 


1 


1 


1 


48 


1 2 




34 


6 


2 




79 


3 





3 


56 


1 3 





47 


7 


3 




34 


1 


1 





75 


2 




38 


5 


2 




49 


3 


1 


3 


63 


1 3 













TIME. 












22. 






23. 






24 






co.ye. da. 


ho. 


m. 


da. 


ho. m. 


sec. 


da. 


ho. 


m. 


sec. 


28 96 


18 


15 


84 


12 56 


59 


55 


18 


54 


11 


38 27 


16 


53 


96 


18 41 


36 


73 


19 


49 


56 


45 99 


23 


59 


72 


23 59 


59 


85 


16 


46 


55 


76 84 


11 


52 


67 


22 48 


45 


98 


17 


41 


36 


35 219 


16 


18 


36 


21 18 


47 


87 


22 


28 


39 


74 361 


15 


55 


79 


20 29 


55 


76 


20 


18 


49 


84 278 


11 


46 


93 


23 51 


42 


65 


23 


54 


51 



COMPOUND ADDITION. 



55 



25. A corn merchant bought 208 qrs. 3 bu. 1 pk. of 
barley ; 336 qrs. 2 pk. of wheat ; 236 qrs. 4 bu. of oats ; 
125 qrs. 1 bu. 3 pks. of rye ; 86 qrs. 1 bu. 1 pk. of pease ; 
and 79 qrs. 2 bu. 2 pk. of beans : how many quarters 
did he buy ? 

26. The distance from A to B is 2 ml. 1 fu. 30 po. 5 yds. ; 
from B to C, 7 fu. 4 yds ; from C to D, 1 ml. 25 po. ; 
and from D to E, 3 ml. 1 fu. 2 yd. : find the distance 
from A to E. 

27. A clothier, at various times, bought 28 yds. 2 qrs. 
1 nl. of cloth ; 37 yds. 2 qrs. ; 47 yds. 1 nl. ; 37 yds, 
1 qr. 2 nl. ; and 67 yds. 2 qrs. 2 nl. : how much did he 
buy in all ? 

28. London is in latitude 51° 30^ 48'' N., and Sydney 
is in lat. 33° 51^ 40'^ S. ; what is the diflference ? 



COMPOUND SUBTRACTION. 



TROY WEIGHT. 





1. 






2. 






3. 


lb. 


oz. dwt. 


gr. 


lb. 


oz. dwt. 


gr. 


lb. 


oz. dwt. gr. 


96 


10 13 


14 


36 


5 17 


21 


82 


2 1 16 


47 


10 19 


21 


19 


7 18 


23 


79 


11 14 20 









apothecaries' weight. 










4. 






5. 


6. 






lb. 


oz. 


dr. 


scr. 


lb. 


oz. dr. Bcr. 


oz. 


dr. 


scr. 


pr. 


39 


2 


3 


1 


52 


7 7 


41 


6 


2 


18 


29 


7 


5 


2 


46 


8 7 1 


34 


7 


1 


19 



84 
65 



avoirdupois weight. 





7. 




8. 






9. 




ton. 


cwt. qrs. lb. 


cwt. 


qrs. lb. 


oz. 


qrs. 


lb. oz. 


dr. 


84 


13 2 11 


46 


1 23 


12 


17 


21 11 


10 


69 


14 3 25 


29 


2 22 


15 


9 


22 13 


14 



10. 

mis. fu. po. yds. 

^ 3 22 4 

3 25 5 



lineal measure. 
11. 

fa. po. yds. ft. 

35 33 4 1 
17 36 4 2 



po. 

39 
19 



12. 

yds. ft. in, 

2' 2 8 

4 2 10 



56 



COMPOUND SUBTRACTION. 









CLOTH MEASURE. 










13. 




14. 




15. 




yds. 


qrs. Ills. 


in. 


E.ell. qrs. nls. in. 


Fr.ell. 


qrs. nls. 


in. 


72 


2 1 


1 


93 4 2 1 


81 


4 2 


1 


66 


2 1 


2 


63 4 3 2 


41 


5 3 


2 



SQUARE OR LAND MEASURE. 
17. 



ae. 


ro. pe. 


yds. 


ro. 


pe. 


yds. 


ft. 


pe. yds. 


ft. 


in. 


65 


2 31 


21 


53 


18 


27 


3 


25 21 


4 


10 


36 


3 31 


24 


19 


28 


29 


5 


8 29 


4 


11 



MEASURE OF CAPACITY. 





19. 






20. 






21. 




qrs. 


bu. pe. 


pa. 


bu. 


pe. ga. 


qt. 


pe. 


ga. qt. 


pt. 


21 


3 2 





54 


2 1 


2 


18 


3 





18 


4 3 


1 


49 


2 1 


3 


9 


1 3 


1 



22. 

co.ye. da. ho. m. 

41 138 14 25 

18 147 16 46 



TIME. 
23. 
da. ho. 

90 13 43 21 
40 18 25 46 



m. sec. 



da. 



24. 

ho. m. BBC. 

70 19 15 55 

31 22 15 59 



25. The latitude of Edinburgh is 55° 57' 23'' N., and 
the latitude of Pekin is 39° 54' 13'' N. ; find the difference. 

26. Mars revolves round the sun in 686 da. 23 ho. 30 m. 
41 sec, and Venus in 224 da. 16 ho. 49 ra. 10 sec. ; find 
the difference. 

27. Three farms contain 4536 ac. 3 ro. 25 per. ; the 
1st and 2d contain 3327 ac. 30 per., and the 1st and 3d 
2752 ac. 15 per. ; what is the size of each? 

28. A merchant bought 756 qrs. 3 bu. 2 pk., and sold 
to A 208 qrs. 3 bu. 1 pk., and to B 315 qrs. 2 bu. 2 pk. ; 
what quantity has he left ? 

29. A piece of silk measured 43 yds. 2 qrs. 1 nl. 1 in. ; 
after 27 yds. 3 qrs. 2 nl. 2 in. have been sold: how much 
remains ? 

30. A traveller arrived at a railway station at 26 min. 
and 32 sec. past 1 o'clock, and found that the train 
did not start until a quarter past 2 o'clock ; how long 
had he to wait ? 



57 



COMPOUND MULTIPLICATION. 

1. 17 lb. 8 oz. 15 dwt. 21 grs. X25, 27, 29, 47 

2. 32 lb. 11 oz. 17 dwt. 19 grs. X 16, 24, 31, 38 

3.25 lb. 4 oz. 3 drs. 2 scr. 18 grs. X 18, 22, 34, 43 

4. 47 lb. 9 oz. 7 drs. 1 scr. 13 grs. X20, 28, 37, 41 

6. 36 ton. 14 cwt. 2 qrs. 21 lb. 1 1 oz. 13 drs. X 30, 32, 39, 46 
6.43ton. 16cwt. 3qrs. 261b. 13oz. 15 drs.X33, 35, 47, 51 
7.21 mis. 5 fu. 29 po. 2 yds. 1 ft. 11 in. X36, 40, 52, 57 

8.37 mis. 7 fu. 36 po. 3 yds. 2 ft. 8 in. X42, 45, 53, 58 
9. 56 yds. 3 qrs. 2 nls. 2 inches X54, 56, 67, 71 

10. 73 E. ells, 4 qrs. 3 nls. 1 inch X60, 64, 68, 17 

11.47 Fr. ells, 5 qrs. 2 nls. 2 inches X^^, 70, 69, 73 

12.38 Fl. ells, 2 qrs. 1 nl. 1 inch X72, 77, 19, 13 

13. 56 ac. 2 ro. 31 pe. 23 yds. 5 ft. 47 in. X44, 48, 59, 61 
U.87 ac. 3 ro. 39 pe. 27 yds. 8 ft. 126 in. X49, 50, 62, 65 
15.43 qrs. 3 bu. 2 pe. 1 gal. 3 qts. 1 pint X80, 81, 75, 78 
16.76 qrs. 4 bu. 1 pe. gal. 2 qts. 1 pint X84, 88, 79, 82 
17. 34 CO. ye. 156 da. 21 ho. 56 min. 57 sec. X90, 96, 86, 98 
18. 71 Ju. ye. 213 da. 19 ho. 42 min. 49 sec. X 108, 121, 107 

19. A sovereign weighs 5 dwt. 3 grs. nearly ; find the 
weight of 1000 sovereigns. 

20. What is the weight of 35 brass guns, each weigh- 
ing 6 cwt. 3 qrs. 9 lbs. ? 

21. How far will a postman travel in a year, if he walks 
9 mis. 3 fu. 8 po. 5 yds. daily ? 

22. How much grain will a farm of 25 fields, each 12 
acres, produce at the rate of 8 qrs. 7 bu. 2 pk. 1 gal. 
per acre ? 

23. A cubic foot of water weighs 2 qrs. 6 lbs. 8 oz. ; 
what weight of water is there in a cistern whose content 
is 72 cubic feet ? 

24. How much cloth would be required to make coats 
for a regiment of 875 soldiers, allowing 3 yds. 1 qr. 1 nl. 
to each ? 

25. A cartload of coal weighs 19 cwt. 2 qr. 18 lb. ; 
how much will 37 cartloads weigh? 

26. Find the content of 17 farms of 14 fields, each con- 
taining 9 ac. 3 ro. 19 per. 4 yds. 



58 



COMPOUND DIVISION. 



1.387 lb. 4 oz. 13 dwts. 18 grs. 
2. 496 lb. 11 oz. 19 dwts. 22 grs. 
3.576 lb. 10 oz. 4 drs. 2 scr. 18 grs. - 
4.765 lb. 8 oz. 7 drs. 1 scr. 12 grs. - 
5.876ton.l5cwt..3qr.201b.l3oz.l2dr.- 
6.987ton. 18cwt.2qr.261b.l5oz.8dr.- 
7. 475 mis. 7 fu. 38 po. 3 yd. 2 ft. 11 in.- 
8. 754 mis. 3 fu. 25 po. 2 yd. 1 ft. 10 iii.- 
9. 375 yds. 3 qrs. 2 nls. 1 inch 
10. 573 E. ells, 4 qrs. 3 nls. 2 inches 
11. 876 Fr. ells, 5 qrs. 2 nls. 2 inches - 
12.768 Fl. ells, 2 qrs. 1 nl. 1 inch 
13. 476 ac. 3 ro. 36 pe. 25 yds. 4 ft. 96 in. ■ 
u. 674ac. 2 ro. 24pe. 28yds. 5ft. 102 in.- 
15. 987 qrs. 7 bu. 3 pe. 1 gal. 2 qts. 1 pint- 
le. 879 qrs. 4 bu. 2 pe. gal. 3 qts. 1 pint- 
17. 578 CO. ye. 134 da. 15 ho. 44 m. 58 sec- 
18. 488 Ju.ye. 341 da. 21ho. 56m. 58 sec- 



16, 18, 
•15,14, 
■20, 22, 
30, 42, 
•28, 25, 
27, 32, 
■33, 40, 
•35, 36, 
•44, 45, 
•48, 49, 
50,54, 
-55, 56, 
-60, 63, 
-64, 70, 
-66, 72, 
-77; 80, 
-81,84, 
-88, 90, 



23, 
17, 
31, 
39, 
37, 
38, 
43, 
46, 
53, 
52, 
98, 



19 
29 
26 
34 
39 
41 
47 
51 
57 
87 
117 



273, 181 
371,811 
713, 645 
298, 364 
756, 643 
209,316 
369, 691 



19. 14 hhds. Jamaica sugar weigh 234 cwt. 2 qr. 14 lb. ; 
find the weight of each. 

20. How many canisters, each containing 1 qr. 7 lb., 
can be filled from 37 cwt. 21 lb. ? 

21. 133 bars of silver weigh 156 lb. 3 oz. 17 dwt. 2 grs. ; 
w^hat is the weight of each ? 

22. Find the circumference of a wheel which revolves 
5267 times on a road 8 mis. 7 fu. 32 po. 5 yds. long. 

23. An estate contains 5837 ac. 2 ro. 29 per. ; into how 
many farms, each containing 32 ac. 3 ro. 37 per., may 
it be divided ? 

24. A spring yields 72 gallons of water an hour, and 
supplies 675 families ; how much may each family use 
daily ? 

25. How many steps, each 2| feet, will a man take in 
walking 9 miles ? 

26. In 2 cwt. 2 qr. 5 lb. 4 oz. 8 drs. ; how many 
parcels of 4 oz. 5 drs., 5 oz. 6 drs., 7 oz. 8 drs., and 8 
oz. 5 drs., and of each an equal number ? 



59 



MISCELLANEOUS EXERCISES. 

1. A was born in 1805, and B 20 years after; when was 
B born, and what are their present ages ? 

2. A general, commanding an army of 45,550 men, fought 
a battle, in which 5217 were killed, 11,781 wounded, and 
518 amissing; he likewise threw 2157 into one garrison, 
and 1786 into another; how many effective men remained 
under his command in the field ? 

3. What number being divided by 374 will give 8647369 
for the quotient, and 76 for the remainder? 

4. The product is 78469468, and one of the factors 4876 ; 
what is the other? 

5. Two persons start from the same place, and travel the 
one 35 miles, and the other 42 miles a-day; how far will 
they be distant from one another at the end of 44 days if 
they both travel the same way, and how far if they travel 
in opposite directions ? 

6. A person, after paying to A £71, to B £84, to C £121, 
to D £118, to E £217, and to F £196, has still remaining 
£254 ; how much had he at first ? 

7. In leap year how many days in each of the 12 calendar 
months, and what is their sum ? 

8. How many days from March 3d to November 1 9th ? 

9. How many days from April 1st to December 29th? 

10. A man was born in the year 1821, when will he be 85 
years of age ? 

11. A man was bom in 1815, what was his age in 1858 ? 

12. A boy can point 1 6,000 pins in an hour, how many at 
that rate will 16 boys point in a year of 365 days, if they 
work ten hours each day ? 

13. If the population of the globe is taken at one billion, 
how many die yearly, if we suppose a generation to last 
36 years? 

14. At a game of cricket A, B, and C score 112 runs, A 
and B score 79 runs and B and C 70 runs ; how many did 
each score ? 

15. The Iliad contains 15683 lines, and the -^neid 9882 
lines, now if a boy reads 112 lines daily; in how many days 
will he finish them ? 

16. A merchant lodged in the bank on Monday £744, lis. 
7^d., and drew out on Tuesday £579, 18s. 6|d. ; lodged on 
Wednesday £1054, 17s. 8d., drew on Thursday £873, 198. 



60 MISCELLANEOUS EXERCISES. 

9id. ; lodged on Friday £1786, 13s. 10|d., and drew out 
on Saturday £1297, 13s. llfd. ; how much remained on 
Tuesday, Thursday, and Saturday after drawing? 

17. If a yard of cloth costs £1 , 2s. 6^d., what cost 85 yards ? 

18. If 74 yards of cloth cost £84, 17s. 6d., what cost 
lyard? 

19. If 25 yards cost £24, 5s. lOd., what cost 5 yards? 

20. What cost 93 cwt. of sugar at £2, 16s. 8^d. per cwt.? 

21. What cost 1 lb. of tea at £96, lis. S^d. for 275 lb. ? 

22. How many letters in a book of 21 volumes, each 840 
pages, each page 48 lines, and each line 41 letters? 

23. If a mason gains 18s. 6d. per week, and lays up 2s. T^d. 
per week ; how much does he spend, and how much does he 
lay up in a year ? 

24. How many revolutions does a wheel, which is 2 J yards 
in circumference, make in 3^ miles ? 

25. A traveller walks 25 miles a-day, after travelling 75 
miles, another follows him at the rate of 30 miles a-day ; 
in how many days will the second overtake the first ? 

26. If a man's wages are 21s. per week, how much may he 
spend weekly to save £13, 13s. a-year? 

27. A farm of 96 acres is let for £96, 16s. 6^d., what is 
that per acre ? 

28. Gained £274, 19s. 8id., but afterwards lost £189, 19s. 
llfd. ; what is my net gain? 

29. How much will a labourer earn in 219 days at 2s. l^d. 
per day ? 

30. A labourer earns £35, 17s. lO^d. a-year, how much 
is that per week ? 

31. 16 men purchased a lottery ticket for £25, which 
turned out a prize of £3150; how much of the ticket did 
each pay, and how much did each receive of the prize ? 

32. A merchant has in cash £2385, 17s. llfd., in bills 
£12,748, 16s. 6d., tea valued at £748, 16s. llfd., raw sugar 
£289, 17s. 6|d., refined sugar £112, 17s. S^d., whisky £348, 
17s. lOd., rum £240, lis. 7id., brandy £497, lis. 7|d., 
gin £241, lis. 7^d., wines £1298, 3s. 4|d., porter £84, lis. 
ll^d., ale £73, 16s. 9d., in other articles £876, 13s. 9^d., and 
debts owing to him £2381, lis. lid.; at the same time ho 
owes to A £481, 17s. llfd., to B £973, 16s. 7^^ ^o C £876, 
16s. lOd., to D £584, 16s. 4|d., to E £683, 13s. ^d., to 
F £297, 16s. lO^d., and in bills £7348, 16s. 7fd.; what is his 
net worth ? 

33. In £23, 2s., how many shillings, sixpences, and four- 
pences, and of each an equal number ? 



MISCELLANEOUS EXERCISES. 61 

34. "Wliat quantity of tea at 3s. 9§d. per lb. should be 
exchanged for 728 lbs. of sugar at 6^d. per lb. ? 

35. A took to market with him £148, 17s. lOfd., and he 
there received from B £741, lis. lO^d., from C £629, 168. 
S^d., from D £946, lis. 6d., from E £493, 16s. llfd., from 
F £748, 16s. 9id., from G £387, 10s. 6fd., and from H 
£876, lis. 7^d. ; but in coming home he was robbed of 
£2587, lis. 8f d. : how much did he bring home with 
him? 

36. A person paid for a feu to build a house £1276, 17s. 
6|d. ; the mason's bill amounted to £1485, 178. 3f d., the 
joiner's to £487, 16s. 9fd., the plasterer's to £184, 19s. 9id., 
the slater's to the same, the painter's to £120, lis. 7fd., the 
plumber's to £56, lis. lO^d., besides other charges to £37, 
lis. 9^d. ; now he wants to sell it so as to gain £470, lis. 
9^d. : how much does he expect for it ? 

37. A person gains £1, 5s. 7jd. per week, and spends 19s. 
8^d. per week ; how much does he save in the year ? 

38. A person gains £1, 2s. 7^d. per week, and spends £45, 
17s. Ifd. in the year; how much does he save in the week? 

39. Divide 91 lb. 7 oz. 11 dr. of tea among 12 men and 24 
women, giving each man | of the share of a woman. 

40. A merchant began business with a capital of £950, 
17s. 6d. ; at the end of the year he had in cash £350, lis. 
8id., in bills £256, 17s. 8^d., in goods £850, lis. 2^d., and 
debts owing to him £572, lis. 7fd. ; at the same time he 
owed in bills £381, 17s. 2Ad., to A £340, 18s. 7^d., to B 
£120, lis. 4fd., to C £49, Hs. 6fd., to D £36, 17s. 8^., to 
E £49, lis. 2^d., and to sundries £134, 18s. 6d. : whether 
has he gained or lost, and how much ? 

41. Bought 24 pieces of cloth, each containing 30 yards, 
for £840, 17s. 6d., and sold 400 yards at £1, 4s. 3d. per yard ; 
how must I sell the remainder per yard to gain £84, 2 s. 6d. 
upon the whole ? 

42. Bought 480 yards of cloth for £560, 6s. 8d., but 120 
yards being damaged, I am obliged to sell them at a loss of 
£20, 13s. 4d. ; how must I sell the remainder per yard so 
as to gain £60, 16s. 8d. upon the whole, and what did the 
damaged part sell at per yard ? 

43. A merchant clears by his trade £1 590, 17s. 6f d. yearly ; 
his household expenses amount to £580, 17s. 7|d., house 
rent £120, lis. 9^, taxes £45, 17s. 8|d., shop rent £140, 
lis. 9id., taxes £56, 17s. 8|d., servants' wages £175, lis. 
llfd., tradesmen's accounts £170, lis. 9|d., and incidental 
expenses £49, 17s. 8|<l. ; what is his net gain ? 



62 MISCELLANEOUS EXERCISES. 

44. What is the value of 12 1 gallons of rum at 18s. 4d. 
per gallon ? 

45. Bought sugar at £3, 16s. 6d. per cwt., how much was 
that per lb. ? 

46. After paying at one time £847, lis. 8|d., at another 
£650, 10s. 4id., at a third £549, 16s. T^d., at a fourth 
£729, 18s. 4|d., at a fifth £1084, 19s. 8id., and at a sixth 
£1578, 15s. 5id., there remained due £2196, 17s. lOfd.; 
what was the original debt ? 

47. What is the stock of a banking company, which con- 
sists of 154 shares, each £578, 17s. 8^d. ? 

48. Divide £17, 12s. lid. among 3 men, 4 women, and 5 
children, giving each man 2 times the share of a woman, 
and each woman 3 times the share of a child. 

49. A gentleman gave £10, 10s. to pay for his lodging 
from 1st May till 10th July, at Is. ll^d. per night; what 
change should be returned to him ? 

50. The longitude of New York is 74° 0' 3" W., and of Cal- 
cutta, 88° 20' 27" E. ; find the difference. 

51. Discounted six bills; the first amounted to £340, 17s. 
8^d., the second to £473, lis. 9|d., the third to £576, 17s. 
8|d., the fourth to £605, 15s. 4|d., the fifth to £680, 17s. 
2|d., and the sixth to £720, Is. 9^d. ; the discount upon 
each was respectively £7, 19s. lOf d. ; £9, 12s. ll^d.; £11, 
18s.8|d.; £12, 16s. 8id.; £12, 19s. 9|d. ; and£13, 5s. ll|d. : 
what was the net proceeds of each, and of the whole ? 

52. A gentleman's yearly income is £1560, 16s. 8^d. ; how 
much may he spend monthly, weekly, and daily, to save 
£500 a-year ? 

53. A gentleman gave his daughter for her fortune an es- 
critoire, containing 12 drawers, each drawer was divided 
into 18 compartments, in each of which was £24, 17s. 6fd. ; 
what was the daughter's fortune? 

54. Divide £1120, 10s. 6d. among 10 men and 3 boys, 
giving each boy only ^ of a man's share. 

55. How many guineas, half-guineas, crowns, and florins, 
and of each an equal number, are contained in £36, lis. 6d. ? 

56. Divide 886 ac. 3 ro. 25 per. of land among A, B, and 
C, giving A 32 ac. 2 ro. 35 per. less than C, and B 98 ac. 3 
ro. 15 per. more than C. 

57. The freights received for a voyage were, from A 
£127, 6s. 8H, from B £141, lis. 7fd., from C £174, 17s. 
lO^d., from D £84, lis. 9|d., from E £79, 12s. 4id., from 
F £112, 13s. 6id., and from G £14, lis. 2Jd.; how much 
was the whole freight ? 



MISCELLANEOUS EXERCISES. 63 

5^3. A merchant bought 87 yards of blue cloth for £1, 2s. 
2^d. per yard; how must he sell it per yard to gam £12, 
13s. 6d. on the whole? 

59. The rent of a shop, including taxes, is £95, 19s. 7Jd, 
a-year ; how much is tliat weekly and daily ? 

60. Bought 9 pieces of cloth, each 35 yards, for £164, 12 s. 
9^d., and sold 108 yards at lis. 2d. per yard; how must 1 
sell the remainder per yard to gain £47, 8s. 7fd. in all? 

61. In 20 lbs. 11 oz. 14 drs. of sugar, how many packages, 
containing 2 lb., 9 oz., and 4 oz., and of each an equal 
Qumber ? 

62. A common consists of 440 ac. 2 ro. 20 per. ; into how 
many fields, each containing 5 ac. 3 ro. 20 per. can it be 
divided ? 

63. Bought 44 pipes of wine for £2640, and gained by 
selling them as much as 11 pipes cost me ; what was a pipe 
of it sold for ? 

64. A ship's company took a prize of £17,240, lis. 9d. ; 
the captain got i of the whole, the 2 lieutenants got each 
y*g of the remainder, the 3 midshipmen got each ^^g of what 
was left, and the remainder was equally divided among i 
crew of 218 men ; what was the share of each ? 

65. Divide £172, 18s. 3d. among 4 men, 7 women, and 13 
children, givmg each man 3 times the share of a woman, ami 
each woman 5 times the share of a child. 

66. A father divides his estate among his 3 sons ; the 
eldest gets £6000, the second | of the eldest, and the third 
f of the second ; what was the value of the estate, and the 
shares of the two younger sons ? 

67. A bankrupt who owed his creditors £7856, paid them 
only £3250, 12s. 6d. ; what was that per pound? 

68. A and B gain joinjtly £56, 17s. llfd., A and C £48, 
17s. lO^d., and B and C £60, lis. 8Jd. ; what is the whole 
gain, and the share of each ? 

69. Received 147 yards of cloth at 14s. 6d. per yard in 
exchange for 441 lbs. of tea ; find the price of the tea per lb. 

70. An equal number of men, women, girls, and boys, are 
employed at a manufactory, each man receives Is. 6d. per 
day, each woman Is. 3d., each girl 7^d., and each I 
now the sum required to pay their daily -^ ^ 
£15, 63. l^d. : how many of each are empla 

71. A merchant purchased 245 yards o^Sid^at 10^ T^dUi 
per yard, now 20 yards became worthlesl^feena >being damj^ ^s -. 
aged ; he sold the remainder for 18s. 9d. v- what did he gaintt a^ i 

72. 14 lbs. of tea at 3s. lOd. per lb., 16 lbs. at 4s. 2d^^ 




64 MISCELLANEOUS EXERCISES. 

lbs. at 4s. 6d., and 35 lbs. at 5s. 3d. are mixed together; 
what should it be sold for per lb. ? 

73. How many packages of coffee, containing respectively 
2 lb., 1 lb., I lb., and ^ lb., and of each an equal number, can 
be made from 16 cwt. 10 lbs.? 

74. A prize of £2982, 14s. 2d. is divided among a captain, 
2 lieutenants, 3 ensigns, and 120 soldiers; the captain is to 
have 5 shares, each lieutenant 4 shares, each ensign 2 shares, 
and each soldier one share : how much should each receive ? 

75. A father left to his eldest son 4500 guineas more than 
he left to his second son, to the second 12500 crowns more 
than to his third son, and to the third he left 9000 guineas ; 
find each son's portion. 

76. Divide £786, 13s. 6^. among 3 persons, giving the 
first £140, 16s. lOd. more than the second, and the second 
£90, 18s. lOd. more than the third. 

77. A merchant bought 145 gallons of whisky at iSs. 6d. 
a gallon ; how many gallons of water must he add to it, 
that he may gain £7, 12s. 6d., and reduce the price to 12s. 6d. 
per gallon ? 

78. £5, 19s. 2d. is to be divided among 3 classes of poor 
people, there are 8 in the first class, 9 in the second, and 10 
in the third; the share of the first class is to be 1^ time 
that of the second, and the second twice the tmra ; find the 
share of each class. 

79. The weekly wages of A and B are £3, 7s. 9d. ; of A 
and C £3, 12s. 3d. ; of B and C £3, 13s. : what are the daily 
wages of each ? 

80. Mercury revolves round the sun in 87 da. 23 ho. 15 
min. 44 sec. ; Venus in 224 da. 16 ho. 49min. 10 sec. ; Mars 
in 686 da. 23 ho. 30 min. 41 sec. ; Jupiter in 4332 da. 14 ho. 
2 min. 8 sec. ; and Saturn in 10,756 da. 5 ho. 16 min. 32 sec. : 
how many revolutions has each of these planets performed 
in 1858 solar years? 



DECIMAL COINAGE. 

In anticipation of a Decimal Coinage being introduced 
into this country, the system most likely to be adopted 
is shown in the following 



DECIMAL COINAGE. 



65 



TABLE OP DECIMAL MONET. 

1 mil (m.) = ^To'oTj = li^- 

10 mils == 1 cent (c.) = £t^o = 2|d. 

100 mils = 10 cents = 1 florin (fl.) = £t'o = 2s. 

1000 mils = 100 cents = 10 florins = £1 = 20s. 

6d. = 25m. = 2c. 5m. ; Is. = 50m. = 5c.; 2s. 6d. = 125m.= 

Ifl. 2c. 5m. ; 5s. = 250m. = 2fl. 5c. ; 1 Os. =500m. = 5fl., etc. 

The pound sterling, which is now divided into 960 parts, 
would thus be divided into 1000 parts, and calculations in 
money would be performed as in the Simple Rules, by placing 
a point after the pounds, and making the florins occupy the 
Jlrst place after the point, the cents the second, and the mils 
the third place ; thus : — 

£24, 2fl. 7c. 5m. would be written decimally, £24-275 



£36, 7c. 
£48, 6fl. 5m. 



1. £25, 

2. 57 
8. 90 
4. 76 



5fl. 

8 

3 

1 



Express decimally, 



6. £27, 

6. 30 

7. 17 

8. 



5fl. 3c. 
9 2 
4 
4 



9. 
10. 
11. 
12. 



£36-070 
£48-605 

£150, 5fl. 8c. 4m. 

490 2 5 

708 5 

910 4 2 



13. £20-450 

14. 36-050 



Read in £'s, florins, etc. 

15. £47-825 I 17. £99-005 | 19. £210-065 

16. 90-605 18. 100-725 20. 102-708 



ADDITION AND SUBTRACTION. 



1. £8, 2fl. 5c. 4- £7, 
£24-133 = £24, Ifl. 3c. 3 



5m. + £8, 3fl. 8m. 
Ans. £24-133 = £24, ifl. 3c. 3m. 



Ex. 2. £85, 3fl 


5m. — 


£58, 4fl 


3c 


. 6m. 


Ans. £26-869. 


Sol. Writ 
cimally unde 
proceed as in 
and in the n 


e the amounts de- 
r each other, then 
Simple Numbers, 
jsult place a point 


Ex. 

Sum 


1. £8-250 
7-575 
8-308 

, £24-133 


Ex 

Dii 


. 2. £85-305 

58-436 

af. £26-869 


below thft ot 




1. 
£ fl. c. 

5 4 3 

6 7 

8 6 

9 5 9 
10 7 1 
15 


m. 
2 
4 
5 

2 
9 


£ 

14 

18 

24 

30 

45 

53 


fl. 
5 
8 


2 
7 


2. 

c. 

9 
9 

4 
2 


m. 

6 

5 

7 

6 

9 

5 






£ 

75 
67 
50 
39 
30 
24 


3. 

fl. c. m. 
8 2 
9 5 

6 

7 6 6 
2 
5 8 



66 

£ 

150 
127 

217 
363 

460 

604 



DECIMAL COINAGE. 



£ 
234 
342 
423 

432 
243 
324 



£ 

100 
140 
104 
110 
101 
104 



6. 
fl. 

6 
2 

2 
2 





7. 






8. 






9. 






185 


4 2 


5 


197 


4 


6 


567 


8 


2 


3 


67 


5 


9 


179 


3 5 


7 


498 


9 


3 


5 




10. 






11. 






12. 






759 


6 3 


2 


842 


1 


6 


975 





2 





699 


7 6 


5 


483 


2 


6 


586 


6 


3 


5 



MULTIPLICATION AND DIVISION. 
Ex. 1. £75, 5fl. 5m. X 42. Ans.£3171-210 = £3171,2fl. Ic. 
Ex. 2. £185, 2c. 5m. — 25. Ans. £7*401 = £7, 4fl. Im. 



Ex. 1. £75-505 

42 

151010 
302020 
Product, £3171-210 



Ex.2, 



25 J 



f 5| £185-025 
(51 37-005 
Quotient, £7-401 



Sol. Multiply or divide the amount, expressed decimally, by 
the multiplier or divisor, and point off three figures from tiia 
right of the result. 

5. £145,5fl.2c.5m. X26,31 

6. £415, 2c. 4m. X 79, 85 

7. £154, 4fl. 8m. X 101,163 

8. £514, 3fl. 8c. 9m. X 695, 2045 

13. £359, 4fl. 5c. 5m. -H 29, 37 

14. 641 2 3 2 -^61,73 

15. 783 1 I 



1. £75, 3fi. 5c. X 25, 45 

2. £63, 7fl. 6c. 5m. X 16,63 

3. £97, 6c. 8m. X 77, 96 

4. £84, 7fl. 5m. X 63, 81 

9. £184, 2fl. 7c. 5m. -f- 25, 45 

10. 127 5 7 5 -^63,8l 

11. 129 7 4 5 -^35,55 

12. 126 5 8 8 -T-33,77 



8 -r- 122, 131 
16. 3083 8 8 5 -i- 365, 355 

17. How much will a man's wages amount to in a year, 
at £1, Ifl. 2c. 5m. per week ? 

18. Divide £68, 3fl. 5c. 5m. among 3 men, 5 women, and 
7 children, giving each woman twice the share of a child, 
and each man thrice the share of a woman. 

19. A man gains Ifl. 2c. 5m. in a day, and spends Ifl. per 
day ; how many days must he work to pay a debt of £9*375 ? 

THE END. 



EDINBUEGH : PRINTED BY OLIVER AND BOTD. 



ARITHMETIC 

f 

FOR 

ADVANCED CLASSES; 

BEING A CONTINUATION OF 

TROTTER'S LESSONS IN ARITHMETIC 
FOR JUNIOR CLASSES : 

CONTAINING 

VULGAR AND DECIMAL FRACTIONS; SIMPLE AND COMPOUND 
PROPORTION, WITH THEIR APPLICATION ; SIMPLE AND COM- 
POUND INTEREST, INVOLUTION AND EVOLUTION, ETC. 

By ALEXANDER TROTTER, 

TEACHER OP MATHEMATICS, ETC., IN EDINBURGH, 

Author of " A Key to Trotter's Complete System of Arithmetic," etc 



feta mtUn. 



EDINBURGH : 
OLIVER AND BOYD, TWEEDDALE COURT., 

LONDON : SIMPKIN, MARSHALL, AND CO. 
1872. 



SCHOOL-BOOKS BY JAMES TROTTER, 

LATE OF THE SCOTTISH NAVAL AXD MILITARY ACADEMY. 

LESSONS in ARITHMETIC for Junior Classes. 6d. 
A Complete System of ARITHMETIC, Theoretical and Practical. 3s. 
Teotteb's Edition of HUTTON'S BOOK-KEEPING. 2s. 
A Complete System of MENSURATION, by Ingram & Trotter. 2s. 
Ingram and Trotter's EUCLID ; containing the Elements of Plane 
Geometry and Trigonometry. Is. 6d. 

Ingram's Concise System of MATHEMATICS. Revised by Mr 
Trotter. 48. 6d. 

Trotter's LOGARITHMS and PRACTICAL MATHEMATICS. Ss, 

Ingram and Trotter's Elements of ALGEBRA. 38. 



EmNBURGH : OLIVER AND BOTD, 
TWERDDALK COURT. 



ADVERTISEMENT. 



This work is designed for those Pupils who have thoroughly 
mastered the Simple and Compound Kules ; and it has been 
tlie Author's aim to adopt as simple language as possible in 
the explanatory remarks. 

Each subject is accompanied by an example fully worked 
out and minutely explained, and has been treated as amply 
and carefully as its importance demanded. 

The Exercises, which are all new, are numerous and 
practical ; and Answers to them are published in a separate 
form. 



CONTENTS. 



Page 

Tables of Money, Weights, and Measures, 3 

Greatest Common Measure, 5 

Least Common Multiple, ib. 

Vulgar Fractions, 6 

Miscellaneous Exercises in Vulgar Fractions, 11 

Ratios and Proportion, 13 

Simple Proportion, ' 14 

Compound Proportion, 21 

Practice, 25 

Miscellaneous Exercises, 28 

Decimal Fractions, 30 

Interminate Decimals, c{4 

Miscellaneous Exercises on Decimals, 38 

Commercial Allowances, 39 

Commission and Brokerage, 40 

Simple Interest, 42 

Discount, 47 

Insurance, 49 

Stocks, 61 

Equation of Payments, 53 

Distributive Proportion, . 64 

Simple Fellowship, ib. 

Compound Fellowship, 66 

Profit and Loss, 57 

Exchange, 60 

Duodecimals, 62 

Involution, .63 

Evolution, 64 

Extraction of the Square Root, . •. . ib. 

Cube Root, . . V 66 

Compound Interest, ,...,.,,.. 68 

Miscellaneous Questions, 70 

Decimal Coinage, 73 



TABLES OF MONEY, WEIGHTS, AND MEASUEES. 



MONEY. 



qrs. 


d. 






4 


1 


8. 




48 


12 


1 


£ 


960 


240 


20 


1 



TROY WEIGHT. 



Grs. 


Dwt. 






24 


1 


Oz. 


1 


480 


20 


1 1 


1 Lb. 


5760 


240 


1 12 


1 1 



Gold, silver, and jewels are weighed 
by Troy Weight. 



APOTHECAR 


lES' 


WEIG] 


HT. 


Gr. 


Scr. 




20 


1 


Dr. 






60 


3 


1 


Oz. 


1 


480 


24 


8 


1 


1 Lb. 


5760 


288 


96 


12 


1 1 



Used only for medical prescriptions. 



AVOIRDUPOIS WEIGHT. 



Dr. 1 


Oz. 










161 


1 


Lb. 




2561 


16 


1 Qr. 




71681 


448 


28 


1 


Cwt. 




28672 1 


1792 


1121 


4 


1 


To. 


573440 1 


35840 22401 


80 


20 


1 



LINEAL MEASURE. 



7000 grs. = 1 lb. avoir. ; 14 lb. = 
1 stone. 

This table is used for all articles, 
except gold, silver, and jewels. 



In. 1 Ft. 




12 1 


Yd. 


36 3 


1 Pol. 


198 1 16^ 


5J1 1 Fur.I 


7920 660 


220 1 40 1 1 Ml. 


63360 5280 


1760 1 320 8 1 1 



4 inches = a hand ; 6 feet, or 2 
yds. = a fathom; 3 miles = a league. 



CLOTH MEASURE. 



In. 1 


NL 


1 




2i 1 


1 


Qr. 


1 


9 


4 


1 


1 Yd. 


36 1 


16 


4 


1 1 



3 qrs. = 1 Flemish ell : 5 qrs. = 
1 English ell ; 6 qrs. = 1 French ell; 
4 qrs. 1 inch, or 37 in. = 1 Scotch ell. 



SQUARE OR LAND MEASURE. 



Sq. in. 


Sq. ft. 








144 


1 Sq.yd.l 




1296 


9 


1 1 


Per.| 




39204 


272i 


30i| 


1 Ro 


1 


1568160 1 10890 | 


1210 1 


40 1 


jAc. 


6272640 


143560 1 


4840 1 160 1 4 


M 



36 sq. yds. = a rood of building, and 
100 square feet = a square of flooring. 

Land is measured by a chain 66 feet 
in length, divided into 100 links, eacli 
= 792 inches. 10,000 square links = 
1 square chain, and 100,000 sq. links, 
or 10 square chains, = 1 acre. 



I 



I 



1 I 



I 



4 TABLES OF MONEY, WEIGHTS, AND MEASURES. 

CUBIC OR SOLID MEASURE. ANGULAR MEASURE. 

1728 cubic inches = 1 cubic foot, 
and 27 cubic feet = 1 cubic yard ; 40 
cubic feet of rough, or 50 cubic feet of 
hewn timber, = a load ; 42 cubic feet 
= a ton of shipping ; 5 cubic feet = 
H barrel bulk. 



MEASURE OF CAPACITY. 



Pts. Qt. 1 


- 




2 


1 Gal. 




^ 8 


4 1 


Pk. 




16 


8 2 


1 


Ba. 1 


64 


32 8 


4 


1 1 Qr. 


512 1 256 1 64 


32 


8 1 1 



3600J 60 |_ l_|_Circ^ 
1296000 I 21600 j 360 | 1 





TIME. 




Min. 


Ho. 1 




60 


1 1 Da. 




1440 


24 1 1 


Co. Ye. 1 


525600 


8760 1 365 


1 1 



60 sees. = 1 min. ; 7 da. = 1 wk. ; 4 
wks. = 1 CO. mo. ; 52 wks. and 1 da. 
= 1 CO. ye.; 365J da. = 1 Julian ye.; 
366 da. = 1 leap ye. ; 365 da. 5 ho. 48 m. 
50 sec. = 1 solar or tropical year. 



FLOUR & BREAD WEIGHT. 
A peck-loaf = 17 lb. 6 oz. avoird. 
A half-peck do. = 8 11 — 

A quarter-loaf =4 5^ — 

A peck of flour is 14-44 lb., or 14J lb. 
nearly, and a bushel 57| lb. very 
nearly. Five bushels =: a sack, which 
ought to weigh 288-8 lb. avoirdupois. 



HAY AND STRAW WEIGHT. 
36 lb. avoir. = 1 truss of straw 
56 lb. = 1 truss of old hay 

60 lb. = 1 truss of new hay 

36 trusses = 1 load 

Hay sold between the beginning of 
June and the end of August, of that 
year's growth, is reckoned new. 



QUARTERLY TERMS. 



In England. 
Lady-day, . March 25. 

Midsummer, . June 24. 
Michaelmas, . September 29. 
Christmas, . December 25. 



In Scotland. 
Candlemas, . February 2. 
Whitsunday, . May 15. 
Lammas, . August 1. 

Martinmas, . November 11, 



MISCELLANEOUS TABLE. 



24 sheets 
20 quires 
10 reams 
12 articles 
20 articles 
12 dozen 
12 gross 
120 articles 
500 bricks 
1000 tiles 



: 1 quire of paper 

: 1 ream 

: 1 bale 

: 1 dozen 

: 1 score 

; 1 gross 

: 1 great gross 

1 great hundred 

1 load 

1 load 



500 herrings : 
500 red do. : 
1000 sprats 

60 herrings ; 
100 lb. avoir. : 

56 lb. 

64 1b. 
256 lb. 
112 lb. 
19J cwt. 



: 1 barrel 

: 1 cade 

: 1 cade 

:lkeg 

: 1 barrel gunpowder 

: 1 firkin of butter 

: 1 firkin of soap 

= 1 barrel of soap 

= 1 barrel of raisins 

= 1 fodder of lead 



AKITHMETIC 



THE GREATEST COMMON MEASURE. 

The greatest common measure or divisor of two or more 
numbers is the greatest number which divides them 
without any remainder. 

Ex. Find the G. C. M. of 201 and 469. Ans. 67. 

Solution. Divide the greater number 201) 469 ( 2 
(469) by the less (201), and the last divi- 402 

sor (201) by the remainder (67) continu- ~67) 201 ( 3 

ally imtil there is no remainder; the last 201 

divisor (67) is the greatest common meas- 

ure of the two numbers. 

The G. C. M. of three numbers is obtained by finding that 
of two of them, and afterwards that of the result and the 
third number. 

Find the G. C. M. of, 



1. 126 & 777 

2. 584, 803 

3. 2449, 2573 



5727 & 7802 
5824, 13376 
1557, 2249 



7. 16531, 31659 
a 3247, 4393 
9. 42039, 23701 



THE LEAST COMMON MULTIPLE. 

The least common multiple of several numbers is the 
least number which contains each of them an exact num- 
ber of times. 

Ex. Find the least common multiple of 4, 6, 10, 18, 
and 30. 

Sol. Arrange the numbers after each 
other in one line ; divide by 2 as often 
as any of the numbers will divide by 
2, then by 3 in the same way, again 
by 5, and so on by all the prime num- 
bers ; the continued product of all the 

divisors (2X2X3X3X5) is the least common multiple of 
the numbers. 

Find the L. C. M. of, 

1. 7, 12, 14, 15, 24 I 6. 27, 32, 36, 72, 108, 144 

2. 8, 16, 20, 24, 36 | 6. 12, 15, 32, 60, 64, 120 

3. 4, 10, 14, 21, 28 I 7. 8, 11, 104, 52, 88, 143 

4. 8, 16, 14, 10, 35 ' 8. 11, 26, 34, 52, 68, 187 









Ans. 180. 


2 


4, 


6, 


10, 18, 30 


2 


2, 


3, 


5, 9, 15 


3 


1, 


3, 


5, 9, 15 


3 


1, 


1, 


5, 3, 5 


5 


1, 


1, 


5, 1, o 




1, 


1, 


1, 1, 1 



6 

VULGAR FRACTIONS. 
A FRACTION consists of one or more parts of unity, and is 
expressed by two numbers, the one placed above the other 
with a line between them ; thus, ^- ^^^^^'^'^l' 

' ' 9 Denommator. 

The lower number is called the denominator, and shows 
into how many equal parts the unit is divided ; the upper 
number is called the numerator, and shows how many of 
those equal parts have been taken to make up the fraction 
— the two together are called tlie terms of the fraction. 

A fraction also indicates an unperformed division ; thufc 
~ signifies 14 divided by 9. 

A proper fraction is one whose numerator is less than 
its denominator, as |, |, -j^. 

An improper fraction is one whose numerator is equal 
to or greater than its denominator, as ^, |, Y. 

A mixed number consists of a whole number (or inte- 
ger) and a fraction, as 3y\, 39^. 

A compound fraction is a fraction of a fraction, as 
f off, i of If of J. 

A complex fraction is one which has a fraction for its 

numerator or denominator, or both, as 3, =1 =• 

^ r 9 4^ 

An integer has one for its denominator, as 12 = K*. 

A fraction is multiplied by multiplying its numerator or 
by dividing its denominator, and is divided by dividing its 
numerator or multiplying its denominator. 

The value of a fraction is not altered by multiplying or 
dividing its terms by the same number. 



REDUCTION OF VULGAR FRACTIONS. 

Case I. To reduce a fraction to its lowest terms. 

Ex. Reduce |^| to its lowest terms. Ans. -Jf. 

Sol. 1. Divide the terms of the fraction I 144^ __ 48-^4 _ 12 
(144 and ]56) by those numbers which I 156-^3 62^4 13 
measure them exactly (3 and 4), until no number can bo 
found that does so, the fraction is then reduced to its lowest 
terms (||). 

Sol. 2. Find the G. C. M. (12) of the terms of the frac- 
tion, and divide them by it for the lowest terms {\ |) of the 
„ , 111 • 12 12 
fraction. ^^ '. .^ = 75 as before. 



VULGAR FRACTIONS. 

Reduce to their lowest terms, 



Case II. To reduce a mixed number to an improper 
fraction. 

Ex. Reduce 5y\ to an improper fraction. Ans. -f j. 

Sol. Multiply the integer (5) by I 5 e =5X11+6 __.55-H_ 61 
the denominator (1 1), and to the I ' ' n n u 

product (55) add the numerator (6), then under the sum (61) 
place the denominator (11) for the fraction (f {). 

Reduce to improper fractions, 
4f; 6f ; 9^; 12^?; 15^^; 17^^; 25^^; 33ii; 45^V; 
57A; 113/^; 237^VV; 69^^^; 147 VA; 178^Vt; 273V^Vt. 

Case III. To reduce an improper fraction to a whole 
»r mixed number. 

Ex. Reduce 4V *o ^ mixed number. Ans. 13y\. 

Sol. Divide the numerator (157) I ,5, .^„ . .« .« , 

bythedenominator (12),andtothe I ^5 — 10/ — 1^ — 10^2 
quotient (13) annex the remainder (1) with the denomina- 
tor below it (j'5) for the fraction (13 j',). 

Reduce to whole or mixed numbers. 



Case IV. To reduce a compound fraction to a 
simple one. 
Ex. Reduce J of 1 J of $ to a simple fraction. Ans. |. 

Sol. 1. Multiply all the I , ^f 1^ of * — «of « of ^— «- —^ 
numerators together and I ^ ^^ ^^^^ 5 — 4 ot gOi g — ^^g—^ 
all the denominators together, and reduce the resulting frac- 
tion (yVs) to its lowest terms (|). 

Sol. 2. Strike out all those factors which j 5 4 5 
are common to the numerators and deno- J ^^ ^ ^^ o ^^ 9 
minators, and proceed with the numbers I ^ ^ " 
that are left, as in Sol. 1, for the fraction in its lowest terms. 

Note. Mixed numbers must be reduced to improper fractiona 
before multiplying. 

a2 



8 VULGAR FRACTIONS. 

Reduce to simple fractions, 
5 of 4 of A; T\of|f ofj; f of I of 15; A of 3^^ of 
lof^V; Aof7f ofl3i; ^Vofl2iof3i; vVof5|ofl3i; 
^\ of 12^ of A ; if of 6| of 3/^ ; 4 of 8 J of 5. 

Case V. To reduce fractions having different deno- 
minators to others of equal value having the least com- 
mon denominator. 

Ex. Reduce f of ^, f, i, 1^ to their least common 
denominator. 

Sol I ^of« - - 1«-^ 3 4 ,,_1><126,3X63 4X28 12X36 
■o J 1^^^-" 4 10' -^7—5^4^ 5' 7 —2X126' 4X63' 9X28 7X36 

Keduce the compound to simple 
and the mixed numbers to impro- 
per fractions ; find the L. C. M. 
(252) of the denominators for the required one, and divide it 
by each of the denominators ; then multiply the quotients 
^126, 63, 28, and 36) by the respective numerators (1, 3, 4, 12) 
for the required numerators. 

The fractions must all be in their lowest terms before pro- 
ceeding as directed. 

Reduce to their least common denominator, 

*T5 TT ^^ 2TJ "^T) TIT 

01 7f5? T2? TT> S 01 -ff-j 

8 4 17 19 111 

aT> T3'? 77? 7F' T^"S" 

13 16 6 7 '7 

•j-g-j ^U) -s^ty? TT? T's^i" 



126 189 112 432 
252' 252' 252' 252 



*■' Si ?' -g^' T3' TTT 

94 2rwf3 11 13 

^* TT' TT 01 T¥? 2T? 7 ^^ ^B" 
4 13 17/^f6 3 19 nf 69 17 



! 10. 



Case VI. To reauce tractions irom one denomination 
to another without altering their value. 

Ex. 1. Reduce £f to the fraction of a penny, i. e. from 
a higher to a lower name. Ans. ^-^d. 

Sol. Multiply the numera- I ^5_ 5x240 ^ =— d =— d 
forby the number of the lower I 9 9 * 9 ' 3 * 

name contained in the higher (240), and reduce the fraction 
to its lowest terms. 

Ex. 2. Reduce ^ lb. to the fraction of a cwt., i, e. from 
a lower to a higher name. Ans. -^^-^ cwt. 

Sol. Multiply the denomi- I iii f _^j. _Lpwf 

nator by the number of the I 9 ^l^- — 9xii2^'^^-— 252^^^' 
lower name contained in the higher (112.) 



VULGAR FRACTIONS. 9 

Ex. 3. Reduce £ J to the fraction of a guinea. Ans. f gu. 

., -3 3X20 3X20 5 

feOL. £4 = 5 S. = ^^ gu. = ^ gu. 

1. Red. I qr., fd., y\s., |cr., & 14s. 7|d. to fractions of a pound 

2. >f £/y, |d., ^|s., fgu., &/i of3s.3d. // n a farthing 

3. ff I lb., /y to., j\ oz., y-V (l^M & 1 cwt. 21 lb. »/ 3 cwt. 

4. n ? ml., I fu., j\ yd., I ft., & 4 ft. 7 ^ in. >- >^ sl pole 

5. ff £|, for., 13s. 4d., ^of 7s,6d.,& fofSh.cr. " aguinea 

6. If y*g Co, ye., { I mi., f sec, & 5 h. 48 m. 50 s. >• a day 

7. ». fE.E.,i?FrE.,|Fl.E.,fSc.E.,&3(ir.3nl.'/ a yard 

Case VIL To find the value of a fraction in units of 
lower names. 

Ex. 1. Findthevalueof f ml. Ans. 4fu.17p.4yd.10in. 

Here, 5 ml. fu. po. &c. -^ 9 = 4 fu. 17 po. 4 yd. 10 in. 

Sol. Divide the numerator, as so many of the given 
name, by the denomuiator, as in Compound Division. 

Ex. 2. Find the value of f of 7s. 6d, Ans. 5s. 

Sol. 7s. 6d. X 2 = 15s. and 15s. -h 3 = 5s. 

Find the values of, 
1- ^tV fs., |d., A cr., ^%gii., and | of 16s. 8d. 

2. ^^ cwt., if qr., f lb., I ml., i^ yd., f of 2 ml. 50 yds. 

3. *E.E., .{-^Fl.E., fac, fro., Js.per., -}f of 4ac. 3ro. 

4. Txto.jAac, T-«y0f3qr. 3b., |ml., /-j- lb.tr., ^-^of 18s.9id. 

5. » of 5s.6id., I of t\ of 3f gu., if co. ye., -,\ Jul. ye. 

6. Joff ofS^cr., jf of|iofl8jbu., fofaS.ye,, f of2i|of4j-'' 



ADDITION OF VULGAR FRACTIONS. 

Ex.1. 5 + |of4|+A=| + | + ,^ = ^iy^±^ 

Sol. Reduce the fractions to their least common deno- 
minator by Case V., then add the numerators, and below the 
sum (509) place the denominator (315). 

Ex. 2. £| + /;^s. + *d. = 7s. 6d. + 2id. + Jd. J 

= 7s.8fd.|. 

Sol. Find the values of the fractions by Case VII., and 
add as in Compound Addition. 



10 

3.3i 



VULGAR FRACTIONS. 



9 T^ T^ 
_L 6 I T 

T6 T^ T2 



5. 4i + 5 

6.7^ 



"6 

13. 



7 _i_ 6 

T-^ nr -^^ 
8-3f + 74 + 6f + 9f 



10. 6^of/^+l|+^3^ofl 

11. l«ofi|+fof/^+lU 

12. 2^of4| + ^\of|+|of| 

13. £f + |s. + |d. 

15. 
16. 
17. 

18. 



^ cwt. + f qr. + 41 lb. 
^\ton+^\cwt.+ T%lb. 
T^oac+TT^o. + Sfper. 



19. £f + * gu. + f cr. + 1 of 8s. lOid. 

20. ^3^ qr. + f bu. + -j^ pk. + ^^ of 9 qr. 4 bu. 
21- tV ye. + ^\ da. + ^V ho. + ^^V of 85 da. 1 ho. 



SUBTRACTION OF VULGAR FRACTIONS. 

Ex. 1. I of 2 - - = |-i| = ^«A = ^7^ 

Sol. Prepare the fractions as in Addition, and subtract the 
numerators. 

■t 3 1 



^' T TT 

3. 14f— 6i 



6. 6- 

6.15- 



T 

-7A 



8.42 — 2441 



13. 8f oflf-^AoflyV 

14. 4-,VofH — 2iof I 



9. 10^-2^ 

10. f of4^— lofJI 

11. ^«^ofH-T\of|| 

12. 7iof4f-6iofA 
15. 134of H — ^ofl^ 



55 



Sol. Find the values of the fractions by Case VII., and 
subtract them as in Compound Subtraction. 



17. 
18. 
19. 
20. 



-4qr. 



Tfgu- 

TuCWt, 

^\ lb. — I oz. tr. 



21. A ml. — 17^\ po. 
^E. E. 



i§Fr.E.-^Vyd. 
.j^ ac. — t of 2 ro. 



25. TVofigye. — 4of^iye. 



MULTIPLICATION OF VULGAR FRACTIONS. 

Ex. T\XilfX4i = H?^g = |; orvVXi|fX4^ 
= |X|Xi = f. 

Sol. 1. Multiply all the numerators (4 X 165x41) to- 
gether for the numerator (27060), and all the denominators 



VULGAR FRACTIONS. 



11 



(11 X 164 X 25) together for the denominator (45100) ; then 
reduce the fraction (||i|§) to its lowest terms (|). 

Sol. 2. Strike out all the factors that are common to the 
numerators and denominators, and proceed with those num- 
bers that are left as in Sol. 1. 

7. 54 X I of 6| 

8. 98 X I of ^\ 

9-TVof^\X T\of6| 
10. 8^of 14f X 7§of6vV 
ii-(12i + 6|)X(4i-2f) 
12. (21 3_14^V)X (6^3^+71) 

} ll^d., Is. 9|d., & 2s. 6|d. p. yd. 
14. // 174ilb.&212^Vlb.@10id.,ls.7TVd.,&3s.4id.p.lb. 



1. 


f 


X 


f 


X 


1 




2, 


t\ 


X 


1 


X 


f 




3. 


4- 


X 


6 

"8 


X 


7 

1X5 




4. 


H 


X 


A 


X 


4 




5. 


27 


X 


2 


of 


6 




6. 


37 X 


tS 


of 


3 3 
T6 




L3. 


Val 


H 


yd 


.&16f 


yd 



DIVISION OF VULGAK FRACTIONS. 

T?Y -♦ nf 5 -1- 1 3 1 O _L. 1 3 1 O V 1 4 2 O 

shx. T or ^ -r- x:f — ¥t ^^ t^? — 21 X tt — -g-^- 
SoL. Invert the divisor (if), and proceed as in Multiplication. 



of 4 



T6 . 

25-^ 
37-^ 



off 
of^l 



7. 42 -^- 

8.56^ Vofil 

9. ■ '^ " 
10. 



nf 2 7 



of if 

63 

s of '— 

7 01 23- 



2T\of|4 



ii-(6f + 7i)^(7i-2|) 
I2.(8t-4i)-f-(4j + 2|) 

l6|,21f,24A,26xV,&32H 
14. G72cwt. 3qr. 14|lb.-Mlf , 12|, 15|, 18/^, 23/,, & 27^^ 



13. £375, 6s. lOJ^d. ■ 



14#, 



MISCELLANEOUS EXERCISES IN VULGAK FRACTIONS. 

1. Find the sum, difference, product, and quotient of 
^\of6f andf of|f 

2. A can do a piece of work in 8 days which B can 
do in 9 days ; what part will they do together in 1 day ? 

3. What number added to 4 of 5^ gives 14|? 

4. What part of 3f is | of f ? 

5. What number is that ^ of which is equal to 30 ? 

6. A and B can do a piece of work in 8 days which 
A alone can do in 12 days ; what part of it can each do 
alone in one day ? 



12 VULGAR FRACTIONS. 

7. A gentleman having ^ of a ship, worth £3115, pur- 
chases another person's share which is ^ of f of it ; what 
part has he now, and what is its value ? 

8. Wliat number divided by ^\ of 7^ gives 240 ? 

9. How many chests of tea, each containing 124f lbs., 
can be filled from 73 cwt. 2 qrs. 1^ lb. ? 

10. What number is that j*-,- of which is equal to 25 ? 

11. What part of 5 guineas is f of £3 ? 

12. A farmer went to market with £2| ; he received 
there £73^\, £89^\, and £49/^: with what sum did he 
return ? 

13. What number multiplied by J of 7| gives | of 15f ? 

14. Divide £4125 among 4 men, 6 women, and 12 chil- 
dren, giving each woman | of a man's share, and each 
child -f of a woman's share. 

15. Two persons, by trading, gained a certain sum, the 
first lodged f of the capital, and received £200 as his 
share of the gain ; what was the whole gain, and the 
second's share ? 

16. What numl 
taken there remains 35 ? 

17. Two places are 72 miles distant from each other : 
A starts from the one at the rate of 12f mis. an hour, 
and at the same time B starts from the other, to meet 
A, at the rate of 18j miles in 2 hours ; when and where 
will they meet ? 

18. A gentleman's income is j\ of || of £7560, and he 
spends | of f of it ; how much does he lay up ? 

19. A person spends ^ of his money + £2, and has 
left :^ of it -f- £3 ; what sum had he at first ? 

20. What number is that from which ^ of it being 
taken there remains 40 ? ' 

21. I of the trees in an orchard are pear trees, Jf are 
apple trees, and there are 50 cherry trees ; what is the 
number of trees ? 

22. A man's present age is 65 years, 5 years since his 
son's age was f of his ; what is the son's present age ? 

23. A cistern can be filled by two pipes in 24 and 25 
minutes respectively, and can be emptied by a third in 
32 min. ; what part of it will be filled in 12 min., the 
three pipes being all open ? 



VULGAR FRACTIONS. 13 

24. A person has f of a ship worth £4200, and he sells 
^ of his share ; what part has he left, and what is its 
value ? 

25. A and B can do a piece of work in 6 days, A and 
C the same in 8 days, and B and C in 12 days ; what 
part could the three together perform in 5 days ? 

26. A ship and its cargo are together worth £23750, 
and the cargo is 5^ times more valuable than the ship ; 
find the value of each. 

27. Simplify (14I + 6VV — 2^V) X ^f-S^V 

28. A father left ^% of his estate to one son, and the 
remainder to another ; the difference of their fortunes 
was £750 : what was the estate worth ? 

29. Divide £2000 among A, B, and C, giving A | of 
the whole, B | of A's share, and C the rest ; find also 
what fraction of the whole C receives. 

30. What number multiplied by } of J, and the pro- 
duct divided by ^-^j^ of 5i, will give for the quotient -j't 
of 64 of 4? 



RATIOS AND PROPORTION. 

In comparing two numbers of the same kind, their ratio 
or relation to one another is found by dividing the first ' 
by the second ; thus, the ratio of 4 to 2, generally writ- 
ten 4 : 2, is 4-^2 = 2; of 3 mis. to 6 mis. is 3-^-6 = 1. 

The first number is called the antecedent, and the 
second the consequent ; the two together are called the 
terms of the ratio. 

Proportion consists in the equality of ratios; thus, 
since 4:2 = 8:4, the numbers 4, 2, 8, and 4, consti- 
tute a proportion : they are generally written 4 : 2 : : 8 : 4, 
and are read as 4 is to 2 so is 8 to 4. 

In every proportion the product of the 1st and 4th 
terms (or of the extremes as they are called) is equal to 
the product of the 2d and 3d terms (or of the means) ; 
thus in the proportion 4 : 2 : : 8 : 4 we have 4 X 4=2 X 8. 
Hence the first three terms of a proportion being given, 
the 4th is found by dividing the product of the 2d and 
3d terms by the 1st. 




£144 



14 



SIMPLE PROPORTION or the RULE of THREE. 

When three terms of a proportion are given, the object 
of this rule is to find its 4th or last term. 

Of the three given numbers, two are always of the 
same kind, and the remaining one is of the same kind as 
that which is required. 

Ex. 1. If 16 men earn £32 in a week; what sum will 
72 men earn in the same time ? Ans. £144. 

Sol. 1. Place that term which is of Men 16 : 72 : : £32 
the same kind as the answer is to be, 
for the third or right-hand term (£32). 

2. Consider from the nature of the 
question whether the answer is to be 
greater or less than the term written down : if greater (as 
in this Ex.), place the greater of the two remaining terms 
(72) in the middle, and the other on the left (16) ; but if less, 
place the less of the two like terms in the middle, and the 
other upon the left. 

3. When none of the terms is compound (as in this Ex.), 
multiply the 2d and 3d terms together (72 X 32), and divide 
the product (2304) by the 1st or left hand- term (16) for the 
answer, in the same name as the 3d or right-hand term (£'s). 

1. If 25 yds. of velvet cost £30; what should 760 yds. 
of the same cost ? 

2. If 14 cwt. of sugar cost £42 ; what should be paid 
for 207 cwt. ? 

3. A train runs at the rate of 73 mis. in 3 hours; in 
how many hours will it run 438 mis. ? 

4. A person spends £500 yearly ; how much will he 
spend in 146 days ? 

5. If 7 men do a piece of work in 36 days ; in how 
many days will 9 men do the same ? 

6. What cost 162 copies of a book, when 171 copies 
cost £19? 

Ex. 2. If 6 cwt. 3 qrs. of tea cost £170, 2s. ; what 
should 27 cwt. 3 qrs. of the same cost ? Ans. £699, 6s. 

Sol. State the question as before. Reduce the 3d term to 
the lowest name in it (shil.), and the 1st and 2d terms to the 
lowest name in either (qrs.) ; then multiply the 2d and 3d 



SIMPLE PROPORTION. 15 

6 cwt. 3 qr. : 27 cwt. 3 qr. : : £170, 2s. 
_4 _4 __20 

27qrs. Ill qrs. 3402s. 

3402 



27 )377622 
2,0 )1398,6 s. 
£699, 6s. 



terms togethef (111 
X 3402), and di- 
vide the product 
(377622) by the 1st 
term (27) for the 
answer, in that 
name to which the 
3d term was re- 
duced (shil.). 

7. What cost 4 yds. 3 qrs. 2nls. of cloth, when 15 yds. 
2 qrs. cost £8, 3s. 4|d. ? 

8. If 13 cwt. 14 lbs. of coffee cost £131, 13s. 9d. ; how 
much may be bought for £13, 3s. 4Jd. ? 

9. If a person walks 14 mis. 2fu. 28 po. in 4 ho. 6min. 
40 sec. ; how far will he walk in 9 ho. 3 min. 20 sec. ? 

10. How many yds. of linen at 3s. 6d. a-yd. should b( 
given for 136 yds. of muslin at 2s. 7^d. a-yd. ? 

11. If 4 yds. of cloth cost 84s. 4d. ; what will 27 yds. 
2 qrs. cost? 

12. Find the value of 2 qrs. 3 pks. of wheat, when 
36 qrs. 2 bu. 2 pks. cost £76, 5s. lid. 

Ex. 3. If 14 lbs. of tobacco cost 73s. 6d. ; what cost 
10 lbs. of the same ? Ans. £2, 12s. 6d. 

Obs. When the first and ^;4 lb. : ^0 lb. : : 73s. 6d. 
either of the other terms can i ^ - ^.^ . 

be divided without remain- j P ^ ^9^a. 

der by the same number, the j 126 

quotients may be used in 5 

place ofthe original numbers. | £2, 12s. 6d. = 630d. 

13. A courier travels 176 miles in 4 days; how far 
will he travel in 15 days? 

14. How much sugar may be bought for £95, at the 
rate of 28 lbs. for 14s. 3d. ? 

15. A man's wages are £37, 2s. 6d. a -year ; what 
should he receive for 219 days' service? 

16. If the 8d. loaf weigh 4 lbs. 5i oz. ; what should the 
shilling loaf weigh ? 

17. How many pairs of stockings, at 14s. 6d. per doz, 
pairs, may be bought for £30, 19s. 10 Jd. ? 

18. Find the value of 1 cwt. of sugar, when 3 cwt. 
14 lbs. cost £10, 18s. 9d. 

b2 



16 SIMPLE PROPORTION. 

19. What cost 5 pieces of silver, each 3 lbs. 4 cz. 
12 dwt., at 5s. 9d. per oz. ? 

20. If the quartern loaf costs lOjd. when wheat is at 
£3, 10s. per qr. ; what should it cost when wheat is at 
£2, 3s. 4d. per qr. ? 

21. A bankrupt's effects an;iount to £3528, and he 
compounds with his creditors for 12s. 3d. per £1 ; what 
is the amount of his debts ? 

22. If 16 men consume £10 worth of beef when the 
price is 7-^d. per lb. ; what value of beef will they 
consume in the same time when the price is lO^d. 
per lb. ?* 

23. Sound moves at the rate of 1142 ft. in a second, 
and the report of a gun is heard 14| sec. after seeing the 
flash ; how far distant is the gun ? 

24. How many paces of a man, each 2i ft., are equal 
to 150 steps of a horse, each 2f ft. ? 

25. A bankrupt's debts amount to £7428, and he com- 
pounds with his creditors for 10s. 9|d. per £1 ; find the 
amount of his effects. 

26. Find the value of 8 cheeses, each 26 J lbs., at T^d. 
per lb. 

27. At what time between 6 and 7 o'clock are the 
hour and minute hands of a watch exactly together? 
Sol. (11 : 12 : : 6 hours.) 

28. Bought 17 yds. 2 qrs. of cloth for £16, 2s. 3id. ; 
what should 4 yds. 3 qrs. be sold for to gain £2, 5s. 2|d. 
on the whole ? 

29. If 36 gallons of whisky, worth 17s. 6d. a-gallon, be 
mixed with 4 gallons of water ; what should be the price 
of a gallon of the mixture ? 

30. A person pays £65, 6d. for income-tax, at the rate 
of Is. 4d. per £1 ; what is his income? 

31. Required the circumference of a circle whose di- 
ameter is 22035 mis., the ratio of the diameter to 
the circumference of a circle being as 113 is to 355. 
Sol. (113 : 355 : : 22035 mis.) 

32. A pound troy of standard gold is coined into £46, 
14s. 6d. ; find the weight of a sovereign. 

* When the same term is twice mentioned in a question, that 
term must he altogether excluded. 



SIMPLE PROPORTION. 17 

33. The ratio of standard to pure gold being 22 to 24; 
what is the value of an ounce of pure gold ? 

34. A garrison of 3300 men have provisions for 12 
months; how long would the same provisions serve 
4950 men ? 

35. A 16 gun-battery discharges 1760 cwt. of shot in a 
certain time ; how much will an 18 gun-battery discharge 
in the same time ? 

36. The chain of QQ ft. for measuring land is divided 
into 100 links ; what is the length of a wall measuring 
1760 links? 

37. What is the commission on £477, 2s. 6d., at £27^ 
per £100? 

38. A pound troy of standard silver is coined into 66s. ; 
find the weight of half-a- crown, and of a florin. 

39. The ratio of standard to pure silver is 37 to 40 ; 
what is the value of a lb. of pure silver? 

40. From a garrison of 2000 men with provisions for 
9 months, 500 are sent out ; how long will the provi- 
sions serve the remaining men ? 

41. If 250 men dig a trench in 5 da. 5 ho., working 12 
hours a-day ; in how many days would they do tlie same, 
working 1 1 hours a-day ? 

42. If 49 men do a piece of work in 3f days ; in how 
many days will 48 men do the same ? 

43. A garrison being besieged, has 49 days' provi- 
sions, at the rate of 15 oz. a-day for each man ; how 
long will they be able to hold out if each receives lOJ oz. 
a-day ? 

44. Required the charge for 12125 cubic feet of gas- 
at 5s. lOd. per 1000 cubic feet. 

45. The rent of a farm of 350 ac. 3 ro. 20 per. is £1710, 
10s. 3|d. ; what should be the rent of another of equal 
quality, containing 525 ac. 1 ro. 20 per. ? 

46. If £14, 8s. be the interest on £360 for a year ; wliat 
sum will gain £33, 12s. in the same time and at the 
same rate per cent. ? 

47. A garrison of 2500 men, with provisions for 7 
months at the rate of 21 oz. a-day for each, is reinforced 
by 1000 men ; how many ounces a-day must each be 
allowed that the provisions may last that time ? and if 

c 



18 SIMPLE PROPORTION. 

each receives the full allowance, hov/ long will the pro- 
visions serve? 

48. Find the value of 5 bars of steel, each weighing 
4 cwt. 3 qrs. 14 lbs., at £12, 14s. 4d. for 10 cwt. 3 qrs. 
21 lbs. 

49. In what time would 6 battalions of foot, each 375 ft. 
in length, march through a town If mile long, at the 
rate of 75 paces of 2| ft. per minute? 

50. A piece of work can be done by 45 men in 13 days ; 
now at the end of 6 days, 10 men leave : in how many 
days will the remaining men finish the work ? 

51. What is the price of 6f Fr. ells, at £66, lis. for 
72|Eng. ells? 

52. What is the price of 7 pieces of cloth, each 16§ 
yds., at £3, 4s. 9d. for 3|- Scotch ells? 

53. A bankrupt's debts amount to £4020, and his assets 
to £3266, 5s. ; how much will this afford his creditors 
per £, and how much will A lose, whose claim is 
£560, 13s. ? 

54. A gentleman's income is £3867, 15s. per annum; 
his expenses amount to £1050, and he wishes to save 
£500 : how much may he spend between Whitsunday 
and Martinmas ? 

55. How many yards at 4s. l^d. are equal in value to 
1231 yards at 12s. 7id. per yd. ? 

56. If 4 to. 5 cwt. 14 lbs. of lead cost £50, 17s. 6d. ; what 
should be given for 20 to. 11 cwt. 49 lbs. of the same ? 

57. A cubic foot of chalk weighs 2784 oz., and a cubic 
foot of basalt 2860 oz. ; how many cubic feet of the 
former are equal in weight to 7830 cubic feet of the 
latter? 

58. A column of chalk weighs 20 cwt. 2 qrs. 24 lbs. ; re- 
quired the weight of a column of basalt of the same 
dimensions. 

59. How much wheat can be bought for £101, 5s. when 
7 qr. 4 bu. 3 pks. cost £20, 10s. 0|d. ? 

60. What should be paid for 102 qrs. 3 bu. 2 pks. of 
oats, at the rate of £5, 4s. ll^d. for 4 qrs. 2 bu. 2 pks. ? 

61. How much water must be mixed with 250 gallons 
of "whisky, at 14s. 6d. per gal. to reduce the price tc 
12s. 6d. per gal.? 



SIMPLE PROPORTION. 19 

62. How much water must be mixed with whisky at 
15s. a-gal. to fill a cask of 360 gals., so that a gallon of 
the mixture may be worth 13s. 4d. ? 

63. If the rent of 4J acres be £7, 13s. ; wliat will be the 
rent of 5^ acres ? 

64. An express train runs 58 mis. in 1 h. 30 m. with 
two stoppages of 3 minutes each ; in what time will it 
run 435 miles with 5 stoppages of 4 minutes each ? 

65. What quantity of linen at 2s. 6d. a-yard should be 
exchanged for 5 dozen pairs of shoes at lis. a-pair? 

66. A and B barter, A has oats at 24s. per qr., which 
he rates at 27s. 6d. to B for sugar at 75s. per cwt. ; at 
Avhat should B rate his sugar to be even with A, and 
how many cwts. should he give for 175 qrs. of oats? 

67. If 78 qrs. 5 bu. of barley be given for 53 qrs. 1 bu. 
of wheat at 64s. 9d. per qr. ; what is the barley valued 
at per qr. ? 

68. A grocer mixes 56 lbs. of tea at 4s. per lb. with 
44 lbs. at 5s. ; how should he sell 11 lbs. of the mixture 
to gain £5, Is. lOd. on the whole? 

69. At what time after 2 o'clock are the hour and min- 
ute hands of a watch exactly together ? 

70. Find the diameter of the earth, whose circumfer- 
ence is 24850 miles nearly. 

71. B gives to C 12 gallons of brandy at 37s. 6d. per 
gal. and £14, 12s. 6d., and receives from him tea at 4s. 
6d. per lb. and 7 cwt. 2 qrs. of sugar at £3, 5s. per cwt. ; 
what quantity of tea did B receive ? 

72. Find the weight of 600000 sovereigns, 1869 sove- 
reigns weighing 40 lbs. troy. 

73. Lent a friend £455 for 6 months ; how long should 
he lend me £630 to return the favour ? 

74. If f cwt. cost £5i ; what should | cwt. cost ? 

75. If ^\ of a ship be worth £420 ; what should | of it 
cost? 

76. What velocity will a falling body have at the end 
of 7i sec, if it acquires a velocity of*168|- ft. in 5i 
sec? 

77. A hare starts 140 yards before a greyhound, but 
while the hare runs 5 yds. the dog runs 7 ; how far 
must the do^r run to catch the hare ? 



20 SIMPLE PROPORTION. 

78. If -/y of an estate be worth £500 ; what is the vaUie 
of f of it? 

79. If 30 horses be maintained for 5 montlis on a cer- 
tain value of oats when the price is 22s. 6d. per qr. ; 
how many horses may be fed for the same sum and time 
when oats are at 25s. per qr. ? 

80. A person, after paying income-tax at Is. 4d. per £, 
has remaining £665 ; required his income. 

81. How long would a cannon-ball with a velocity of 
2000 ft. per second take in passing from the earth to 
the moon, a distance of 237630 miles ? 

82. The distance of Jupiter from the sun is 494513000 
mis. ; what is the length of its orbit, supposing it circular ? 

83. The same planet performs its revolution round the 
sun in 4332-| days ; what is his mean motion in 365^: 
days? 

84. Jf a tower 150 ft. 4 in. high cast a shadow of 181 ft. 
1 in. : what length of a shadow wiU a pole 38 ft. 6 m. 
high cast at the same time ? 

85. How many revolutions will a coach-wheel 3^ ft. ii? 
diameter make in 4 miles ? 

86. The weight of an 18-pounder iron gun being 41 
cwt. 2 qrs., and the weight of a 12-pounder 33 cwt. 2 qrs. ; 
how many 12-pounders will be equal in weight to 469 
18-pounders? 

87. What should be paid for 15 cwt. 1 qr. 14J lbs. of 
lead, when 14 cwt. 3 qrs. 16 lbs. cost £17, 7s. 6d. ? 

88. A person whose annual income is £650, spends 
£15, 2s. 6d. a-week for the first 20 weeks ; what should 
his daily expenses be during the rest of the year, to save 

89. Bought 7 pieces of cloth, each containing 61 yds., 
for £424, 6s. 7^d. ; what should 241 yds. of the same be 
sold for to gain £5, 6s. 9d. on the whole? 

90. A can do a piece of work in 9 days which B can 
do in 12 days ; in how many days would they be able 
to finish the work, working together? 

91. A cistern has two spouts, by one of which it can 
be filled in 3 months, and tfy the other it can be emp- 
tied in 8 months ; in what tune will it be full, supposing 
it empty and both spouts running? 



SIMPLE PROPORTION. 21 

92. A can do a piece of work in 6 days, which B can 
do in 8 days ; after A has been working 2 days, B comes 
to help him ; in what time will they finish the work to- 
gether ? 

93. A starts from a certain place at the rate of 5 miles 
an hour ; after 2 hours, B starts from the same place at 
the rate of 6^ miles an hour ; when will B overtake A, 
and how far will each have travelled ? 

94. A grocer uses a weight of 15|oz. instead of the pound 
avoirdupois ; how much does he cheat his customers by 
selling 365 such pounds ? 

96. A cistern, containing 399 gallons, is emptied in a 
certain time by a pipe which discharges 4| gals, per 
minute, and another is emptied in the same time by a 
pipe which discharges 7-§- gals, per minute ; how many 
gallons does the last cistern contain? 

96. A wine merchant uses a measure containing 1224 
cub. in. instead of 131^ c. in. ; of how many gallons, each 
277 J c. in., does he defraud the public by selling 739 J 
such measures ? 

COMPOUND PROPORTION. 
When a question requires for its solution two or more 
statements of Simple Proportion, the method of finding 
the answer by one operation is called Compound Pro- 
portion. 

Ex. •!. If 30 men eat £9 worth of bread in 12 days, 
when the price of the loaf is 8d. ; what value will 64 men 
eat in 10 days, when the loaf is at 6d. ? Ans. £12. 



Sol. 1. Place upon the right 
hand that term which is of the 
same kind as the answer is to be 
(£9). 

2. Take from the question two 
terms that are like one another 
(30 men and 64 men) and state 
til em, without any reference to the 



Men, 30 : 64 : : £9 
Days, 12 : 10 
Price, 8 : 6 



2880 : 3840 : : £9 
9 



2880 )34560 

£12 worth 
other similar terms, as in Simple Proportion ; in the same 
way, take other two similar terms (12 da. and 10 da.), and 
state them as in Simple Proportion below the last pair, and 
proceed thus till all the terms are stated. 



22 COMPOUND PROPORTION. 

3. Multiply all the left-hand terms together, and also the 
middle terms, then work out the resulting Proportion 
(2880 : 3840 : : £9) as in Simple Proportion for the an- 
swer (£12). 

When some of the terms are Compound, they must be re- 
duced as in Simple Proportion ; the work may be greatly 
abridged by cancelling. 

Ex. 2. If 14 persons spend £5, 5s. in 10 days ; how 
long will £42 serve 16 persons? Ans. 70 da. 



Sol. State the 
question as in Ex. 
1, and reduce £5, 
OS. and £42 to sh. 
Arrange the mid- 
dle and the right- 
hand terms, with 
the sign of Multi- 
plication between 



£ 5, OS. £42 

105s. : 840s. : : 10 da. 

Persons 16 : 14 

8 7 
$0XUX^O 1X7X10 



^0X10 



70 da. 



them above a line, and the left-hand terms below it ; then 
cancel the upper and under numbers as much as possible, as 
in fractions, and divide the product of the remaining numbers 
above the line by the product of those below for the answer. 

1. If 45 men cut down 120 acres of grass in 7 days ; 
how many acres will 84 men cut down in 10 days ? 

2. If 300 soldiers consume 4 barrels of flour in 10 
days; how many soldiers will 12 barrels serve for 15 
days? 

3. If 48 yds. of cloth, 4 quarters wide, cost £24, 12s. ; 
what should be paid for 36 yds. of the same, 6 quarters 
wide ? 

4. What is the interest on £383, 5s. for 325 days at 4^ 
per cent, per annum ? 

5. If 30 men consume £7 worth of bread in 10 days, 
when the price of the loaf is 8d. ; what value of bread 
will 40 men consume in 15 days, when the loaf is at 7id. ? 

6. If 30 men can do a piece of work in 12 days of 10 
hours each ; in how many days of 8 hours each will 45 
men do a piece of work 6 times as large ? 

7. If 63 cwt. be carried 42 mis. for £3, 10s., when tho 
rate of carriage is ^d. per mile per cwt. ; what distance 
should 142 cwt. be carried for £8, 17s. 6d., when the 
rate is Id. per mile per cwt. ? 



COMPOUND PROPORTION. 23 

8. At 2^ per cent, per annum £375 was lent, and it 
now amounts to £431, 5s. ; how long has it been lent ? 

9. The pound weight of standard gold is coined into £46, 
14s. 6d. (22 carats in 24 being pure gold) ; what is the 
value of 3 ounces of pure gold ? 

10. If 3 men or 5 boys do a piece of work in 8 days of 
10 hours each ; in how many days of 9 hours each 
would 4 men and 10 boys do a piece of work 3 times as 
large ? 

11. If 40 masons build a wall 56 yds. long in 10 days 
of lOj hours each ; how many hours a-day must 60 ma- 
sons work to build a wall 120 yds. long in 20 days? 

12. If 120 men can dig a trench 150 yds. long, 4 yds. 
wide, and 2 deep, in 7^ days of 10 hours each ; what 
length of a trench, 5 yds. wide and 3 deep, will 200 men 
dig in 15 days of 12 hours each? 

13. If 14 horses plough 112 acres in 40 days ; how 
many horses would plough 64 acres in 16 days ? 

14. If 30 men earn £80, 14s. in 15 days ; how many 
men will earn £107, 12s. in 12 days ? 

15. A traveller completes a journey of 240 miles in 3 
days of 12^ hours ; in how many days will he complete 
a journey of 360 miles, travelling 9 hours a-day? 

16. If the 8d. loaf weighs 3 lbs. 4 oz. when wheat is at 
64s. per qr. ; what should the shilling loaf weigh when 
wheat is at 72s. per qr. ? 

17. Required the avoirdupois weight of 600000000 
sovereigns, there being 1869 sovereigns in 40 lbs. troy, 
and 7000 grains in a pound avoirdupois. 

18. A certain value of bread is sufficient to serve 3200 
men for 44 days when the loaf is at 9d., allowing each 
man 16 oz. a-day ; how many men will 7 times the value 
serve for 112 days, at 20 ounces each per day, when the 
loaf is at lid.? 

19. If 135000 bricks, 8 in. long, 3^ in. broad, and 2f in. 
thick, be required to build the walls of a magazine ; how 
many bricks, 14 in. long, 4 in. broad^ and 3 in. thick, 
would be sufficient for the same ? 

20. If 7 compositors set up a volun^e of 12 sheets in 21 
days of 12 hours each ; how many would be required to 
set up 3 volumes of 10 sheets in 35 days of 9 hours each? 



21 COMPOUND PROPORTION. 

21. 35 masons build 48 yds. of a wall which is to be 
192 yds. long in 12 days of 12 hours each ; how many 
additional masons will be required to finish the wall in 
18 days of 10 hours each? 

22. If 15 men build a wall, 80 ft. long, 3§ ft. thick, and 
9 ft. high, in 27 days of 10 hours each ; in how many 
days of 12 hours each will 25 men build a wall 100 ft. 
long, 2 J ft. thick, and 8 ft. high? 

23. A garrison of 4050 men, with provisions for 5 
months at the rate of 32 oz. a-day for each, is reinforced 
by 750 men, and cannot be relieved for 8 months ; how 
many oz. a-day must each man be allowed that the pro- 
visions may last that time ? 

24. The cost of papering a room with paper 3 qrs. wide, 
at 3f d. a-yard, is £2, 3s. 9d. ; what would be the cost if 
the paper were 1^ yd. wide, and the price 4|d. a-yard? 

25. A block of marble, 5 ft long, 4 wide, and 1 ft. 3 in. 
thick, weighs 39 cwt. 2 qrs. 8 lbs. 13 oz. ; what is the 
weight of another block, 8 ft. long, Ah wide, and 2 ft. 4 in. 
thick? 

26. In what time will the interest of £750, r2s. 6d. be 
sufficient to pay a debt of £112, lis. 10^ d. at 4 per cent. 
per annum ? 

27. Find the interest of £1418, Os. 6d. for 375 days, at 
3^ per cent, per annum. 

28. If the 6d. loaf weighs 3 lb. 4^ oz. when the wheat 
is at 56s. a-quarter ; what is the price of wheat per qr. 
when the 8d. loaf weighs 3 lb. 13| oz. ? 

29. If 18 men working 9 hours a-day, or 36 boys work- 
ing 6 hours a-day, can do a piece of work in 8 days ; in 
how many days would 10 men and 24 boys do a piece 
of work 5 times as large, all working 8 hours a-day ? 

30. A contractor engages to construct 3 J mis. of a road 
in 90 days, and for this purpose he employs 120 men, 
who work 8 hours a-day, but after 60 days, he finds they 
have only accomplished 2 mis. of the road ; how many 
additional men must he employ to finish the work in 
the appointed time, the men working 9 hours a-day ? 



J] 



25 



PRACTICE -^^^sss^ 

Is an expeditious method of finding the values of goods 
by means of aliquot parts. 

A less number is said to be an aliquot part of a greater 
when the less is contained an exact number of times in the 
greater ; thus 3 is an aliquot part of 24, which contains it 
exactly 8 times ; so also is 2 s. 3d. of 18s., which contains it 
exactly 8 times. 

TABLE OF ALIQUOT PARTS. 



lOs. = £i 


lid. = i^of 6d. = is. 


6s. 8d.= £i. 


Id. = £^i^ = ^\s. 


5s. — loflOs.— £i 


|d. =iof6d. = ^Vs. 


4s. = £i 


7 1 , 


3s. 4d.— ^ of 10s. — £i 


id. = £^1^ = ^Vs- 


2s.6d.= iofl0s. =£i 


AVOIRDUPOIS WEIGHT. 


2s. —i of 10s. — £Vo 


10cwt.= i ton 


ls.8d.= iof6s.8d.=£V^ 


5 cwt. = J ton 


Is. 4d.= £^V 


4 cwt. = \ ton 


Is. 3d.— J of 10s. — £Ve 


2 cwt. = -^-Q ton 


Is. =- £^V 


2 qr. = i. cwt 


6d. = is. =£^^^ 


161b. = 1 cwt 


4d. = |s. 


14 lb. = ^ qr. = ^ cwt 


3d. = is. 


71b. =^qr. = TVcwt 


2d. = is. 


41b. = 1 qr. 



This table should be extended by the pupil. 

Case I. When the price is an aliquot part of £1, Is., or Id. 
Ex. Find the price of 2744 yds. at 4d. and 3s. 4d. per yd. 
4d. = is.) 2744s. = val. at Is. 
2,0) 914s. 8d. val. at 4d. 
Va.at4d.=£45, 14s.8d. 



Sol. 1. Since 4d.=r^s. the 
value at 4d. = ^ of the va. 
at 1 s. ; now 2744 yd. at Is. 
=2744s., hence ^ of 2744s. 



= 914s. 8d., or £45, 14s. 8d. is the value at 4d. 

Sol. 2. Since 3s. 
4d. =£^, the va. at 
3s. 4d. = I of the va. 



3s. 4d. = £i)£2744va. at £1 

£457, 6s.8d. va. at3s.4d. 

at £1 ; now the va. at £1 is £2744, hence \ of £2744 = £457; 
6s.8d. =va. at 3s.4d. 

Find the values of, 
1. 7459 oz. at id., fd., Id., Ijd., 2d., 3d., 4d.,&6d.per oz. 

c2 



26 



PRACTICE. 



2. 1786 yds. at Is., Is. 3d., ls.4d., Is. 8d., 2s., 2s. 6d., 
3s. 4d., and 6s. 8d. per yd. 

3. 3457 lbs. at 10s., 5s., 4s., 3s. 4d., Is. 8d., Is. 4d., 6d., 
and 4d. per lb. 

Case II. When the price is not an aliquot part of 
£1, Is., or Id. 

Ex. Find the value of 575 lbs. at 3s. 9d. per lb. 



2s. 6d. =£i)£ 575 va. at £ 1 

£71, 17s. 6d.va.at2s.6d. 
ls.3d.=:riof 2s.6 d. 35, 18s. 9d . >> Is. 3d. 

3s. 9d. 



Sol. 3s.9d.= 
2s.6d. + ls.3d.; 
now the va. at 
2s. 6d. by Case I. 

is £71, 17s. 6d., £107, 16s. 3d. 

and since Is. 3d. = ^ of 2s. 6d., the va. at Is. 3d. = i of the 
va. at 2s. 6d. = ^ of £71, 17s. 6d., or £35, 18s. 9d. The sum 
of the values at 2s. 6d. and Is. 3d. = the value at 3s. 9d. 

Note. When there are £'s in the price, multiply the quantity 
by them, and take aliquot parts for the s. and d. 

Find the values of, 

4. 375 at 4s. 4d., 4s. 8d., 5s.6d., 6s.3d., 7s. 4d., 8s. 4d., 
10s. lOd., and 13s. 4d. each. 

5. 692 at 12s. 4id., 13s. 9id., 14s. 4d., 15s. 7id., 
18s. lOd., 19s. 5d., 19s. 7id., and 19s. lOd. 

6. 1476 at Hd., 2id., 3f d., 4id., 6|d., 7id., 8id. & lOid. 

7. 297 at £1, 14s. 8d., £1, 18s. lOd., £2, 5s. 7d., £3, 15s. 
lUd., £5,17s.l0d., £6,16s.6d., £7,lls.9d.&£9,18s.4id. 

8. 379 at £2, 2s. 2d., £3, 3s. 3d., £7, 7s. 7d., £11, lis. 



Case III. When the price consists of £ and s. only. 

Ex. Find the value of 493 cwt. at 39s. per cwt. 

Sol. Multiply the quantity (493) by 493 
half the number of shillings (19|) ; then 19 J 

double the right-hand figure of the pro- ^^7^ /?q/.i r. 

duct (3^) for shillings (7s.), and the ybid^_£Jbi, /s. 
rest C961) are £'s. 

Find the values of, 

9. 1476 at 2s., 3s., 7s., 9s., lis., 13s., 17s., 19s., 29s., 
43s., and 47s. 

10. 1729 at 16s., 18s., 21s., 37s., 95s., £5, 5s., £5, lis., 
£16,4s., and£17, lis. 



PRACTICE. 27 

Case IV. When the quantity contains a fraction. 
Ex. Find the value of 579| yds. at 21s. 3d. per yd. 
Sol. 1. Is. 3d. = £j\ ) £579 value at £1 

36, 3s. 9d. va. at Is. 3d. 
I of 21s. 3d. = 15s. ll^d . 

Val. of 5791 yds. = £615, 19s. 8id. 

Sol. 2. 579| X 4 

Is. 3d. = £j\ ) £2319 value at £1 

144, 18s. 9d . va. at Is. 3d. 

4 ) £ 2463, 18s. 9 d. va. of 4 X 579| 

£615, 19s. 8jd. va. as before. 

Find the values of, 

11. 476| and 549| at 14s. 8d., 15s. 5d., 17s. 8d., & 19s. 6d. 

12. 375^ and 742^ at 13s. 9d., 12s. 8d., 14s.lld., & 17s.6d. 

13. 1146f&1763/Tat26s.4d.,37s.9d.,46s.7id.,&76s.4id. 

14. 2986f and 4863,-V, at £4, 17s. 5d., £6, 14s. 7id., 
£7, 2s. 2id., and £10, lis. 9d. 

Case V. When the quantity is compound, and the 
price of one of the highest name is given. 

Ex. Find the price of 4 cwt. 3 qrs. 14 lbs. at £3, 16s. 
7|d. per cwt. 

2qr. = ^cwt.)£3 16 



Sol. Find the va- 
lue of the quantity 
of the highest name 
given, then take ali- 
quot parts for the 
lower names, and 
add. Thus, 2 qr. = 
^ cwt., va. of 2 qr. = 
i of £3, 16s. 7id. ; 
1 qr. = ^ of 2 qr., va. of 1 qr. 



15 6 

1 18 

lqr.=^of2qr. 19 

141b.=iqr. 9 



7^ va. of 1 cwt. 

6 va. of 4 cwt. 
3i '' 2qr. 
Ifi'- Iqr. 
6||" 141b. 



£18 13 



6JJva.of4cwt. 
3 qr. 14 lb. 

^of£1,18s. 8|d.; and 141b. 
='iqr.,"va. of 14 lb. = | of 19s. Ifd.^. The sum of the 
separate values gives the whole value. 

Find the values of, 

15. 3 cwt. 3 qrs. and 6 cwt. 2 qrs. 21 lbs. at £4, 5s. 4d. 
and £4, 7s. 6d. per cwt. 

16. 7 cwt. 1 qr. 16 lbs. and 21 cwt. 2 qrs. 18 lbs. at £5 
16s. 8d. and £6, 17s. 8d. per cwt. 



"« PRACTICE. 

17. 12 lbs. 3 oz. 15 dwt. and 27 lbs. 5 oz. 6 dwt. at 
£3, 3s. 4d. and £5, 16s. 8d. per lb. 

18. 17 yd. 3 qr. 2 nl. and 37 yd. 2 qr. 3 nl. at £1, 3s. 6d. 
and £1, 17s. 6d. per yd. 

19. 27 ac. 3 ro. 12 per. and 47 ac. 2 ro. 25 per. at £4, 
lis. 8d. and £5, 15s. per acre. 

20. 33 qr. 3 bu. 3 pk. and 67 qr. 1 bu. 2 pk. at £2, 2s. 
4d. and £2, 7s. 4d. per qr. 

21. 14 bu. 3 pk. 1 gal. and 17 bu. 2 pk. 1 gal. at £2, 4s. 
and £2, 12s. per qr. 

22. 45 ac. 3 ro. 24 per. and 67 ac. 1 ro. 14 per. at £5, 
13s. 4d. and £6, 8s. 4d. per ac. 



MISCELLANEOUS EXERCISES. 

1. Find tlie price of 116 cwt. of sugar at £3, 14s. 8d. 
and £4, lis. 9d. per cwt. 

2. Kequired the value of 1147| yds. of cloth at £1, 2s. 
7id. and£l,4s. 8id. per yd. 

3. 'What should be given for 18 cwt. 3 qr. 21 lbs. 
and 27 cwt. 2 qr. 21^ lbs. of tea, at £25, 7s. 6d. and 
£27, 19s. 8d. per cwt. ? 

4. A bankrupt's debts amount to £1250, and he com- 
pounds with his creditors for lis. 10|d. per £1 ; find his 
effects. 

5. How much sterling money is equal to 1000 francs, 
each 9fd. sterling? 

6. Find the cost of digging a ditch, the solid content 
of which is 6753 cubic yds., at Is. 8|d. per cubic yd. 

7. The daily pay of a foot-soldier is Is. Id. ; how much 
does it take to pay a regiment of 750 men for a year at 
that rate ? 

8. The annual cost of the Police of Paris amounts to 
5335295 francs of 9|d. each ; express this in sterling 
money. 

9. How much sterling money is equal to 2000 rupees, 
each2s. l^d.? 

10. Required the income-tax on £975, 17s. 6d. at Is. 
4d. per £1. 

11. The annual rent of a parish is £36750, and a tax is 



PRACTICE. . 29 

assessed for the poor at 2s. IJd. per £ ; how much will 
it amount to ? 

12. In 1856, the expenses of the British Postal Service 
were £1660229, and the net revenue was £1207725; 
express each of these in francs and rupees of Is. lOJd. 

13. Sold 273 qrs. 5 bu. of wheat at £2, 15s. per qr. ; 
159 qrs. 3 bu. of barley at 42s. 8d. per qr. ; and 79 qrs. 
6 bu. of oats at 22s. 7d. per qr, ; find what sum was 
received in all. 

14. Find the value of 14 cwt. 3 qrs. 16 lbs. of tobacco at 
£23, 7s. lOd. per cwt. 

15. A farm, containing 675 ac. 3 ro. 24 per., is let at 
£l, 17s. 6d. per acre; what is the whole rent? 

16. Edinburgh, May 15th, 1871. James Drummond, 
Esq., bought of Robert Hunter, 163| lbs. tea at 3s. 9d. 
per lb., 167i lbs. sugar at 7id., 147i lbs. coflfee at Is. 8d., 
1 1 cheeses, each 56 lbs., at 8Jd. per lb. ; what is the whole 
value ? 

17. Leith, April 17th, 187 1 . Alexander Clark bought of 
Scott and Co., 179J doz. sherry at 27s. 6d., 185J doz. 
port at 36s., 163 gals, aqua at 17s. 6d., 17 gals, brandy 
at 36s. 6d., and 21 doz. claret at 47s. 6d. ; what is the 
whole value ? 

18. The number of sovereigns coined in 1855 was 
8448482, each weighing 5 dwt. 3y\ grs. ; required the 
whole weight. 

19. The number of shillings coined in 1855 was 
1368499, each weighing 3 dwt. 15y\ grs. ; required the 
whole weight. 

20- What is the value of 3 casks ot molasses, each 7 cwt. 
3qr. 3iib.,at 12s. 7|d. per cwt., and duty 4s. 2d. per cwt.? 

21. A gentleman has 3 farms ; the first contains 450 
ac. 3 ro. 24 per., and is let at £1, 13s. 4d. per ac. ; the 
second contains 564 ac. 1 ro. 36 per., and is let at £1, 16s. 
per ac. ; and the third contains 635 ac. 2 ro. 16 per., and 
is let at £2, Is. 8d, per ac. ; the taxes which he pays 
upon each are respectively 5s., 6s. 8d., and 3s. 4d. per 
ac. : what is the full rent of all his farms, the amount or 
taxes which he pays, and his net income ? 

22. A bankrupt owes £7580, and he can pay 15s. 7id. 
per £ ; what are his effects worth ? 



30 

DFXIMAL FRACTIONS. 
A FRACTION which has unity with one or more ciphers 
after it for its denominator is called a Decimal fraction ; 
as, -j%, T^^TJ- Such fractions are expressed without 
their denominators by pointing off, from the right of the 
numerators, as many figures as there are ciphers in the 
denominators; thus, -^^ ^§§, g-%Vtr ^^^ written '4, 1'69, 
•412. "^^^len the number of figures in the numerators is 
less than the number of ciphers, the deficiency is made 
up by prefixing ciphers to the numerators ; thus, -j^^ 
= -04, TTi%%V^ = -00251. 

Ciphers on the right of a decimal do not alter the 
value; thus, -040 = ^^g^, = ^^^ = -04. 

The fii'st figure after the point indicates tenths ; the 
second figure, hundredths ; the third, thousandths, and 
so on ; that is, in decimals, as in integers, the value in- 
creases in a tenfold ratio from right to left. Decimals 
are therefore operated upon in the same way as integers, 
due attention being paid to the placing of the point. 



80 ) 7-0000 

«^o=-0875 



REDUCTION OF DECIMALS. 

Case I. To reduce a vulgar fraction to a decimal. 

Ex. Reduce ■^''■^ to a decimal. Ans. -0875. 

So L. Divide the numerator (7 ) by the denom- 
inator (80), annexing ciphers to the numerator 
until the division terminates or repeats ; then 
point off as many figures from the right of the quotient (875) 
as there were ciphers annexed (4), and make up the defi- 
ciency (if any) in the quotient by prefixing ciphers to it. 

When the division terminates, the result is called a 
Finite decimal ; if not, it is called a Repeating or Cir- 
culating decimal, according as one or several figures 
recur, and a dot is placed above the repeater, or above 
the first and last figures of the circulate ; as, -|, = '6 ; 
1= -142857 (seep. 34). 

Reduce to decimals, 

1 1 3 i 13 27 231 19 511 17 23 197 n-nA 1001 
O 1 19 173 153 11 183 214 363 279 87_ 

'^- ¥7? TaT' 6^5? TTT-^J 2T5) T3T5) SJ-^T^ TdTTJ -g^TsJ T3'6 25- 

«14 7 6 25 6 36 54 121 143 15 .?,111 

*• T! ^J -ST? TJ T2 6' 115") 2lT^> TTbOJ TTeXy? ^¥7^J -^^'4^ ^ T 6 4^' 



DECIMAL FRACTIONS. 31 

Case II. To reduce a finite decimal to a vulgar fraction. 
Ex. Reduce '0375 to a vulgar fraction. Ans. -g^, 

Sol. Write the given decimal (-0375) as the | Tofeao = /o 
numerator of the fraction, and for the denominator write 
unity ^ with as many ciphers after it as there are figures in 
the decimal (4) ; then reduce the fraction dlg^o) t^ ^^ \ow- 
est terms (g^^). 

Reduce to vulgar fractions, 

1.-5; -25; -75; -625; -3125; -03125; •18725r096875; -000575 
2. -48; -364; -4248; -0672; -4152; -04096; -03136; '00048 
3. -525; 6-0425; -00675; 8-0864; -0001875; 1-04264; 2-18575 

Case III. To reduce a compound quantity to the 
decimal of a higher name. 

Ex. Reduce 4 cwt. 3 qr. 21 lb., or 553 lb., to the dec- 
imal of a ton. Ans. -246875 ton. 

Sol. Reduce the given | 5531b. = ^V?^ to- = •246875 ton. 
quantity (553 lb.) to the fraction of the required name (by 
Case YI., p. 8), and again (by Case I. of dec.) reduce the 
fraction (/2V5) to a decimal (-246875). 

1. Reduce 2s. 6d., 3s. 9d., 53. 6d., 12s. 8id., 15s 9f d., 
and lO^d., to the decimal of £1. 

2. Reduce 3 qr. 211b., 2 cwt. 141b., 4 cwt. 17^^., 
141b., 2 qr. 141b., and 981b., to the dec. of 1 ton. 

3. Reduce 2 ml. 7fu., 4 ml. 16 po., 37 po. 5^ yd., 7fu. 
34 po., 8 ml. 16 po., and 374 yd., to the dec. of 9 ml. 

4. Reduce 2 ac. 3 ro., 3 ac. 24 per., 2 ro. >21 yd., 17 per. 
151 yd., 1 ac. 363 yd., and 363 yd., to the dec. of 3 ac. 

5. Reduce 4 oz. 1 dwt., 19 dwt. 15 gr., 21 gr., 11 oz. 
15 gr., 10 oz. 10 dwt., and 1 dwt., to the dec. of 1 lb. tr. 

6. Reduce 14s. 7d., 16s. lid., 3 cr., 4 half-cr., f of 
14s. 5id., and 3^d., to the dec. of 1 guinea. 

7. Reduce £14, 5s. lOd., and £16, 17s. 6d., to the dec. 
of 20 guineas. 

Case IV. To find the value of a dec. in lower names. 
Ex. Find the value of 1-375 ac. Ans. 1 ac. 1 ro. 20 per. 



Sol. Multiply the given decimal (-375) 
by the number of the next lower name 
contained in that given (4), and point off, 
from the right hand of the product, as 



1-375 ac. X 4 
1-500 ro. X 40 
20-000 per. 



.?2 DECIMAL FRACTIONS. 

many figures as are in the decimal (3) ; again, mnltiply tho 
decimal part of the last product (-500) by the number of the 
next lower name contained in this last name (40), and point 
off as before ; proceed in the same way as far as necessary. 
The figures on the left of the points are integers of the re- 
spective names. 

Fii>d the values of, 

1. £-4625; -37258.; -6875 gu.; '3425 or.; £-7725; -9258. 

2. -3775 cwt.; -4275 ton; -68725 or.; -3975 cwt. ; 
•4375 ton; •4651b. 

3. -8975 ml. ; -3875 ac. ; -496725 da. ; -8975 co. ye. ; 
•1875 bu. ; -3875 ro. 

4. -4725 Eng. E. ; -45875 yd. ; -2875° ; -9875 Ju. ye. ; 
£8-6775; 9*725 gu. 

5. -242242 da.; £-8794^ 8-746 ton; 10-12125 ac. ; 
11-6874 ml.; 14-72 yd. 

Case V. To reduce shillings and pence to the deci- 
mal of £1 mentally. 

Ex. 1. Reduce 4s. 10|d. to the dec. of £1 mentally. 

Ans. £-24375. 

Sol. Divide the shillings by 2 for the first figure of the 
decimal (-2) ; the farthings in the pence and farthings (42), 
increased by their 24th part (l^f or If), gives the next two 
figures (43) ; then to the third figure annex the remainder 
(f ), reduced to a decimal (75), for the value (£-24375). 

Ex. 2. Reduce 15s. 8id. to the decimal of £1. 

Ans. £'784/^, or £-784375. 
When the shillings are odd, 50 must be added to the far- 
things, increased as above. 

Reduce to the decimal of £1 mentally, 

1. 7s. 6d. ; 10s. 7id. ; 14s. 8id. ; 15s. 9d. ; 19s. 8id. ; 
12s. 7id; 18s. 9id. 

2. lis. 8d.; 128. 4d.; 13s. 5d. ; 14s. lljd. ; 16s. 8ad.; 
£1, 17s. 9d.; £3, 18s. 7d. 

Case VI. To value the decimal of £1 mentally. 
Ex. Value £-6354 mentally. Ans. 12s. S^d. 

Sol. Divide the first two figures (63) of the dec. by 5 for 
shillings (12) ; to the remainder, if any, annex the thin! 



DECIMAL FRACTIONS. 



33 



figure (5), and tins number (35) diminished by its 25tli part 
(1) gives farthings (34), which must be reduced to pence (8^d.) 
Note. Since three places of the decimal only are required, 
call the third figure one more than it is, when the fourth is 5 or 
upwards, otherwise reject it. 

Find mentally the values of, 
£•972; £-496; £'896; £1-8914; 
•873; -785; -999; 6-4377; 



1. £-525; 

2. -675; 



£11-7364 

22-8976 



Sum 
Diff. 



7-96752 

-0478 
8-01532 
7-91972 



ADDITION AND SUBTEACTION OF FINITE DECIMALS. 

Ex. Fmd the sum and difference of 7-96752 and -0478. 

Sol. Arrange the numbers so that the 
decimal points may be directly under each 
other, and proceed as in integers ; then 
place the point in the result directly under 
the other points. 

Find the sum of, 

1. -25, 4-675, -00475, 84, 96-23725 

2. -0046, 217, -284, -0478, 3-44756 

3. -728921, -00043, 211-2, 86-114875 

4. -00867, 1-432, 247, -00083, -674 

5. 9-732, -048076, -1234, 6-7289, -214, -7 

6. -6498, -37293, 311-4, 21-72, -00875 

7. -046, 36-479, 2-101, -111, -04789 

8. -3596, -24798, -35, 37, -00705 

9. £375, 16s. 6d., £331,14s.9d., £375, 18s.9|d., £157,7s.8id., 

£97 4s. 6d. 5s. 9d. 
10.47-98625— 13-97846; 7-0423— -4789; 28-23546— 16^479258 
11.29-46537—21-57698; 8-2458— -0034; -6728934— -00628575 
12.1-4386- -004289; -04657- '00827 ; -4798231- -46991482 
13. 17 cwt. 2 qr. 14 lb.— 14 cwt. 3 qr. 21 lb. ; 29 qr. 5 bu. 2 pk. 

— 23 qr. 7 bu. 3 pk. 



MULTIPLICATION OF FINITE DECIMALS. 

Ex. Multiply 4-7025 by -0025. Ans. -01175625. 

Sol. Multiply the factors together, as in in- 
tegers, disregarding the point ; then, from the 
right hand of the product, point off as many 
figures as there are decimal places in both fac- 
tors (8), making up the deficiency (if any) by 
prefixing ciphers (1) to the product. 



4-7025 

♦0025 

235125 

9405 

•01175625 

d2 



34 DECIMAL FRACTIONS. 

Note. A decimal is multiplied by 10, 100, 1000, &c. by re- 
moving the point one, two^ three, «&:c. places to the right; an, 
2-134 X 10000 = 21340. 

1.4^6275x4-63, 5-75, -046, -824, 86-4, -005, 1000, 10001 
2. •00796x37-8, 42-89, 7-824, -046, -3724, 1-738, 100, 10101 
3.27-8372x8-434,96-429,-00429,-7426,3-14152,-001,1001 
4. Val.27yd. 3qr . 2nl., at 2/6, 4/9|,23/4^,27/10|,31 /I li p.yd. 



DIVISION OF FINITE DECIMALS. 
Ex. Divide 3-146 by 42-8. Ans. -073505 nearly. 

Sol. Make the decimal places in 42800 )3146-000000 
both numbers alike by annexing ci- -073505 

phers (2) to that which has the least 
number ; then divide as in integers, and to the remainder 
(if any) annex ciphers to carry on the division : the number 
of ciphers last annexed (6) is the number of decimal places 
in the answer (-073505). 

Note. A decimal is divided by 10, 100, 1000, &c. by removing 
the point one, two, three, &c. places towards the left; as, 2-134 -f- 
100 = -02134. 

1. 382-8825-7-55, 1-36, 31-5,-325, -1309, -00119, 2-75, 81-9, 100 

2. 24-22728-r-l-15, 85-5, -805, -0368, 103-5, 369-6, -01539, 1000 
3. -0483923^-20-35,475-6, 8-584,-03157,-002552,l-221, -0019721 
4. £4779, 17s. 8jd.-M7-5, 4-375, 281-25, 687-5, -03125, -1875 



INTERMINATE DECIMALS. 

In reducing vulgar fractions to decimals, when one or 
more figures of the quotient recur, the result is called 
an Interminate decimal. 

Decimals consisting of one or more figures which re- 
cur, are called pure repeating or circulating decimals ; 
as, -3, -142857. 

Decimals consisting of a non-recurring and a recurring 
part are called mixed repeating or circulating decimals ; 
as, '46, '3796 : the non-recurring parts (4 and 37) are 
generally called the finite parts of the decimals (-46 and 
'37960 



INTERMINATE DECIMALS. 35 

REDUCTION OF INTEEMINATE DECIMALS. 

Case I. To reduce a pure repeater or circulate to a 
vulgar fraction. 

Ex. Reduce '75 to a vulgar fraction. Ans. ^| or -§f. 

Sol. Write the given decimal for the numerator, and be- 
low it, for the denominator, place as many nines (2) as there 
are decimal places; then reduce the fraction (||) to its 
lowest terms (y). 

Reduce to vulgar fractions, 
1.-3, -6, -4, -9, -27, -36, -396, -594, -185, -259, -063, -0072 
2. -571428, -153846, -190476, -171, -428571, -095238 

Case II. To reduce a mixed recurring decimal to a 
vulgar fraction. 
Ex. Reduce '0476 to a vulgar fraction. 

-MII&. -g-goo -5900' 2^T5 

Sol. From the given decimal (-0476), considered as an 
integer, subtract the finite part (04) for the numerator, be- 
low which, for the denominator, place as many nines as there 
are figures in the circulating part (2), with as many ciphers 
annexed to them as there are figures in the finite part (2) ; 
then reduce the fraction (/9V0) to its lowest terms l^^^^^^). 

Reduce to vulgar fractions, 

1. -472, -583, -16, -027, -QliS, -4891, -6381, -729693 

2. -146, -2359, -0026, -06563, -11818, -4585, -68472 

Case III. To make circulates similar. 

Ex. Make -03, -775, and -76034 similar. 

Sol. Extend each decimal as many places 
beyond the longest finite part (2), as is indi- 
cated by the L. C. M. of the number of places in 
the several circles (6). 

Make the following circulates similar. 



•03333333 
-77575757 
•76034034 



1. -143, ^037, -014 

2. -3742, -0089, ^476 

3. -1769, -2456, 'im 

4. -402, '179, •0423 



5. -117, -1146, -0894 

6. -2486, -1175, -0624 

7. 1^729, •2684, -0046, 2-478 

8. 4-3, 8-729, •4673, -OOl 



9. -00101, -26770, -1421, 3-428 

E 



36 



INTERMINATE DECIMALS. 



ADDITION AND SUBTRACTION OF INTERMINATE 

DECIMALS. 
Ex. 1. Find the sum and difference of 37-143 and 29-8736 



Sol. Since there are only repeaters given, 
extend them one place beyond the longest 
finite part, and carry or borrow at 9 on the 
right hand; the right-hand figure of the 
result is a repeater or 0. 



37-1433 
29-8736 



Sum 67-017 
DifF. 7-2696 

Ex. 2. Find the sum and difference of 71-857 and 
43-97642. 

Sol. Make the circulates similar, 



and add the carriage (if any) from the 
left-hand column of the circles to the 
right-hand figure of the under circle, 
before adding or subtracting. 



71-85757575 

43-97642642 

Sum 115-83400218 

Diff. 27-88114933 
After the right-hand figure of the result has been obtained, 
proceed as in Finite decimals. 

Find the sum of, 

1. 1-6, 23-052, -583, 6-3, -05i I 3. -7, -245, -006, -043, -i 

2.7-8, 8-964, -729i, 14-0561 4. -72, -345, -854, '00625 

5. 9-76, 8-427, -0864, -75, 8-4572 

6. -1341, -672, -1487, -05, 6-4576 

7. 11-i, 1-63, -9625, -03, 7-1167 

O 2 5 3 4 6 or\f\ 3 

9. £12, 14s. 5d., £27, 16s. 7id., £33, 16s. 6^d., £17, 

lis. 8d., and lOfd. 
10.29-146— 13-17, 16-72—4-6583, 57-6854-14-976851 
11.17-36—3-143, 21-867—7-863, 41-6872-19-478623 
12. 17 ml. 3 f. 4 yds.— 6 ml. 39 po. 5 yds., 18 cwt. 3 qr. 

161b.— 7 cwt. 181b. 



MULTIPLICATION OF INTERMINATE DECIMALS. 
Ex. Multiply 42-375 by -037. 
Sol. When the multiplicand is a repeater, 
and the multiplier a finite decimal, multiply as 
in integers, but add 1 to the right-hand figure 
of the product for every 9 in it; then extend 
the several products the same length and add 
them. 



42-375 
•037 



296628 
1271266 
1-567895 



INTERMINATE DECIMALS. 



37 



7-14672 
'69 

6432054 
42880360 



Ex. 2. Multiply 7-14672 by -69. 

Sol. When the multiplicand is a circulate and 
the multiplier a finite decimal, multiply as in 
integers, and add the carriage from the left of 
the circle to the right-hand figure of the circle ; 
then extend the several products the same length 
and add them. 4-9312414 

When the multiplier is interminate, or when both are in- 
terminate, reduce the multiplier to a vulgar fraction, then 
multiply by its numerator and divide by its denominator. In 
dividing, instead of ciphers, the repeating or circulating 
figures must be annexed in their order to carry on the 
division: thus, 

6-285714 X -3 = 5-2857142 X ^ = 1-761904. 

1.5-7963 X 4-8, 5-76, 8-942, 7-63, 11-5, -0042, -176, -0087 

2.8-1426 X 7-3, 6-84, 9-428, 3-76, 1-51, -43, -0074, -4875 

8. 6-8726 X -4, 6-6, 7-2, -043, -069, -0428, '0072, -1456 

4.7-8763 X -6, -63, -171, -069, -487, 3-i48, 6-709, 8-472 



DIVISION OF INTERMINATE DECIMALS. 
Ex. 1. Divide 26-80583 and 21-18729 by 8. 



Sol. When the dividend only is inter- 
minate, divide as in finite decimals, and in 
carrying on the quotient, instead of ciphers, 
annex the repeating or circulating figures 
in their order, until a repeater or circulate 
is obtained in the quotient. 



8 )26-80583333 
3-35072916 

8)21-18729729 
1-64841216 



Ex. 2. Divide 6-7283 by G'6. Here 6'6z=z6^=^z=y> 

Sol. When the divisor or both are inter- 
minate, reduce the divisor (6-6) to a vulgar 
fraction (6 §), then multiply by its denomi- 
nator (3), and divide by its numerator (20) 
for the quotient, which may be carried on 
as in Ex. 1. 

1. 7-416-^-125, 187-5. 43-75, -52, -427, -729 

2. -2307692 -^ -65, 4-16, -975, -0208, 4-*63, 7-83 
8. 14-i42857 -r- '84, -583, 68-4, 7-23, 81-6, 9-63 



6-7283 
3 

20 )20-18498 

1-009249 



38 

MISCELLANEOUS EXERCISES ON DECIMAL FRACTIONS. 

1. Find the values of £-31416; -142857 ton; -12645 
ml. ; -846283 lb. troy; -1728 yd. ; and '78646 day. 

2. From the sum of 7-6, 8-24, 9*1583, subtract 4-72, 
and multiply the remainder by 21-24. 

3. Find the value -875 of 17s. 6d. + -143 guinea — 
-725 of 8s. 6d. 

4. Express 1456*725 cub. ft. in French steres, each . 
35*31658 cubic feet. 

5. Find by decimals the value of 14 cwt. 3 qrs. 14 lbs. 
of coffee at £9, 6s. 8d. per cwt. 

6. The ratio of the diameter of a circle to its circum- 
ference is 1 : 3*14159 ; required the mean equatorial cir- 
cumference of the earth, the diameter being 7925*626 mis. 

7. Find the diameter of the planet Jupiter, its circum- 
erence being 273318*33 miles. 

8. Reduce £4, 13s. 4d. to the dec. of £5, 12s. 6d. 

9. The gold eagle of the United States weighs 270 
grains, 21*875 carats fine; what is its value in sterling 
money, 46*725 sovereigns weighing a lb. troy, 22 carats 
fine? 

10. A and B can do apiece of work in 4*8 days, A and 
C the same in 4*4 days, and B and C in 5*45 days ; find 
by decimals in what time the three together could do it, 
and also separately. 

11. Find the value of -1875 ton + -375 qr. + -8751b., 
and reduce the result to the decimal of 3 cwt. 3 qrs. 

12. The whole area of France is 131017513*33242 acres; 
find the area in hectares, each 2*473614 acres. 

13. Multiply -06723 by -00401, and divide 301*5 by 
-00045. ^ 

14. A French metre is 3*2808992 imperial feet ; how 
many imperial feet are there in a quadrant of the me- 
ridian, or in 100000565*268 metres ? 

15. What is the hourly motion of the earth, whose 
distance from the sun is 95 millions of miles and period 
of revolution 365 days ? 

16. An ounce of tea costs 2-8125d. ; what should be 
paid for 6 583 lbs. of the same? 



EXERCISES ON DECIMAL FRACTIONS. 39 

17. Find the value of 14-8745 ml. — 3*427 mile. 

18. £4, 6-625S. X 27-45 and 993-714285-^234-2. 

19. Keduce -025 of 4 ml. 3 fu. 19-264 pole to the dec, 
of 2 ml. 5 fu. 

20. Keduce 2-275 of 4i gu. to the dec. of £20, 9s. 6d. 

21. Find the values of -073 of 8s. 6d. and -785 of 15s.9d. 

22. Reduce '2 of |- of 4 cwt. 3 qrs.23 lbs. to the dec. of 
31cwt. 2qrs. 24 lbs. 

23. Divide £1050, 3|d. among 5 men, 8 women, and 16 
boys, giving each woman -5 of I of a man's share, and 
each boy -5 of 1-25 of a woman's share. 

24. Divide £1125 among A, B, and C, giving A 4- of 
2-625 of the whole— £45; B 1-025 of what A receives 
-|- £75, and C the remainder. 



COMMERCIAL ALLOWANCES. 

The Gross weight of goods is their whole weight, including 
the weight of the cask, barrel, &c., which contains them. 

Tare is the weight of the cask, barrel, &c., which con- 
tains the goods, or it is an allowance made for it. 

That which remains after deducting the tare is called 
the Tare Suttle. 

Tret is an allowance of ^V? or 4 lbs. on every 104 lbs. 
of the Tare Suttle for waste. — Draft is also an allowance 
sometimes made, and is deducted before the Tare. 

The Net weight is what remains after all the allow- 
ances have been deducted. 

Questions under this head may be solved by Practice. 

Ex. Find the net weight of 5 hhds. sugar, each 10 
cwt. 3 qrs. 4 lbs., allowing tare 14 lbs. per cwt., tret 4 
lbs. per 104 lbs., and draft 4 lbs. per hhd. 

10 cwt. 3 qr. 4 lb. gross weight of each hhd. 
4 draft on 1 hhd. 



10 


3 


0X5 


141b.= icwt.)53 


3 





6 


2 


24^ tare. 


4lb.p.l04lb.=^'^)47 





3i tare suttle. 


1 


3 


6H tret. 



45 24 1 7 net weight. 



40 COMMERCIAL ALLOWANCES. 

Find the net weight of, 

1. 48 cwt. 3 qr. 14 lb., tare 16 lb. per cwt. & tret as usual. 

2. 79 cwt. 2 qr. 21 lb., tare 7 lb. // // // 

3. 147 cwt. 1 qr. 7 lb., tare 81b. // // // 

4. 984 cwt. 3 qr. 16 lb., tare 14 lb. // // ^ 

5. 748 cwt. 2 qr. 12 lb., tare 12 lb. // // // 

6. 896 cwt. 1 qr. 241b., tare 18 lb. // // // 

7. 4 chests of tea, each 12 cwt. 3 qrs. 14 lbs., allowing 
tare 15 lbs. per cwt., tret as usual, and draft 3 lbs. per 
chest. 

8. 7 casks of sugar, each 14 cwt. 2 qrs. 18 lbs., allowing 
tare 14 lbs. per cwt., tret as usual, and draft 4 lbs. per 
cask, and the value of the net weight at 6id. per lb. 

9. 3 hhds. tobacco ; the first, 8 cwt. 3 qrs. 14 lbs., tare 
3 qrs. 7 lbs. ; the second, 9 cwt. 2 qrs. 7 lbs., tare 2 qrs. 
19 lbs. ; and the third, 10 cwt. 1 qr. 16 lbs., tare 3 qrs. 
7 lbs., allowing draft 7 lbs. per hhd., and tret as usual. 

10. Bought 2709 lbs. of coffee, and was allowed 1 lb. 
gratis to the score; what did I pay for it at 16id. per lb.? 

11. How much pure silver in a mass weighing 42 lbs., 
allowing 15 dwt. of alloy in each lb. of the mass? 

12. Purchased 4 bags of rice, each 265 lbs., and was 
allowed 3 lbs. gratis to every 50 lbs. ; what did it cost 
at 3id. per lb. ? 

COMMISSION AND BROKERAGE. 

Commission is an allowance of so much per cent, paid 
to one person for transacting the business of another. 
Brokerage is a smaller allowance of the same nature. 

Ex. 1. Find the commission on £475, 12s. 6d., at 
£li per cent. Ans. £7, 2s. S^d. 

Sol. Multiplythesum(£475,12s.6d.) | £475 12 6 

by the rate per cent. (1^), and divide 1^ 

the product (£713, 8s. 9d.) by 100. 100)713 8 9 

^ Com. £7 2 "81 

When the rate is guineas, add :^\ of the sum to itself, 
then multiply by tlie rate as £'s, and divide by 100 
when the rate is shillings, &c., take aliquot parts of £1, 
and divide by 100. 



Sol. 1. 5^0) £322 10 

16 2 

338 12 



6 
6 


1,00)8,46 11 
Com. at 2^ p. c, £8 9 


3 

3f 



COMMISSION AND BROKEKAGE. 41 

Ex. 2. Find the commission on £322, 10s., at 2^ gu. 
and 8s. 9d. per cent. 

Sol. 2. 5s.r=£|) £322 10 

80 12 6 
2s.6d.=:^of5s.= 40 6 3 
ls.3d.=iof2s.6d.=20_3__l| 

100 )141 1 10^ 

Com.at8s.9d.p.c.,£l 8 2^:} 

1. Find the com. on £148, 2s. 6d., at 2,^, 3, 3i, and 
3| per cent. 

2. Find the brok. on £152, 10s., at ^, f, -j*^, andl^p.cent. 

3. Find the com. on £500, at 2s. 3d., 3s. 9d., 4s. 3d., 
and 16s. 9d. per cent. 

4. Find the brok. on £4216, 5s., at 3s., 2s. 6d., 3s. 4d., 
and 4s. per cent. 

5. Find the com. on £2850, at 1|. gu.. If gu., l-^ gu., 
and 2^ gu. per cent. 

6. Find the brok. on £375, 17s. 6d., at 3s. 9d., 5s. 3d., 
lis. 3d., and 13s. 4d. per cent. 

7. An agent sells for his employer goods to the amount 
of £1260, 17s. 6d. ; the expenses attending the sale amount 
to £14, 2s. 6d. : what is his commission at 3^ per cent. ? 

8. A banker discounts bills to the amount of £1252, 
10s. ; what is his commission at ^ per cent. ? 

9. An agent charges 3| per cent, for commission and 
risk of bad debts ; his sales during the year amount to 
£9275, 15s., and his losses to £150 : required his net 
income. 

10. A broker is authorized to purchase £1120, 10s. of 
3 per cent, stock ; what is his brokerage at \ per cent. ? 

11. An agent's annual sales amount to £12783, 13s. 4d. ; 
his bad debts, valued at 12s. 6d. per £1, amount to £360, 
and his losses to £150 : what is his income, if he is al- 
lowed 5 per cent, for commission and guarantee ? 

12. A factor collects the half-yearly rents of 3 farms ; 
the annual rent of the 1st is £1250 ; of the 2d, £775 ; and 
of the 3d, £840; the charge for repairs on each is f, 1^, 
and 2 per cent. : what sum will he remit to the landlord, 
his factorage being 3} per cent, upon the rental ? 



42 



INTEREST. 
Interest is the money paid for the loan of money. 

The money lent is called the principal^ and the sura 
of the principal and its interest is called the amount. 

Interest is divided into simple and compound. 



SIMPLE^ INTEREST. 

Case I. To find the interest for any number of years. 

Ex. Required the interest of £375, 2s. 6d. for 4 years, 
at 3i per cent. Ans. £50, 0%. 4d. 

Sol. Multiply the principal by £375 2 6 

the rate per cent. (3J), and by the 
number of years (4) ; and divide the 
product (£5001, 13s. 4d.) by 100. 



£1250 8 



I 



100) £50,01 13 
Int. £50 



3 
4 
4 

4 



Note. For months take parts of a year, or multiply by them 
and divide by 12. 

1. Find the interest of £1345, 10s. for 1 year, at 5, 
5|, 5^, 4^, 4|, and 3| per cent. 

2. Find the amount of £575, 13s. 4d. for 1 year, at 2^, 
3, 3J, 4i, 5, and 5f per cent. 

3. Find the interest of £1200, 13s. 4d. for 5 years and 
G years, at 2i, 3J, and 4i per cent. 

4. Find the amount of £150, 17s. 6d. for 6f yrs. and 
7^ yrs., at 2i, 3, and 5 per cent. 

5. Required the interest of £1244, 15s. for 5 ye. 7 mo. 
and 4 ye. 5 mo., at 3i, 4, and 5f per cent. 

6. Borrowed £750, at 2J per cent. ; what sum will be 
required to discharge the loan at the end of 5 ye. 8 mo. ? 

Case II. To find the interest for any number of days. 
Ex. Find the interest of £675, 10s. for 195 days, at 



4 per cent. 

Sol. Multiply the princi- 
pal by twice the rate per 
cent. (8), and by the number 
of days (195) ; and divide 
the product by 73000 (i. e. 
2 X 365 X 100). 



Ans. £14, 8s. 8id. |f f 
£675 10 

8 



5404 




195 



73,000) £1053780 
£14 



_0 _ 



INTEREST. 43 

7. Required the interest of £677, 10s. 7icl. for 198 
(lays and 364 days, at 2^, 3^, and 4i per cent. 

8. Find the amount of £1436, 14s. 7id. for 1 ye. 95 da. 
and 2 ye. 5 da., at 2^, 3^, and 4 J per cent. 

To divide by 73000. 

Taking Ex. 2— To the pounds ^) £1053780 

of the dividend add ^ of itself, yV) 351260 

j'^ of this third, and ^^^ of the t*^) 35126 

last; then point off 5 figures 3513 

of a decimal from the right £14^ gs. 8^d. = £14-43679 
hand of the sum. This gives 

the interest too much, by about Jd., for every £10 of 
interest. 



9. Required the interest of £483, 12s. 6d. from Mid- 
summer to Christmas, and from Christmas to Midsum- 
mer, at 2^, 4, and 5 per cent. 

10. Lodged in the bank £748, 5s. on March 1st, find 
the amount of this on Dec. 31st, interest at 2i per cent. 

11. Borrowed £1051, 4s. on April 4th ; ^ at 3^, and the 
rest at 3^ per cent. ; what sum should be returned on 
Nov. 11th? 

12. Find the interest of £210, 12s. 8id. for 275 days, 
at 4J and 4^ per cent. ; and of £445, 18s. 2d. for 252 
days, at 2^ and 3i per cent. 

13. Find the amount of £4482, 4s. from Feb. 23d to 
June 13th, at 3-^, 4-f, and 5^ per cent. 

14. What is the interest of £1005, 17s. 7d. from Jan. 
1st to May 16th, and from April 7th to Dec. 15th, at 
3|, 3^, and" 4^ per cent. ? 

15. Borrowed £340, 19s. 5d. on Lammas-day at 4 per 
cent., and £361, 7s. at 4-i- per cent, on Michaelmas-day ; 
what sum will discharge the whole loan on Whitsunday 
following ? 

Case III. To find the interest when a debt is dis- 
charged by partial payments at short intervals of time. 

Ex. Borrowed £750 on Jan. 1st, of which £200 was 
paid on March 4th, £250 on May 15th, and the balance on 
August 1st ; what was then due, interest at 2^ per cent. ? 

Ans. £307, 10«. 



44 INTEREST. 



Obs. J rom Jan. 
1 st to March 
4th is 62 days, 
Mar. 4th to May 
15th is 72 days, 
and from May 
15th to Aug. 1st 
is 78 days. 

The balances 
are multiplied 
by the respective 
days. 



Jan. 1. Borrowed £750X62=46500 
Mar. 4. Paid 200 

Balance 550X72=39600 
May 15. Paid 250 

Balance 300X78=23400 
£109500 

(Mult, by 2^X2=) 5 

Divide by 78000) £547500 

£7, 10s. 

Balance as above 300 

Aug. 1. Amount due £307, 10s. 



16. A bill of £960 was due Jan. 4th, of which £300 
was paid on April 9th, £260 on July 11th, £200 on 
Nov. 11th, and the balance on Dec. 31st ; what was then 
due, interest at 3 per cent. ? 

17. Lodged in the bank £1500 on May 13th, and drew 
£300 on July 11th, £400 on Oct. 1st, £350 on Dec. 14th, 
£200 on March 29th, and the balance, along with the 
interest, on June 9th ; what was then drawn, interest at 
2J per cent. ? 

18. Borrowed £1050 on March 9th, of which ^ was 
paid on June 14th, £200 on Sept. 23d, -f of the remain- 
der on Nov. 29th, and the balance on Feb. 11th; what 
was then paid, interest at 3^ per cent. ? 

19. Lent, Jan. 15th, £1320, and received -25 of it on 
March 31st, £400 on June 18th, -5 of the remainder on 
Aug. 19th, £100 on Dec. 30th, and the balance on March 
1st ; what was then received, interest at 3| per cent. ? 

Case IV. To calculate interest on Accounts-Current. 

An Account-Current is a statement of the mercantile 
transactions of two persons when immediate payments 
are not made. It is written on two pages marked Dr. 
and Cr. ; the Dr. or left-hand side containing all sums 
paid by the person furnishing the account ; the Cr. or 
right-hand side those 2:>a^c? to him. 

Ex. Required the interest on the following Account- 
Current between March 2d and Nov. 11th, interest at 
3i per cent. 



INTEREST. 



45 



Dr. Wilson & Co. in Account-Current with Murray & Co. Or, 



Mar. 2. To Cash, £550 

June 30. " Do. .320 

Sept. 15. >^ Do. .470 

Nov. 11. » Int. . 1 16 2| 

£ 1341 16 2f 

Nov. 11. ToBal. £166 16 2i 

Dr. da. Prod. 

Mar. 2. £550X254=139700 

June 30. 320X134= 42880 

Sept. 15. 470X 57= 26790 

209370 



April 14. ByCash, £400 
May 17. >' Do. .350 
July 31. >' Do. . 425 
Nov. 11. /' Bal. . 166 16 2| 
£1341 16 2| 



Cr. da. Prod.* 

April 14. £400X211= 84400 

May 17. 350X178= 62300 

July 31. 425X103= 43775 

190475 



1 90475 
£ 18895 X 7 
73000) £132265 
Interest =£1, 16s. 2|d. 

Sol. Multiply each sum by the number of days between 
the date opposite to it and the last date (Nov. 11). Add the 
Dr. and Cr. products separately, and multiply the sum of 
each by twice its respective rate per cent. ; subtract their 
products, and divide by 73000 for the interest which is entered 
on the Dr. or Cr. side of the Account, " To or By Interest ;" 
as the Dr. or Cr. products, after multiplying by twice the 
rates, is the greater. Then add each side of the Account, 
and write the difference on the less side, with the words 
*' To or By Balance." 

20. Find the interest, at 3 per cent., on the following 
Account-Current from March 2d to Oct. 28th, 1871. 

Dr. J. Brown in Account-Current with A. Anderson, Cr, 



To Cash, . 
. Do.. . 
» Do.. . 



£750 
. 240 
. 560 



April 17. By Cash, . 


. £640 


May 30. " Do. . 


. .550 


July 18. - Do. . 


. .310 



Mar. 2. 
June 3. 

Aug. 30. 

21. Required the interest on the following Account- 
Current, at 4 per cent., to April 8th, 1871 

Dr. R. Scott in Account- Current with Thos. Younger, Cr. 



April 14. To Goods, . . £650 
Aug. 12. » Cash, ... 400 
Dec. 15. /' Do 700 



June 11. By Goods, . . £740 
Oct. 19. '/ Cash, .... 625 
Feb. 14. // Do 300 



4G INTEREST. 

22. Eequired the interest on the following Account- 
Current to Oct. 15th, allowing Smith 3J per cent., and 
Weddell 3J per cent. 

Dr. Jas. Smith in Account-Current with Henry Weddell, Cr, 



June 3. To Cash, . 


. £700 


Aug. 1. By Cash, . 


. £1050 


Oct. 7. " Do. . . 


. .500 


Dec. 12. n Do.. . 


. . 600 


Jan. 9. " Do. . . 


. . 650 


Mar. 15. » Do.. . 


. . 450 


May 29. f Do. . . 


. . 420 


July 30. '/ Do. . . 


. . 160 



23. Required the principal and interest on the follow- 
ing Account-Current to Nov. 29th, allowing Harrison 
4 per cent., and Cochrane 4 J per cent. 
Dr. H.Harrison in Account-Current with John Cochrane, Cr. 



Sept. 11. By Cash, . . £750 

Jan. 1. '/ Do 360 

May 9. '' Do 250 

Sept. 20. " Do 540 



July 4. To Cash, . . £600 

Nov. 11. " Do 240 

Mar. 2. - Do 400 

July 12. /' Do 300 

24. Required the principal and interest on the follow- 
ing Account-Current to Jan. 12th, allowing Henderson 
2^ per cent., and Clark 2i per cent. 
Dr. Henderson & Son in Account-Current with Jn. Clark, Cr. 



Aug. 2. To Cash, . . £840 
Dec. 11. " Goods, . . 800 
April 9. " Cash, ... 700 
Aug. 14. " Goods, . . 840 



Oct. 17. By Cash, . . . £960 

Feb. 3. // Do 750 

Jmie 9. " Do 900 

Nov. 1. " Goods, ... 600 



The following examples are solved by Simple and Com- 
pound Proportion : 

25. In what time will the interest of £725, 16s. 8d. at 
2.^ per cent, pay a debt of £81, 13s. Ud.? 

26. How long must £532, 5s. lOd. be lent to amount to 
£548, 4s. 4d. at 3 per cent, per annum ? 

27. What sum will amount to £476, 9s. 5id. in 224 
days, at 3| per cent, per annum ? 

28. In what time will £1825 amount to £1840, 18s. 6d. 
at 3J per cent. ? 

29. In what time will any sum of money double itself at 
2 J, 2f , 3, 3^, 3|, and 4 per cent. ? and in what time would 
any sum of money treole itself at each of these rates ? 

30. At what rates per cent, will any sum of money double 
itself in 7^, 10, 11^, 12^ 15, 16, 20, and 25 years? 

31. How long must £1125 be lent to amount to £1188. 
15s. at 4 per cent. ? 



DISCOUNT. 
Discount is an allowance granted for discharging a 
debt before the period allowed for payment has expired. 

The p7^esent value of a debt due at the end of a certain 
time is that sum tlie amount of which for the given 
time is equal to the sum due at the end of that time : 
Thus, the present value of £105, due 2 years hence, at 
2a per cent., is £100; for the amount of £100, for 2 
years, at 2^ per cent., is £105 ; and the discount allowed 
for present payment is £105 — £100 = £5. 

Ex. Find the present value of £913, 10s., due 6 months 
hence, at 3 per cent., and also the discount. 

Ans. £900 and £13, 10s. 

Sol. The interest on £100 for 6 months, at 3 per cent., is 
3 X A = £1 i, and the amount of £100 for that time is £101 ,. 
Then, by Proportion, 101^ : 100 : : £913, 10s. : £900 present 
value, and £913, 10s. — £900 = £13, 10s. is the discount, or 
by Proportion £101^ : £1^ : : £913, 10s.: £13, 10s., discount 
as before. 

1. What is the present value of £1158, lis. 6d., due 4 
months hence, at 2^- per cent. ? 

2. Wliat is the discount upon £345, Is. lO^d., due in 9 
months, at 3 per cent. ? 

3. What sum will amount to £285, 4s. 4d. in 3 years, 
at 3 per cent. ? 

4. A debt of £188, 12s. Sjd. is to be paid; £47, 16s. 
4d. in 2 months, £89, 8s. G^d. in 3 months, and the rest 
in 4 months ; wliat discount should be allowed for pre- 
sent payment of the whole, interest at 4 per cent. ? 

5. Required the present value of £527, lOs. 4d., due 219 
days hence, at 3j per cent. 

6. What is the difference between the interest of £608, 
10s. 6d. for 146 days, and the discount upon it due in 
146 days, interest at 2i per cent. ? 

7. Bought goods to the amount of £2400 ; ^ due 1 month 
lience, ^ due 2 months hence, i due 4 months hence, and 
the rest due 6 months hence ; what sum will be sufficient 
to pay the whole now, interest at 3 per cent. ? 

8. Required the discount on £373, 16s. IJd,, due 3, 4, 
and 6 months hence, at 4 per cent. 



48 discoujST. 

9. 1 am offered a discount of £40 for present payment 
of £640 worth of goods to be paid 3 months hence ; at 
what rate per cent, is the offer made? 

10. The present value of £436, 5s. 4id. due a certain 
time hence, is £420, 10s. ; required the time, interest 
at 2i per cent. 

In discounting Bills, bankers find the interest on the 
amount for the time which the bill has to run for the 
discount ; the difference between this discount and the 
amount is called the net j)roceeds. 

In this country three days, called Days of Grace^ more 
than the term of the bill are allowed. 

Ex. Find the net proceeds of a bill of £572, 10s., dated 
April 8th, at 3 months, and discounted June 3d, at 3i 
per cent. 

Here, 3 months from April £572, 10s. 

8th is July 8th, and adding 3 38 

'lays of grace, the bill is due on 



July 11th; again from June 
3d to July nth is 38 days. 
Then the interest on the 
amount (£572, 10s.) for 38 
days, at 3^ per cent., viz. 
£2, Is. 9d., is the discount, 
and the net proceeds is found 
by subtracting £2, Is. 9d. from £572, 10s. 

The interest is calculated to the nearest penny. 



21755, Os. 



73,000)£ 152285, Qs. 

Discount = £2, Is. 9d 
Amount = £572, 10s. Od. 



Net proceeds =£570, 8s. 3d. 

L £572, 10s. 
the nearest penny. 

Find the net proceeds of the following biUs : 



Amount. 


Date. 


Term. 


Discounted. 


Rate. 


11. £672, 12s. 


Jan. 4. 


4 mo. 


Mar. 5. 


2^ per cent. 


12. 743,11s. 


Feb. 9. 


6 // 


May 11. 


3 // z^' 


13. 897.15s. 


Mar. 11. 


5 // 


June 14. 


31 // // 


14. 983, 4s. 


May 12. 


7 // 


Aug. 17. 


3|: // // 


15. 1260, 14s. 


June 15. 


3 V 


July 26. 


4 // // 


16. 1340, 17s. 


Oct. 14. 


5 // 


Dec. 26. 


4i // // 


17. 1572, 8s. 


Apr. 10. 


8 // 


Sept. 30. 


4| // ^ 


18. 2183, 16s. 


Dec. 30. 


7 // 


Mar. 1. 


2| // // 



Discounts on merchants' bills are generally calculated the 
same way as m Commission. 



49 



INSURANCE 

Is a contract by which an individual or company, in con- 
sideration of a certain allowance called premium, agrees 
to repay the owners of the goods, or other property in- 
sured, any loss or damage which they may have sus- 
tained to the amount stated in the written agreement or 
Policy of Insurance. 

The policy of insurance in this country must be written 
on Stamped Paper, the amount of which is called Policy-duty, 
and is always charged upon exact hundreds ; thus, if the sum 
insured be £510 or £570, the duty is charged on £600. 

The calculations are made the same way as in Commis- 
sion and Brokerage. 

Ex. 1. Find the insurance on £310 at 3s. 6d. per cent., 
and policy-duty 2s. 6d. per cent. 

3s. 6d. per cent, on £310 = £0, 10s. lO.^d. 

2s. 6d. " » on 400 = 10 
Sum required for insuring £310 = £1, Os. 10|d. 

1. What must be paid for insuring £920 at 3s. 6d., 4s., 
OS. 6d., 6s. 3d., 12s. 3d., and 13s. 4d. per cent.? 

2. What is the premium for insuring property to the 
amount of £3530 at 2i, 3i, 4^, 5^^^ H gu- and 3^ gu. 
per cent. ? 

3. What must be paid for insuring £4350 at £4^, £2, 
2s. lOd., £3, Is. 6d., 2igu., 3^ gu., 3| gu. per cent., and 
policy 3s. per cent. ? 

4. What is the expense of insuring £12500 on the ship 
Isabella from Leith to Calcutta, at 2i gu. per cent., policy 
2s. 6d. per cent., and commission \ per cent. ? 

5. Insured £12520 on a ship at 5 gu. per cent., and 
policy 3s. per cent. ; she received damage to the extent 
of £3250 ; what sum will be recovered, allowing If per 
cent, discount on the loss ? * 

6. Insured £14350 on the ship Ohio from Leith to New 
Orleans at 4^ gu. per cent., policy-duty 2s. 6d. per cent., 
and commission i per cent. ; she received damage tc 

* To find the sum recovered, from the amount of the damage, 
subtract the premium and other charges. 



50 INSURANCE. 

the amount of £2580 ; hoAv much will be recovered, al- 
lowing 2^ per cent, discount on the damage ? 

7. Insured £6750 on a ship at 7^ gu. per cent., £10050 
on the cargo at 3| gu. per cent, and £500, the net 
freight at 5 gu. per cent. ; the policy-duty was | per 
cent, and commission i per cent. ; required the whole 
expense of insurance. 

Ex. 2. What sum must be insured to recover £7700 
at 2^ gu. per cent., policy 5s. per cent., and commission 
17s. 6d. per cent., in case of total loss? 

Sol. From I £100— (£2,12s.6d.+5s.+17s.6d.)=£96,5s. 
£100 subtract | and £96, 5s. : £100 : : £7700 : : £8000 sum. 
the rate and other charges; then state, as the remainder 
(£96, 5s.) is to £100, so is the given sum (£7700) to the sum 
to be insured (£8000). 

How much must be insured to recover in case of total 
loss, 

8. £2365 at 5gu. per cent., and policy 3s. per cent.? 

9. £4459 at If gu. per cent., and policy 5s. per cent.? 

10. £1384, 10s. on a single voyage at 6|- gu. per cent., 
policy 5s. per cent., and commission f per cent. ? 

11. What must be insured on a ship worth £6750, and 
the value of the cargo £15954, to cover the whole value; 
premium 8 gu. per cent., policy 5s. per cent., and com- 
mission ^ per cent. ; 3^ per cent, to be returned if the 
ship sailed with convoy, which she did ? 



Ex. 3. How much must be insured on a voyage out 
and home to cover £9120, 5s. at 3| gu. per cent., policy 
5s. per cent., and commission -^^ per cent. ? 

Here £100— (£3, 18s.9d.-f 5s.+6s.3d.) = £95,10s.; hence 
by Comp. Proportion / £95^ : £1 00 : : £9120, 5s. : £10000 sum. 
I 95^: 100 

How much must be insured on a voyage out and home 
to cover, 

12. £223729 at 4igu. p. c, pol. 5s. p. c, & com. 8s. 6d. p. c. ? 

13. £145924 // 3|-gu. // ^ 3s. // // lOs. 

14. £580326 // 5^gu. // '^ 5s. /^ // 13s.6d. '// 
i5.£157323// 7^gu. // // 6s. // // 5s.6d. // 



INSURANCE. 51 

16. Insured 250 hlicls. sugar, at £24 per lihd., from Ja- 
maica to Leitli, at 10 gu. per cent. ; policy-duty 5s. per 
cent., and commission | per cent. ; to return 5 per cent, 
if the ship sailed with convoy and arrived, which she did . 
on her arrival, however, it was found that 200 hhds. only 
were shipped : required the sum due to the insurers. 

Note. The insurers charge ^ per cent, on the value of the 
goods not shipped, in returning the premium upon them. 

17. Insured 350 chests of tea, at £12, 10s. per chest, 
from Canton to Leith, at 9i gu. per cent. ; policy-duty 
5s. per cent., and commission 5s. lOd. per cent. ; to re- 
turn 4 per cent, if the ship sailed with convoy and arrived, 
which she did : on her arrival it was found that only 300 
chests were shipped, and these were so much damaged 
that they sold only for £11, 10s. per chest; whereas, 
had they been undamaged, they would have brought 
£13, 16s. : how much is due by the underwriters ? 



STOCKS. 
Stock is the name given to the money borrowed by 
government to defray the expenses of the nation ; it is 
also the term applied to the capital of any bank, rail- 
way, or trading company. 

AVhen £100 of stock is sold for £100 sterling, the price of 
stock is said to be at par ; the price of stock, however, is 
continually fluctuating. When we see the 3 per cents, 
quoted at 93, it signifies that £93 sterling is the selling price 
of £100 stock, and that £3 is the annual dividend on £100 
stock, or £93 sterling. 

Stock is bought and sold through the agency of brokers, 
who charge usually i per cent, on the amount of the 
stock for their trouble. 

The following examples illustrate the several cases 
which are met with in stocks : 

Ex. 1. How much 3 per cent, stock at 93 can be purchased 
for £3131, 7s. 9d.? 

Here £93 : £3131, 7s. 9d. : : £100 : £3367, Is. 8d. stock. 

Ex. 2. How much will be received by selling £2150 Bank 
stock (7 per cent.) at £220^, and brokerage ^ per cent. ? 

Here £220^ — | = £220 sum received for £100 stock. 
Hence £100 : £2150 : : £220 : £4730 sum received. 



52 STOCKS. 

Ex. 3. What rate per cent, is derived from the 3 per cents, 
at £96? £96 : £100 sterling : : £3 : £3i per cent. 

Ex. 4. How much must be invested in Russian 5 per cents. 
at 104i to produce an annual income of £300, allowing ^ per 
cent, for brokerage? Here 104^ + 5 = 104|. Hence 
£5 : £300 : : £104| : £6262, 10s. sum to be invested. 
Ex. 5. At what rate should money be invested in the 4 per 
cents, to yield 3^ per cent, interest? 

Sol. 3^ : 4 : : £100 : £114f per cent. 

1. How mucli stock can be purchased for £68728, Os. 
O^d. in the 3 per cents, at 91^, 91 J. 92, 92 1, 93, 93-», 
93i, and 93j per cent. ? 

2. How much sterling money will be required to pur- 
chase £5750, 3 per cent, stock at 92|, 92^, 92i, 93, 93^, 
and 93^ per cent., including brokerage ^ per cent.? 
(Here £100 stock will cost | more tlian the prices given.) 

3. Find the yearly income derived from investing £6012, 
7s. O^d. in the 4 per cents, at 84, 84i, 85, 85^, 88, and 92^. 

4. What rate per cent, is derived from the Russian 4^ 
per cents, at 95, 95j, 95i, 96, 96f , and 99 ? 

5. How much sterling must be invested in the 4 per 
jcnts. at 83^ to produce an annual income of £252, 10s.? 

6. At what rate should money be invested in Bank 
stock to produce 3^, 3f , 4, 4i, 4^, and 5 per cent. ? 

7. What is the price of India stock (lOi per cent.), when 
£4752 can purchase £1728 stock? 

8. What is the price of the 3 per cents., when £3412, 
lOs. invested in them produces £105 per annum? 

9. If £8932 be invested in the 3j per cents, at 101^, 
and sold out at 102| ; what difference will it make in my 
income to reinvest the proceeds in Bank stock at 220? 

10. When the 3 per cents, are at 93, India stock at 
230, and Bank stock at 208 ; which is the preferable 
investment, including brokerage -| per cent. ? 

11. Invested £3196 in the 3 per cents, at 94, and was 
obliged to sell at 92-| ; what was the whole loss ? 

12. Invested £5194 in Danish 3 per cents, at 53, and 
sold out so as to gain £294 ; at what price was it sold ? 

13. Invested £3570 in Bank stock at 212|, and sold 
out at 228^ ; what is gained, allowing -| per cent, for 
brokera<2fe ? 



STOCKS. 5.3 

14. How mucli is derived annually by investing £5590 
in India stock at 215 per cent. ? 

15. A has £2400 in 3 per cents. ; how much must he 
invest in 3^ per cents, at 84 to have an income of £350 V 

16. At what rate must money be invested in Russian 
4i per cents, to yield 3| per cent. ? 

17. If £2261 be invested in 3 per cents, at 84, and sold 
out at 85 J ; what difference will it make in my income 
to reinvest the proceeds in Dutch 4 per cents, at 95? 

18. How much 3 per cents, at 99 f must be sold out to 
pay a debt of £931 ? 

19. A father leaves his son ^ of his fortune in 3 per 
cent, stock, i in the 3| per cents., and the remainder 
£2100, in 4 per cent, stock ; what is his annual income ? 

20. Invested £3683 in Russian 4 J- per cents, at 95}, and 
sold out so as to gain £43-5 ; at what price was it sold ? 



EQUATION OF PAYMENTS 

Is the method of finding the time when two or more 
debts due at different periods may be discharged at one 
payment without loss to either party. 

Ex. Find the time for discharging at one payment 
£300 due in 3 mo., £200 in 4i mo., and £400 due in 6 mo. 

Sol. Multiply each sum by its 3 X 300 = 900 
respective time (3 X 300, &c.) ; then 4^- X 200 = 900 
divide the sum of the products 6 X 400 = 2400 
(4200) by the sum of the debts (900). 9^00 ) 4200 

Ans. 4§ mo. 
Find the time for discharging at one payment, 

1. £40 due in 3 mo., £45 in 4 mo., and £55 in 6 mo. 

2. £110 due in 72 da., £140 in 84 da., £200 in 96 da., 
and £240 in 108 days. 

s. £300 due in 210 da., £420 in 340, £500 in 365 da. 

4. A debt, -i of which is due in 6 mo., | in 7 mo., ^ in 
9 mo., and the remainder in 10 months. 

5. A debt, i of which is due on Christmas-day, ^ on 
Whitsunday, -J on Nov. 11, and the rest on Jam 1. 

6. A debt, -^ of which is due on March 14th, and \ on 
the 14tli of each succeeding month. 



54 EQUATION OF PAYMENTS. 

The following exercises may be solved in a similar mamier: 
What is the average price per qr. of, 
• 7. 40 qrs. wheat at 60s. 6d. per quarter, 20 qrs. at 65s., 
30 qrs. at 75s. 6d., and 60 qrs. at 80s. ? 

8. 12 qrs. barley at 42s. per qr., 18 at 45s., 20 at 
39s., 24 at 36s. 6d., 30 at 45s., and 36 qrs. at 43s. 4d. ? 

9. 10 qrs. oats at 25s. per qr., 20 qrs. at 23s. 6d., 25 
qrs. at 26s., 30 qrs. at 26s. 6d., and 45 qrs. at 27s. ? 

10. A wine-merchant mixes 5 gals, sherry at 28s. per 
gal., Avith 8 gals, at 30s. 9d., 10 at 36s., 12 at 42s. 8d., 
and 16 at 42s. 6d. ; what is the average price per gal. ? 

11. A grocer mixes 12 lbs. tea at 3s. 4d. with 42 lbs. 
at 3s. 8d., 25 lbs. at 4s., 28 lbs. at 4s. 3d., and 30 lbs. at 
4s. 6d. ; what should the selling price per lb. of the mix- 
ture be to gain £4, lis. 4d. upon the whole ? 

12. 8 oz. of gold, 24 carats fine, are melted with 16 oz. 
23 carats fine, 18 oz. 21-| carats fine, and 20 oz. 18 carats 
fine ; what i^ the average fineness of the mixture per oz. ? 



DISTRIBUTIVE PROPORTION 

Is the method of dividing a number into parts propor- 
tional to as many given numbers. This rule is employed 
to divide the gain or loss of a company in proportion to 
the shares or stocks of eacli partner, and is then termed 
Felloivship or Partnership^ which is either Simple or 
Compound: Simple Fellowship, -when each partner's gain 
is proportional to his stock only ; Compound Fellowship, 
when each partner's gain is proportional to his stock 
and the time of its being employed. 

SIMPLE FELLOWSHIP. 

Ex. Three merchants, A, B, and C, in company, gain 
£420; A\s stock is £500, B's £400, and C's £300: re- 
quired eacli man's share of the gain. 

Sol. Add the ^^00 + £400 + £300 = £1200 

stocks; then state ^1200 : £500 : : £420 : £175 A's share. 
asthesum(£1200) 1200: 400:: 420: 140 B's >• 
IS to each part- 1200 : 300 : : 420 : 105 C's .> 
ner's stock, so is Whole gain, £420 

the gain (£420) to each partner's gain. 



DISTRIBUTIVE PROPORTION. 55 

1. Divide 7020 into 3 parts proportional (1) to tlie niim- . 
bers 55, 65, and 75, and (2) to the numbers 3, 4, and 5. 

2. Three merchants, X, Y, and Z, gain by trade £225 ; 
X's stock is £425, Y's £350, and Z's £225 : find each 
man's share of the gain. 

3. A bankrupt owes £1470 ; A's claim is £350, 17s. 
od., B's £415, 8s. 9d., C's £420, 16s. 3d., and D's the 
rest ; his effects amount to £980: what will each receive? 

4. Divide 4428 into 3 parts proportional (1) to the num- 
bers 2, 3, and 7, and (2) to the fractions a, i, and i. 

5. A tax of £2997 is to be raised from 4 towns ; the 
number of inhabitants in each is respectively 2100, 2400, 
3000, and 3600 : how much should each town pay ? 

6. Three graziers, L, M, and N, rent a park for £104, 
7s. 6d. ; L puts in 12 oxen and 8 horses, M 8 oxen and 
12 horses, and N 10 oxen and 10 horses ; how much 
ought each to pay, if 2 oxen eat as much as 3 horses ? 

7. Gunpowder consists of 74-8 parts of nitre, 13*3 of 
charcoal, and 11*9 of sulphur ; how much of each will be 
required to make 214 cwt. 32 lbs. of gunpowder? 

8. Gun-metal consists of 100 parts of copper and 11 of 
tin ; how much of each of these is there in a brass-gun 
which weighs 19 cwt. 3 qrs. 8 lbs. ? 

9. Divide £1620, 15s. among D, F, and E, giving D 6 
as often as F 5, and E 4 as often as F 5. 

10. A pound troy of sterling silver consists of 37 parts 
of pure silver and 3 parts of alloy, and is coined into 
66s. ; how much of each is in 231s. ? 

11. A pound troy of sterling gold consists of 22 carats 
of pure gold and 2 carats of alloy, and is coined into 
£46-725 : what quantity of each is there in £700, 17s. 6d. ? 

12. 37 ac. 3 ro. 2 per. of ground is to be divided among 
three persons. A, B, and C, in proportion to their estates ; 
A's being worth £560 a-year, B's £640, and C's £700 : 
what part should each receive ? 

13. Four companies of 60, 56, 52, and 36 men, require to 
furnish 51 men daily for a particular duty, in proportion 
to their strength ; how many must each furnish ? 

14. A gentleman hired a carriage for 40 miles for £5, 
5s. ; at the 10th milestone he admits 3 others, and at the 
15th milestone other two : what should each pay? 



56 DISTRIBUTIVE PROPORTION. 

COMPOUND FELLOWSHIP. 
Ex. A and B enter into partnership ; A contributes 
£500 for 5 months, and B £630 for 10 months ; they 
gained £572 : what share of the gain should each receive? 
Sol. Mult, eachpart- 500 X 5 = 2500 

ner's stock by the 630 X 10 = 6300 

time it continues, Sum of prod. =. ggQQ 

then State as the gSOO : 2500 : : £572 : £162, 10s. = A. 
sum of the products 8800 : 6300 : : 572 : 409, 10s. = 13. 

and 6300), so is the whole gain (572) to each partner's gain. 

15. L and M enter into partnership ; L advances £525 
for 6 months, and M £375 for 8 months ; they gain 
£221, 8s. : what is the share of each? 

16. A, B, and C, engage in trade ; A's stock of £1200 
continues for 8 months, B's of £1575 for 10 months, 
and C's of £1455 for 12 months ; they gain £998, 18s. : 
what is each man's share ? 

17. X, Y, and Z, rent a grass-park for £39, 19s. ; X put8 
in 12 oxen for 4 months, Y 15 for 6 months, and Z 18 foi 
8 months : what part of the rent should each pay? 

18. E, F, and G, enter into company; E advances 
£1200 at the first, after 3 mo. F advances £1400, and 
after 5 mo. G advances £1600; the whole gain during 
12 mo. was £573 : required each man's share. 

19. A and B engage in trade for 12 months ; A advan- 
ces at first £1200, and after 7 mo. withdraws £500 ; and 
B advances at first £800, and after 5 mo. £400 more ; 
they gain £2004, 15s. : how much of it belongs to each ? 

20. The wages of A and B for 4 weeks amount to £12, 
19s. ; A works 9 hours a-day for f of the time, and 10.^ 
ho. a-day for the rest of the time ; while B is idle one 
day a-week, and works 11 ho. a-day the rest of the week : 
how much of the wages should each receive ? 

21. A, B, and C, rent a grass-park for 14 months at a 
rent of £97 ; A put in 20 oxen, and paid £30 ; B put in 
25 oxen, and paid £40 ; and C put in 36 oxen, and paid 
the remainder : how long should each hold the park ? 

Note. Each party's proportional is here found by dividing the 
sum which he paid by the number of oxen he put into the park ,* 
thus, A's proper, is here 30 -^ 20 = 1^, &c. 



DISTRIBUTIVE PROFORTIOX. 57 

22. Four graziers rented a field for 9 mo. at a rent of 
£80 ; A pat in 120 sheep, and paid £14 ; B 30 oxen, and 
paid £24; C 180 sheep, and paid £18 ; and D 36 oxen^ 
and paid the remainder : liow long should each man re- 
tain the field, if 5 sheep eat as much as an ox ? 

23. A common, consisting of 506 ac. 23 per., is to be 
divided among 4 persons. A, B, C, and D, whose estates 
on which their claims are founded are respectively 
£8000, £7500, £6400, and £6000 yearly, while the value 
of the land allotted to each is 64s., 60s., 50s., and 48s. per 
acre : what quantity of the land should each receive ? 

24. Tlie gain of three merchants was £802, 10s., of which 
A's share was £360, B's £262, 10s., and C\s the remain- 
der ; now A's stock of £4000 continued 6 mo., B's 5 mo., 
and C's 4 mo. : what was the stock of each ? 



PKOFIT AND LOSS 
Is that branch of Arithmetic which treats of the gains 
and losses of merchants, and which enables them to fix 
the prices of their goods so as to gain or lose so much 
per cent, upon them. 

The price at which goods are bought is called the 
prime cost, tlmt at which they are sold the selling pt^ice ; 
when the selling price is greater than the prime cost^ 
the difference is called gain, otherwise it is called loss. 

The calculations are made by means of the Compound 
Rules, Practice and Simple & Compound Proportion. 

Ex. 1. Bought tea at £21 per cwt., and sold it at 4s. lO^d. 
per lb. ; what was the gain or loss per cwt. and per lb. ? 



Obs. The S. P. being 
greater than the P. C. 
per cwt., the difference 
(£6, 6s.) is the gain per 
cwt., from which the 



S. P. of 112 lbs. at 4/101 — £27,6s. 
Prime cost of do. =21 



Gain per cwt. = £6, 6s. 
£6, 6s. H- 112 = 1/1^ gain per lb. 
gain per lb. is found by dividing by 112. 

Ex. 2. Bought tea at 3/9 per lb. ; at what price should it 
be sold per lb. to gain 10 per cent.? Obs. £100 worth is 
sold for £110; hence £100 : £110 : : 3/9 : 4/1^ S. P. per lb. 

Ex. 3. Bought tea at 3/9 per lb., and sold it at 4/1^ ; what 
was the gain per cent. ? Obs. 4/1 1 — 3/9=4^d. is the gain on 
8/9; hence 3/9 : 4id. : : £100 : £10 the gam per cent. 



58 PROFIT AND LOSS. 

Ex. 4. Gained 10 per cent, bv selling tea at 4/1^ per lb. ; 
what was the P. C. per lb. ? Sol. £110 : £100 : : 4/1^ : 3/9 
P. C. per lb. 

Ex. 5. Bought sugar at 37/6 per cwt. ; at what price should 
it be sold to lose 8 per cent. ? Obs. £100 worth is sold for 
£92 ; hence £100 : £92 : : 37/6 : 34/6 S. P. per cwt. 

Ex. 6. Gained 7^ per cent, by selling coffee at 1/9^ per lb. ; 
what is gained or lost per cent, by selling it at 1/10 per lb. ? 
Sol. 1/9| : 1/10 : : 107^ : 110, & 1 10— 100=£10 per cent. gain. 

Ex. 7. Bought goods at 15/3 and 4 months' credit, interest 
at 5 per cent. ; at what rate should they be sold to gain 6 
per cent., and allow a discount of 4 per cent. ? 
For the 4 months' cred. 101§ : 100 : : 183d. : 16/6| S. P. 
" the gain ... 100 : 106 

" the discount . . 96 : 100 

1. Bought 3 cwt. 3 qrs. 14 lbs. of tea at 3s. 9d. per lb. and 
sold it at £23, lis. 4d. per cwt. ; what was the gain per lb., 
per cwt., and on the whole? 

2. Bought 4 casks sugar, each 3 cwt. 2 qrs. 21 lbs., at od. per 
lb. ; what should the whole be sold for to gain 14s. per cwt ? 

3. Sold 143 yds. at 10s. 3d. per yd. and gained £13, 8s. l^d. ; 
what was the P. C. of 1 yd. and of the whole ? 

4. Bought muslin at Is. 4^d. per yd. ; how should it be soh 
to gain 7^ per cent. ? 

5. Bought soap at 4|d. per lb., and sold it at 5|d. ; how many 
lbs. must be sold to gain 13s. 9d. ? 

6. Sold 326 dozen wine at 31s. 6d. per doz. and gained 
£24, 9s. ; what was the P. C. of 1 doz. and of the whole ? 

7. How much per cent, is gained by selling Is. worth of 
goods for Is. l^d. ? 

8. Bought goods at £3, 6s. 8d. ; how should they be rated to 
gain 4 p. cent., and allow the purchaser a discount of 5 p. cent.? 

9. Bought sago at 70s. per cwt., and sold it at 73s. 6d. ; 
what was the gain per cent. ? 

10. Gained 3^ per cent, by selling 126 yds. of cambric for 
£48, 16s. 6d. ; what was the P. C. per yd. and of the whole? 

11. Bought linen at 3s. 2d. per English ell, and sold it at 
the same per yd. ; what was the gain or loss per cent. ? 

12. At what price should a yard of gingham which cost 
Is. 5d. a-yard, be sold to gain 15s. 8|d. on 151 yds.? 

13. Lost 4* per cent, by selling goods at £72, lis. 3d.; 
what was their prime cost ? 

14. Gained 10 per cent, by selling coffee at £10, 10s. lOd. 
per cwt. ; what was the prime cost per cwt. and per ton? 



PROFIT AND LOSS. 59 

15 Bought 4 cwt. 3 qrs. 21 lbs. of raisins at 98s. per owt. ; 
how much per cent, was gained by selling the whole for 
£28, 2s. lO^d., the expenses of the sale being 16s. 5|d.? 

16. Grained 3^ per cent, by selling tea at 5s. 3d. per lb. ; 
what was gained or lost per cent, by selling it at 5s. per lb. ? 

17. The prime cost of a book is 6s. 8d., the expense of sell- 
ing is 3 per cent., and the gain is 12 per cent. ; what is the 
selling price of 40 copies of the book ? 

18. Lost 3 J per cent, by selling butter at 16s. 3|d. per stone ; 
what was gained or lost per cent, by selling it at 1 s. 4d. per lb.? 

19.. By selling 5 apples for 2d., 3 per cent, is gained; what 
is gained or lost per cent, by selling 18 for 6d. ? 

20. How much per cent, is 2s. 6d. profit per £1 ? 

21. Bought 50 reams of paper at 18s. 6d. per ream; 3 per 
cent, was lost in selling : what was the whole loss ? 

22. A merchant bought 252 gallons of wine at 35s. 6d., but 
J of it being damaged, he sells it at a loss of 2^ per cent. ; 
how must he rate the remainder per dozen to gain 5 per cent, 
on the whole ? 

23. Bought 4 casks of brandy, each 126 gallons, at 5s. 3d. 
a -bottle : now each cask leaked a gallon ; how should the re- 
inainder be rated per gallon to gain 10 per cent, and allow a 
discount of 4 per cent. ? 

24. Bought a horse for £40, and sold it for £45, and 3 mo. 
credit, interest at 5 per cent. ; required the gain. 

25. Purchased 108 yds. of cloth at 18s. 9d. a-yd., but being 
damaged, I am willing to lose 5 per cent, in selling it ; for how 
much must a yard and also the whole be sold ? 

26. A buys goods to the amount of £2025, and sells them 
to B for £2250, who in turn disposes of them to C at a profit 
of 4 per cent. ; how much per cent, above their prime cost 
did C pay for them ? 

27. Bought 350 qrs. of wheat at £2, 12s. 6d. per qr., and 
sold f of them at a profit of 7^ per cent., and the rest at a 
loss of 2^ per cent. ; what was gained upon the whole? 

28. Purchased 4350 yds. of linen at 2s. 7^d. per yd., and 
field i of the whole at 2s. 8^d., | at 2s. 9d., and the remain- 
der at 10 per cent, profit; requu-ed the price of the remain- 
der per yd., and the gain upon the whole. 

29. By selling an article for £43, 10s. I lost 3 J per cent., 
and recovered the loss by selling another for £19, 10s. ; what 
was the gain per cent, on the second article ? 

30. Bought sugar at 70s. per cwt. ; how must I sell it per 
cwt. to gain 5 per cent., and allow the purchaser a discount 
of 4 per cent, and 4 months' credit, interest at 6 per cent. ? 



60 

EXCHANGE 

Is the method of valuing the money of one country in 
that of another, according to a certain rate. 

The intrinsic value of the money of one country com- 
pared with that of another is called the Par of Exchange, 
and is determined by the weight and fineness of their coins. 

The Com'se of Exchange at any time is the value of a 
fixed sum of the money of one country estimated in that 
of another : from various circumstances this is contin- 
ually fluctuating. In some countries, money is distin- 
guished into Banco and Currency, or into Specie and 
Paper money, — the former being more valuable than 
the latter by a certain rate per cent., which is called 
agio, discount or premium. 

TABLES OF FOREIGN MONEYS. 

France. — 100 centimes=10 decimes=l franc=9^d. ster. 
nearly. Par of exch. with London in gold, 25 francs 22 cents 
for £1 ster. ; in silver, 25 francs 57 cents for £1 ster. 

Holland and Belgium.— 100 cents = 20 stivers = 1 florir 
= Is. 8d, Par of exch. with London, 12 fl. 9 cents for £1. 

Hamburg. — 192 pfennings — 16 schillings = 1 mark. 
3 marks or 48 schillings = 1 rixdoUar of exchange. 
Par of exch. with London, 13 marks 10^ sch. for £1 ster. 
Money is here divided into banco and currency ; the agio 
fluctuates between 20 and 25 per cent. Accounts are kept 
in currency, and exchanges are made in banco. 

Portugal. — 1000 reas = l milrea=:57p. ster.; 400 reas 
= 1 crusado, and 1000000 reas = 1 conto = £239, lis. 8d. 
ster. The discount on paper money is about 24 per cent. ; ex- 
change money is ^ in paper. 

Russia. — 100 copecs=: 1 silver ruble = 37 Jd. ster 
1 paper ruble = 10| ster. nearly. 

Turkey. — 40 paras = 1 piastres 2 |d. ster. Par of exch. 
with London, 100 piastres for £1 ster. 

North America and West Indies. — £100 ster. at par == 
£llli currency, or £100currency= £90 ster. In Jamaica, 
£1661 currency = £100 ster. 

United States. — 100 cents=10 dimes=1 dol.=4s. 6d. ster. 
The par of exch. with London was originally 4| dol. for £1 
Bter. ; this value being now too small, a variable premium 
of 9 or 10 per cent, is added to the par value. 



EXCHANGE. 61 

East Indies. — 192 pice = 16 annas = 1 sicca rupee = 2 s. 
ster. nearly. 116 current rupees =100 sicca rupees; 
100000 rupees = a lac, and 10 million rupees =: a crore. 

The Calculations of Exchange are made by means of 
Proportion or Practice. 

Ex. How much sterling money is equal to 750 copecs, 
exchange at 3s. 2id. per ruble ? 
Sol. 100 copecs : 750 copecs : : 3s. 2^d : £1, 4s. Ofd. ster. 

1. How much sterling money in 11619 francs 30 cents, 
and in 21126 fr., exch. at 25 fr. 20 cents, and at 25 fr. 15 
cents per £1 ster. ? 

2. In £420, 17s. 6d. and £580, 13s. 4d., how much French 
money, exch. at 25 fr. 20 cts., and 25 fr. 16 cts. per £1 ster. ? 

3. How much sterling money in 2145 marcs 15 sch. and in 
5845 marcs 2 sch., exch. at 13 marcs 10 sch. and 13 marcs 
8 sch. per £1 ster. ? 

4. In 456325 reas, and in 874625 reas, how much sterling, 
exch. at 56d. and at 57|d. per milrea ? 

5. In £212, 17s. 6d. and in £318, 2s. 6d., how much money 
of Holland, exch. at 12 fl. 8 cts. and at 12 fl. 9 cts. per £1 ster.? 

6. How much Turkish money in £124, 5s. and in £340, 7s. 
6d., exch. at 100 piastres, and at 103^ piastres per £1 ster.? 

7. How much sterlhig money in 100 rubles 50 copecs, and 
in 1825 rubles 25 copecs, exch. at lOd. and 10|d. per ruble? 

8. How much Hamburg currency in £360, and in £756, 13s. 
4d., exch. at 13 marcs 8 sch. banco per £1 ster., agio 20 per 
cent., and at 13mar. 1 sch. banco per £1 ster., agio 2 5 p. cent.? 

9. How much sterling in 435 rupees 9 annas, and in 750 
rup. 5 an. 8 pice, exch. at 2s. and 2s. 4d. per rupee? 

10. How much United States cun-ency in £250, 12s. 6d., 
and in £742, 17s. 6d., exch. at 4| dollars per £1 ster., pre- 
mium 8 and 10 per cent. ? 

rr: How much sterling in £364, and in £1008 Canadian 
currency, exch. at 112 and 112^ per cent.? 

12. How many current rupees in £376, 5s. and in £980, 
exch. at 2s. and 2s. O^d. per sicca rupee? 

13. How many rupees in 3452 dollars 80 cents, and in 5179 
dol. 20 cents, exch. at -415 dol. and '416 dol. per rupee? 

14. How much Hamburg currency in 706 francs 70 cents, 
and in 869 francs 50 cents, exch. at 100 marcs banco for 185 
francs, agio 20 and 25 per cent. ? 

15. In 11880 milreas current, and in 10560 milreas current, 
how much ster. at 56d. per milrea, agio on paper money 20 per 
cent., and at 57}d. per mil., agio on paper money 24 p. cent.? 



62 

DUODECIMALS 
Is a method employed for multiplying feet and inches, 
&c. by feet and inches, &c. 

A foot is divided into 12 inches, an inch into 12 parts or 
primes, and a prime into 12 seconds. 

Ex. Multiply 6 ft. 3 in. 4 pts. by 7 ft. 2 in. 5 pts. 

Sol. Arrange the numbers so that 
ft. may be below ft., in. below in., &c. 
Multiply by the ft. (7) in the multi- 
plier as in Compound Multiplica- 
tion ; in the same way, multiply by 
the inches (2), but write the pro- 
duct one place nearer to the right 
hand ; again, multiply by the parts (5), and write the pro- 
duct one place nearer to the right hand than the last ; then 
add the separate products, carrying at 12. 

The answer is 45 s. ft., 2 twelfths of a s. ft., six 144ths 
of a s. ft. {i. e. 6 s. in.), and eight 144ths of a s. in. ; now 2 
twelfths = twenty-four 144ths ; hence the answer may be 
written 45 s. ft. (24 + 6 y^^) s. in. = 45 s. f. 30 y?^ s. in. 



6 ft. 3 in. 4 pts. 

7 2 5 




43 11 4 

12 6 8 
31 4 


8 



45 2 6 8 





ft. 


in. 


pt. 




ft. 


in. 


pt. 


ft. 


in. 


pt. 


ft. in. 


pt. 


1. 


7 


4 


6 


X 


4 


6 





5 


7 





6 4 





2. 


10 


5 


3 


X 


3 


5 





4 


3 





10 5 





3. 


11 


6 


9 


X 


2 


2 


4 


3 


4 


8 


6 11 


9 


4. 


12 


8 


4 


X 


3 


6 


9 


7 


3 


6 


9 10 


3 


5. 


15 


9 


10 


X 


2 


6 


3 


3 


9 


6 


8 9 


4 


6. 


16 


11 


2 


X 


3 


9 


6 


6 


8 


9 


10 11 


3 


7. 


18 


9 


8 


X 


4 


7 


6 


7 


9 


3 


12 11 


9 


8. 


21 


10 


7 


X 


6 


3 


5 


9 


5 


4 


11 3 


6 


9. 


48 


4 


9 


X 


7 


10 


11 


10 


10 


5 


11 8 


9 


10. 


56 


3 


6 


X 


14 


6 


4 


15 


9 


2 


17 6 


6 


11. 


78 


6 


4 


X 


21 


4 


6 


25 


7 


9 


32 8 


4 


12. 


99 


11 


8 


X 


36 


10 


3 


49 


11 


9 


54 7 


6 



Note. The area of a board is found by multiplying the length 
by the breadth, and the cubic content by multiplying the length, 
breadth, and thickness together. 

13. Find the area of a board 4 feet 7 in. broad and 18 feet 

9 in. long. 

U. Find the area of a floor 12ft. 6 in. 4 pts. by 18 ft. 6m. 3pts. 

15. Find the area of a wall 17 ft. 4 in. 6 pts. long and 

10 ft. 6 in. high. 

16. Find the content of a cistern 7 ft. 4 in. long, 6 ft. 6 in. 



DUODECIMALS. 63 

deep, and 3 ft. 9 in. wide, and the number of gallons it would 
contain, each 277J c. in. 

17. Find the cubic content of a block of marble 3 ft. 4 in. 
long, 2 ft. 10 in. wide, and 1 ft. 8 in. thick. 

18. What is the length of a floor containing 44 s. yd. 96 s. 
in., whose breadth is 17 ft. 6 in. ? 

19. What length of carpet f wide will cover a floor 22 ft. 
G in. long and 18 ft. 4 in. broad? 

20. How much paper will be required to cover the walls of 
a room 27 ft. 8 in. long, 20 ft. 3 in. broad, and 12 ft. 6 in. 
high? 

21. How many gallons of water must be run off from a 
cistern 8 ft. 6 in. long, 4 ft. 3 in. broad, and 6 ft. 8 in. deep, 
to make the surface sink a foot ? 

22. The paving of a court-yard cost £13, 4s. at 5s. 6d. per 
sq. yard ; how broad is it, its length being 36 ft. ? 



INVOLUTION. 

When a number is multiplied by itself any number of 
times, the process is called Involution, or the raising 
of Powers. 

The original number is called the root^ and the products 
powers of the root. Powers are often indicated by writing 
the number once, and a small figure (called the index or ex- 
ponent of the power) a little to the right above the number, 
denoting how many times the number is to be taken as a 
factor. Thus, 

5 2=5x5 = 25, is the second power or square of 5. 

53 =5 X 5x5=1 25, is the third power or cube of 5. 

5 7 = 5X5X5X5X5X5X5=78125, is the 7th power of 5. 
r ^ \K 3X3X3X3X3 243 ,, ^ „,, - _ 

(A)'= 11X11X11X11X1 1 = 161051 = t^^ ^^*^ P^^^^ ^^ I'l- 

It may be noticed that 5^=53 X 5*= 125 X 625 = 78125 
as above, i. e. the sum of the indices of powers of the same 
number, is the index of their product. 

1. Find the cubes of 21, 33, 44, 67,89,11-9, l-25,& 1-075. 

2. Raise 24«, 75^, l-05«, 2-15«, •025r and 1-025^ ^-^=£=25^ 
3.Raise(f)«, (|)«, i^sy, {^%y, GV)^ and(^)^: .^:^ 

4. The side of a square is 11 feet; finS its- area. (ll<*=::r 
area in s. feet.) X* ' [ i 

5. The side of a cube is 8 feet; find its content. {S^S' " ^ 
content in c. feet.) c^sr ^ 



64 INVOLUTION. 

6. The side of a square court-yard is 22 ft. 6 in. ; what is 
its area ? 

7. The side of a cubic cistern is 6 ft. 3 in. ; what is its 
content ? 

8. A cubic foot of quartz weighs 2640 oz. ; required the 
weight of a piece 4^ in. in the side. 

9. A cub. ft. of chalk weighs 2784 oz. ; find the weight of 
a column 4 ft. 6 in. in the side. 

10. A cub. ft. of water weighs 1000 oz. ; what weight of 
water does a cubic cistern contain, whose side is 4 ft. ? 

11. How many dice, i in. in the side, can be cut from a 
cubic piece of ivory 6 in. in the side ? 

12. How many squares, 3 in. in the side, can be cut from 
a square piece of pasteboard, whose side is 1 ft. 6 in. ? 



EVOLUTION 

Is the method of extracting the root of a given power. 
The square root is the method of extracting the second 
root of a given number, or of finding a number which, 
when raised to the second power, produces the given 
number; thus, the square root of 169 = 13, for IS'* = 

The cube root is the method of extracting the third 
root of a given number, or of finding a number which, 
when raised to the third power, produces the given num- 
ber]^ thus, the cube root of 1331 is 11, for 11 ^ = 1331 ; 

The sign V placed before a number indicates that the 
square root of the number is to be taken ; %/ placed before 
a number indicates that the cube root of the number is to 
be taken. 

EXTRACTION OF THE SQUARE ROOT. 

Ex.1. Extract the square root of 9177-64. Ans. 95-8. 

91,77,-64(95-8 root. 
81 
185 1077 
5 925 



Sol. 1. Divide the given num- 
ber into periods of two figures 
each, beginning at the units^ 
figure. 

2. Find the greatest square 
number in the first period (81), 
place its root (9) on the right 



1908 15264 
15264 

of the given number, and subtract its square (81) from the 



EVOLUTION. 65 

first period (91) ; then to the remainder (10) annex the next 
period (77) for a resolvend (1077). 

3. Write the double of the figure in the root for a partial 
divisor (18), and find how often it is contained in the resolv- 
end (1077), omitting its right-hand figure (7); place the 
number of times (5) after the last figure of the root, and after 
the partial divisor (18), for a complete divisor (185); then 
multiply the complete divisor (185) by the figure last placed 
in the root (5), and subtract the product (925) from the re- 
solvend (1077) : to the remainder (152) annex the next period 
(64) for a new resolvend (15264). 

4. To the last complete divisor (185) add its right-hand 
figure (5) for a new partial divisor, and so proceed until all 
the periods are brought down. 

Note. When there is a remainder, after bringing down the 
last period, the root may be carried on decimally, by annexing 
periods of two ciphers each to the remainder. 

The square root of a fraction is found by taking the square 
roots of its terms, if they are exact squares ; if not, the frac- 
tion must be reduced to its equivalent decimal and its square 
root taken. 

Extract the square roots of, 
1. 5184, 6889,9801, 14884, 17161, 22201, 297025,&958441 
2.1100401,1279161,3786916,4008004,14356521,60481729 
3. 9862-4761, 99-980001,56-725, 597-184, 674-85,&948-625 
4.127-3,2479-6, 118-63, 2459-147, 4-8, 5-4245, & 121-45 

Note. The repeating figures of the decimals must be annexed 
in their order, in periods of two figures each. 

5.2, 3, 5, 7, 11, 12, 13, 17. and 19, each to 6 places of dec. 
6-tVt, t%V nh 3^1, Hff, Hi, 14^, 17Vt, and 24f. 
7. 102030201, 10020210201, and 9018027018009. 

Ex. 2. Find a mean proportional between 9 and 25. 

Ans. 15. 



Sol. V9 X 25 = V225 = 15, for 9 : 15 : : 15 : 25. 
8. Find a mean proportional between 7 and 28, 15 and 
135, 24 and 96, 18 and 288, 44 and 396, 19 and 46. 

Note 1. The side of a square equal to any given area is the 
square root of that area. 

2. Circles are to each other as the squares of their diameters. 

3. In a right-angled triangle, the square of the hypothenuse, 
or side opposite the right angle, is equal to the sum of the squares 
of the other two sides. 



GQ EVOLUTION. 

9. Find the side of a square to contain 756 s. yds. 

10. A gentleman's estate contains 4851 ac. 1 per., and ho 
wishes another of equal area in the form of a square ; required 
its side. 

11. An army of 58564 men is to be formed into a square ; 
how many men will the front contain ? 

12. The diameter of a circular pond is 540 ft. ; what is the 
diameter of another 5 times as large ? 

13. Two ships sail from the same port, the one due east 
180 mis., and the other due south 230 mis. ; what is the dis- 
tance between them ? 

14. A wall is 83 ft. high ; what length of line will reach 
from the top to a point 67 feet from its base ? 

15. The wages of a certain number of men amounted to 
£561, 2s. 6d. at 2s. 6d. per day ; they wrought as many days 
as there were men employed ; what was the number of men ? 

16. A ladder 84 ft. long reaches from the edge of a ditch, 
40 ft. wide, to the top of a wall on the opposite side of the 
ditch; what is the height of the wall? 

17. A room is 48 ft. long, 36 ft. broad, and 16 ft. high ; what 
is the length of each of the diagonals, and also the diagonal 
of the contained space ? 

18. What is the length and breadth of a parallelogram 4 
times as long as it is broad, whose area is 3 ac. ? 

19. 79524 trees 16 ft. distant are planted in a square plan- 
tation ; what is the length of the side ? 

20. A room as broad as it is high, and 32 ft. 6 in. long, 
contains 8937 c. ft. 1 254 c. in. ; find the height. 

21. Arrange 24964 soldiers so that the number of men in 
rank may be 4 times the number in file. 

22. The paving of a square enclosure cost £36, 9d. at 9d. 
per square yard ; find the length of its side. 

EXTRACTION OF THE CUBE EOOT. 

Ex. Extract the cube root of 12-812904. Ans. 2*34. 

Sol. 1. Divide the 
given number into pe- 
riods of 3 figures each, 
beginning at the units^ 
figure. 

2. Find the greatest 
cube number in the first 
period (8), place its root 
(2) towards the right of 
the given number, and 
subtract its cube (8) from the first period (12); then to 



2"-X 300 


12-812,904 (2-34 


1200 


8 4 


189) 


4812 63X3 


1389 y 


4167 6 


9) 


645904 694 X ^ 


158700 


645904 


2776 





161476 



EVOLUTION. 67 

the remainder (4) annex the next period (812) for a resolvend 
(4812). 

3. Write 300 times the square (4) of the figure in the root 
for a partial divisor (1200), and find how often it is contained 
in the resolvend (4812), then place the number of times (3) 
to the right of the figure in the root. Again to the former 
part of the root (2) add its double (4), to the sum (6) annex 
the trial figure (3), and multiply this number (63) by it (3) ; 
then add the product (189) to the partial divisor (1200) for 
a complete divisor (1389). Multiply this number (1389) 
by the figure last placed in the root (3), subtract the pro- 
duct (4167) from the resolvend (4812), and to the remainder 
(645) annex the next period (904) for a new resolvend 
(645904). 

4. Place the square of the last figure in the root (9) below 
the last complete divisor (1389), add it (9) and the two lines 
above it (189 and 1389) together, and to the sum (1587) 
annex two ciphers for a new partial divisor (158700). 

5. With this partial divisor find another figure (4), and 
place it in the root. To the number on the right (63), which 
was multiplied by the last figure of the root (3), add the 
double of that figure (6), annex to the sum (69) the new 
trial figure (4), then multiply the number thus found (694) 
by the trial figure (4), and add the product (2776) to the 
partial divisor (158700) for a complete divisor (161476), and 
so proceed till all the periods are brought down. 

Note. When there is a remainder, after bringing down the 
last period, the root may be carried on decimally by annexing 
periods of three ciphers each to the remainder. 

The cube root of a fraction is found by taking the cube 
roots of its terms when they are exact cubes ; if not, the 
fraction must be reduced to its equivalent decimal and its 
cube root taken. 

Extract the cube roots of, 

1. 76765625, 143877824, 260917119, 485587656. 

2. 997002999, 25128-011089, 143795466-919, 865-250742889. 

3. 14-75, 118-62, 1-47825, 7-6, 8-36, 94-8, to 6 places of dec. 

4. 2, 4, 6, 7, 9, 12, 13, 16, to 6 places of decimals. 

5. 1030607060301, 27054306369020601. 

«• Uh mh HU, H, 51, -000000405224. 

Note. Similar solids are to each other as the cubes of their 
like dimensions. 



68 EVOLUTION. 

7. The side of a cubic vessel is 10 in. ; what should be the 
side of another to contain ^ as much ? 

8. A block of granite is 6 ft. long, 6 ft. broad, and 4 ft. 
thick ; what are the dimensions of another 3 times as heavy? 

9. A stone is 8^ ft. long, 7 ft. broad, and 5 ft. thick ; what 
are the dimensions of another 9 times as large, and the side 
of a cube equal to both ? 

10. A cubic block of marble is 8 ft. in the side ; what are 
the length and breadth of another 3 times the weight, whose 
thickness is 3 ft., and length twice the breadth ? 

11. The solid content of a cube is 407 ft. 1673-in. ; how 
many square ft. are in its surface ? 

12. A vessel contains 411540 c. in., and has its sides in 
proportion to the numbers 3, 4, and 5 ; what are its sides? 



COMPOUND INTEREST. 

When a sum of money is put out to interest, and its 
amount at the end of a fixed period is considered the 
principal for the same period and at the same rate, the 
original sum is said to be improved at Compound Interest. 
Case I. Given the principal, rate, and time ; to find 
the amount and the interest. 

Ex. 1. Find the compound interest of £100 for 3 
years at 2 per cent, per annum, the interest payable 
yearly. Here 2 per cent. =: j^-^ = ^\^. 

j5»5 ) £1 00 Principal for 1 st year. 

2 Interest for 1st year, 

jig) 102 Principal for 2d year. 

2*04 Interest for 2d year. 
3^) 104-04 Principal for 3d year. 
2-0808 Interest for 3d year. 
106-1208 Amount at end of 3 years. 
100 Principal for 1st year. 

£6, 2s. 5d. = £6*1208 Interest for 3 years. 

1. Find the compound interest of £875 for 5 years at 2, 2|, 
4, 5, 7|, and 10 per cent., the interest payable yearly. 

2. Required the amount of £450, 10s. for 6 years at 2, 2^, 
4, 5, 7^, and 10 per cent, per annum, compound interest. 

When the number of payments of interest is small, and 
the rate an aliquot part of 100, this method answers very 
well. The followiner method is suitable for all cases : 



COMPOUND INTEREST. 69 

The amount of £1 for 4 years at 3 per cent., when the in- 
terest is payable yearly, is that power of the amount of £1 
for 1 year (1'03) which corresponds with the number of years 
(4), i.e. (l-OS)* ; when the interest is payable half-yearly, the 
amount of £1 for half-a-year is 1-015, and for 4 years or 8 
half-years it is (1-015)« ; in the same way when the interest 
is payable quarterly the amount of £1 for 4 years is (1 -0075) ^ «. 

Ex. 2. Find the compound interest of £375 for 5 years 
at 5 per cent., the int. payable (1) yearly, (2) half-yearly. 

Sol. 1. Amt. of £1 for 5 ye. at 5 p. cent.=(l-05)s=l -276282 

Multiply by 375 

Amt. of £375 for 5 ye. at 5 per cent. = £478*605750 

Subtract 375 

gQj^ 2. Compound interest of £375=£103,12s.l4d. 

Amt.of£lfor5ye.,i.e.l0h.-ye.at5p.c.=(l-025)^<'=£l-28008 

Multiply by 375 

Amt. of £375 for 10 h.-ye. at 5 p. cent, per an.=:£480-03000 

Subtract 375 
Compound interest of £375=£105,0s.7^d. 

3. What is the compound interest of £750 for 5 years at 3 
per cent., 8 years at 4 per cent., and 7 years at 3 J per cent., 
the interest payable yearly ? 

4. What is the amount of £350 for 6 years at 2 p. c, 8 ye. 
at 2 J p. c, and 10 ye. at 3i p. c. compound interest, the in- 
terest payable yearly ? 

6. What is the compound interest of £120, 10s. for 4 ye. at 
2 p. c, 5 ye. at 4 p. c, and 6 ye. at 5 p. c, interest payable 
half-yearly ? 

6. What is the amount of £240, 12s. 6d. for 2 years at 3 
p. c, 3 ye. at 4 p. c, and 2f ye. at 5 p. c. compound interest, 
the interest payable quarterly ? 

7. What is the compound interest of £375, 14s. for 3J ye. 
at 3 p. c, 4 ye. at 2J p. c, and 4^ ye. at 6 p. c, the interest 
payable three times yearly ? 

8. A merchant began business with £1000, which he in- 
creases every half-year by J ; what will his capital be at the 
end of 5 J years ? 

Case II. To find the interest on bonds when the in- 
tervals between the payments are great. 

Ex. Lent on bond £1050 at 4 per cent., Aug. 12th, 
1855; and received on Sept. 15th, 1856, £300; on Oct. 



70 COMPOUND INTEREST. 

20th, 1869, £350 : what was the balance due, including 
the interest on Dec. 15th, 1870 ? Ans. £502, 19s. 84d. 
Aug. 12, 1867. Lent at 4 per cent., . . . £1050 

Interest on ditto for 399 days, 45-9123 

Amount, 1095-9123 

Sept. 15, 1868. Received in part, 300 

Balance, 795-9123 

Interest on ditto for 400 days, 34-8893 

Amount, 830-8016 

Oct. 20, 1869. Received in part, 350 

Balance, 480-8016 

Interest on ditto for 421 days, 22-1827 

Amount, 502*9843 

Dec. 15, 1870. Received in full, 502-9843 

9. A bond of £975 became due on January 15th, 1866, of 
which was paid April 21st, 1867, £250; July 29th, 1868, £200; 
Oct. 16th, 1869, £300; and the balance on Dec. 17th, 1870: 
what was then paid, including interest at 4J per cent. ? 

10. Lent on bond £1225, at 2^ per cent., on March 4th, 

1864, and received £320 on June 17th, 1865 ; £250 on Aug. 
7th, 1866, £300 on Nov. 12th, 1867; £200 on Jan. 13th, 
1869 ; and the balance on April i9th, 1870 : what was then 
due, including the interest ? 

11. Borrowed on bond, at 3 per cent., £875 on Jan. 4th, 

1865, and paid £200 on March 7th, 1866; £150 on June 13th, 
1867 ; £200 on Sept. 11th, 1868; £150 on Nov. 17th, 1869; 
and the balance on Jan. 4th; 1871 : what was then paid, in- 
cluding the interest ? 

12. Borrowed, at 3 J per cent, £1500 on June 4th, 1865, of 
which was paid, Aug. 1st, 1866, £350; Oct. 9th, 1867, £250; 
Nov. 21st, 1868, £400; and the balance on Dec. 31st, 1869: 
what was then paid, including the interest ? 



MISCELLANEOUS QUESTIONS. 

1. How many francs, each 9^d., are equal in value to 209 
half-crowns ? 

2. If whisky at 14s. 6d., 15s. 6d., 16s., and 17s. a-gallon, 
be mixed in equal quantities ; what should a gallon of the 
mixture be sold for to gain 5 per cent, and allow a discount 
of 6| per cent. ? 

3. A cubic foot of water weighs 1000 oz. ; how many tons 
of water will a cistern 16 ft. 6 in. long, 15 ft. 4 in. broad, 
and 5 ft. 6 in. deep contain ? 



MISCELLANEOUS QUESTIONS. 71 

4. Find the value of § gui. ; reduce 5s. 7^d. to the frac. of 
9 gui., and 3 ml. 2 fur, to the frac. of 1 ml. 6 fur. 12 poles. 

5. A ladder, 45 ft. long, reaches to a window 27 ft. from 
the ground on one side of a street, and, without moving the 
foot, it reaches to a window 36 ft. high on the other side ; 
find the breadth of the street. 

6. 248 trees are planted in the breadth of a plantation at 
a distance of 5 ft. 4 in. from each other; what is the breadth 
of the plantation, allowing the same distance between the 
trees and the fence on both sides ? 

7. If £435 gains £58, 14s. 6d. in 4 J years ; what is the rate 
per cent. ? 

8. The side of a cubic piece of marble is 32 ft. ; find the 
side of a piece 7^ times as large. 

9. Find the value of a rectangular piece of ground 48 ft. 

4 in. by 34 ft. 6 in., at 24s. per s. ft. 

10. Exchanged 19 cwt. 2 qr. 12 lb. of cofiee at £9, 6s. 8d. 
p. cwt. for sugar at 7^d. and tea at 4s. 6d. per lb. ; there was 

5 times as much sugar as tea : how much was there of each ? 

11. If 7 lb. sugar be equal to 3 of cofi^ee, and 6 of cofiee to 
2^ of tea; how many lbs. tea are equal to 168 lbs. sugar? 

12. A cask is f full, and after 40 gals, were run off", it was 
^5 full ; how many gals, could the cask contain ? 

13. If a globe 9 in. diameter weighs 27 lbs. ; what will a 
globe weigh whose diameter is 25 in. ? 

14. Purchased 1260 lbs. tea at 4s. per lb., but J of it being 
damaged, 25 per cent, was lost in selling it ; the remainder 
was sold at 4s. 6d. per lb. : how much per cent, was gained 
at the latter price and on the whole ? 

15. In 1854, the number of births registered in England 
was 324069 males and 310336 females; how many males 
were bom for 100 females ? 

16. What fraction multiplied by the square of 1^, and the 
product divided by the cube root of §i§, produces 3 ? 

17. Invested £10710 in new 2^ per cents at 74f ; how 
much must I invest in 3 per cents at 90J to produce an in- 
come of £500 yearly ? 

18. In 1801 the population of Scotland was 1608420, and 
in 1851 it was 2888742 ; what was the increase per cent, 
during that time ? 

19. What is the thickness of a solid foot of stone that is 
9 ft. 4 in. lon^ and 2 ft. 6 in. broad? 

20. A certain number of persons were fined 5s. 6d. each, 
but 3 of them having no money, each of the others had to pay 
Is. lOd. more than their fine ; how many persons were there ? 



72 MISCELLANEOUS QUESTIONS. 

21. Reduce 14s. 11 Jd. to the dec. of £5, 19s. 6d., and y\ of 
2f d. to the dec. of half-a-crown. 

22. In 1855 the number of births registered in Scotland 
was 93498, of which 47872 were males, and 45626 females ; 
what decimal of the whole were males and females ? 

23. Find the present value of £475, 15s. due 4 years hence, 
at 2^ per cent, simple interest. 

24. A grocer buys sugar at 5d. and 7d. per lb. and mixes 
them in the proportion of 3 ; 5 ; what will he gain per cent, 
by selling it at 7id. per lb. ? 

25. A square contains exactly 2^ ac. ; find its side. 

26. In the Centigrade thermometer the freezing-point is 
zero, and the boiling-point 100°; in Fahrenheit's the freezing- 
point is 32° and the boiling-point 212° : what degi*ee C. corre- 
sponds to 68"" F., and what degree F. corresponds to 45° C. ? 

27. What is the shortest piece of cloth that shall at the 
same time be an exact number of yards, EngHsh ells, Flem- 
ish ells, and French ells ? 

28. A person spends £10, 4s. 2d. in 35 days, and he saves 
£93, 10s. lOd. yearly; what is his income? 

29. ^ of an army was killed in battle, j'jj was taken pris- 
oners, Y*^ died from sickness, ^'^ was in hospital, and 31375 
effective men remained ; how many were there at first ? 

30. A person being asked his age, answered, if to my age 
you add ^ and i of it, the sum will be 59 ; what was his age? 

31. The corn produced by a field was found to be 200 qrs. 
or ^ more than what was sown ; how much was sown ? 

32. Bought £126 worth of tea at 4s. 6d. per lb., some of 
which being damaged, I sold the remainder at 4s. 9d. per lb., 
which produced £106, 17s. 6d. ; what quantity was damaged? 

33. A gentleman gave to three persons £78, 6s. 6d. ; the 
second received § of the first, and the third f of the second : 
what did each receive ? 

34. A person bought a horse, gig, and harness for £60 ; the 
horse cost 7 times as much as the harness, and the gig was A 
the price of the horse and harness ; what was the price of each? 

35. What must be the depth of a cistern which is 6 ft. 3 in. 
long and 4ft. 6 in. broad, to contain 481*665 gals, of water? 

36. Light travels at the rate of 192000 miles per sec. ; how 
long does it take to travel from the sun to the earth, a dis- 
tance of 95 millions of miles ? 



73 



DECIMAL COINAGE. 

The pupil, having worked the Elementary Exercises in 
Decimal Coinage, at the end of the " Lessons in Arith- 
metic," and also those given under Decimal Fractions 
(page 30), may now solve the following questions. 

TABLE OF DECIMAL MONEY. 

lmil(m.) =£^^V^ = |4f. 

10 mils = lcent(c.) =£'iio = 2|d. 

100 mils = 10 cents = 1 florin (fl.) = £^V = 2s. 

1000 mils = 100 cents = 10 florins = £l = 20s. 

Ex. 1. Reduce £12, 17s. 9d. from the present to the 

proposed system. Ans. £12-8875 = £12, 8 fl. 8 c. 7i m. 

Here, bv Case V. p. 32, £12, 17s. 9d. = £12-8875 = £12, 

8fl. 8c. 7^m. 

Ex. 2. Reduce £7, 8 fl. 2 c. 5 m. from the proposed to 
the present system. Ans. £7, 16s. 6d. 

Here, by Case VI. p. 32, £7, 8fl. 2c. 5m. = £7-825 = £7, 
16s. 6d. 

Reduce from the present to the proposed system, 

1. 6s. 6d. 

2. 7 3 

3. 18 4 

4. 19 7 

Reduce from the proposed to the present system, 



5. 


14s. 


2^d. 


9. 


£2, 8s. 9d. 


13. 


£12, 13s 


4d. 


6. 


13 


7^ 


10. 


4 15 8 


14. 


15 16 


8 


7. 


15 


8i 


11. 


7 6 8 


15. 


17 14 


7 


8. 


17 


5 


12. 


9 10 10 


IG. 


21 12 


8 



17. 


£-425 


18. 


•675 


19. 


•850 


20. 


•925 



21. £-763 

22. ^574 

23. -235 

24. -075 



25. £4-6375 

26. 6-8125 

27. 7-4025 

28. 9-7875 



29. £10-7750 

30. 12-6666 

31. 15-3333 

32. 17-8166 



33. A man earns £58, 7fl. 7c. 5m. per annum, his expenses 
are £49, 8fl. 9c. 7m. ; how much does he save ? 

34. What is the value of 27oz. of silver at 2fl. 7c. 5m. 
per oz. ? 

35. A man's wages are £1, 2fl. 7c. 5m. weekly ; how much 
do they amount to in a year ? 

36. What is the weekly rent of a house, when the yearly 
rent is £65, Ifl. 4m. ? 

37. If 35 quarters of oats cost £53, 3fl. 7c. 5m. ; what is 
the rate per quarter ? 



74 DECIMAL COINAGE. 

38. A bankrupt who owed £3595, paid his creditors £2786, 
Ifl. 2c. 5m. ; how much did he pay per £1 ? 

39. If 15 gallons of whisky cost £13, Ifl. 2c. 5m.; what 
should he paid for a cask containing 125 gals. ? 

40. Find by practice the value of 17cwt. 2qrs. 14 lbs. of 
sugar at £2, 4fl. 5c. per cwt. 

41. A man's wages are £50, 2fl. 2c. 5m. for 146 days; how 
much is this per annum ? 

42. What is the commission on £575, 2c. 5m. at 2 and 3J 
per cent, ? 

43. What is the brokerage on £796, 2fl. 5c. 6m. at J, J, 
and § per cent. ? 

44. How much should be paid for insuring £5750, 2fl. 5c. 
at 3 per cent., and policy Ifl. 2c. 5m. per cent. ? 

45. What is the interest on £487, 7fl. 5c. for 4 years, at 
2^ and 4 per cent. ? 

46. Find the amt. of £896, 5fl. for 3 years, at 2 and 5 p. c. 

47. Find the interest on £228, Ifl. 2c. 5m. for 198 days, at 
4 and 4^ per cent. 

48. What should £2851, 5fl. 6c. 2Jm. amount to in 1 year 
and 99 days, at 4 per cent. ? 

49. What sum will amount to £251, 8fl. 7c. 5m. in 4 
months, at 2^ per cent. ? 

50. Divide £153, Ifl. 4m. among 4 persons, so that J the 
share of the first, J of that of the second, J of that of the 
third, and \ of that of the second may make up the same sum. 

51. What is the rent of a farm of 525 ac. 3 ro. 25 per. at 
£3, 5fl. 2c. 8m. per acre ? 

52. A bill of £919, 8fl., dated Feb. 14, at 6 months, was 
discounted June 13, at 3^ per cent. ; what was the net pro- 
ceeds, deducting commission ^ per cent. ? 

53. If 7 1 per cent is gained by selling tea at £22, 5fl. 7c. 
5m. per cwt. ; what is gained or lost per cent, by selling it 
at £22, 8fl. 9c. per cwt. ? 

54. In what proportions should tea at Ifl. 2c. 5m., and 2fl. 
per lb. be mixed to reduce the price to Ifl. 7c. 5m. per lb. ? 

55. What part of £9, 7fl. 5c. is £8, 4c. 3|m. ? 

56. In what time will the interest of £437, 6fl. 7c. 5m. pay 
a debt of £52, 5fl. 2c. Im., at 4 per cent, per annum? 



KDIKBURGH : PRINTED BY OLIVER AND BOYD. 



EDUCATIONAL WOEKS 

PUBLISHED BY 

OLIVER AND BOYD, EDINBURGH; 

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A Specimen Copy of any worh mil be sent to Principals ofScliools^ 
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Oliveb and Boyd's New Code Class-Books, page 4. 



English Reading, G-rammar, etc. 
Armstrong's Eng. Composition.P. 7 

Eng. Etymology 7 

Colville's NewCode Reading-Books 4 

Connon's English Grammar 6 

First Spelling-Book 6 

Dalgleisli's English Grammars... 6 

Gram. Analysis 6 

Eng. Composition 6 

Demaus's Paradise Lost 8 

;. Analysis of Sentences .. 8 

Douglas's English. Grammars 5 

Progressive Eng. Reader 5 

Selections for Recitation 5 

Spelling and Dictation. 5 

English Etymology 5 

Ewing's Elocution 8 

Fisher's Assembly's Catechism... 8 

Lennie's English Grammar 6 

M'CuUoch's Reading-Books 3 

English Grammar.... 3 

M'Dowall's Rhetorical Readings.. 8 

Milieu's English Grammar 8 

Morell's Poetical Reading-Book... 7 
Pryde's Studies in Composition... 7 

Reid's English Grammar 7 

English Composition 7 

English Dictionary 7 

Sess. School Etymological Guide.. 8 
...... Old & New Test. Biogi-aphies 8 

Shakspeare's Richard II 5 

Spalding's English Litei-ature 7 

White's English Grammar 8 

"Wordsworth's Excursion 5 

Object-Lessons. 

On the Vegetable Kingdom 8 

Ross's How to Train Eyes and Ears 8 



Geography and Astronomy. 

Clyde's School Geography P. 9 

Elementary Geography.. 9 

Douglas's Introductory Geogy 10 

Progressive Geogy 10 

Text-Book of Geogy 10 

Edin. Acad. Modern Geography ..11 

Ancient Geography..ll 

Ewing's Geography 11 

Atlas 11 

LawBon's Geog. of British Empire 10 

New Code Geographies 4 

Physical Geography..., 4 

Murphy's Bible Atlas 11 

Reid's First Book of Geography.. 10 

Modern Geography .',..10 

Sacred Geography 10 

Atlases 11 

Reid's (Hugo) Elements of Astro- 
nomy 11 

Phys. Geography..ll 

Stewart's Modem Geography 9 

White's Abstract of Geography... 9 

System of Geography.,.. 9 

Atlas 11 

School Songs. 
Hunter's Books on Vocal Music... 17 
School Psalmody 17 

Household Economy. 
Gordon's Household Economy 8 

History. 

Corkran's History of England 12 

Simpson's Scotland 13 

Goldsmith's England..l3 

Greece ...,13 

Rome 13 



INDEX. 



Tytler's General History P. 13 

Watt's Scripture History 13 

White's Universal History 12, 13 

England for Jun. Classes 12 

History of France 12 

Great Britain and Ireland 12 

Sacred History 13 

Histories of Scotland 12 

History of Rome 13 

Writing, Arithmetic, etc. 

Gray's Arithmetic 15 

Hutton's Arithmetic, etc 15 

Ingram's Principles of Arithmetic 15 

Maclaren's Arithmetic 16 

Book-keeping 16 

Melrose's Arithmetic 15 

Scott's Arithmetical Works 16 

.-, Copy Books & Copy Lines..l6 

Smith's Arithmetical Works 14 

Stewart's Arithmetical Works 15 

Trotter's Arithmetical Works..l4, 16 

New Code Arithmetic... 4 

Hutton's Book-keeping. 15 

Gaelic. 
Forbes's Gaelic Grammar 16 

Mathematics, etc. 
Ingram's System of Mathematics. .16 

Mensuration, by Trotter 16 

Trotters Key to Ingram's Mathe- 
matics 16 

Manual of Logarithms...l6 

Ingram's Euclid 16 

Algebra 16 

Nicol's Sciences 17 

French. 
Beljame's French Grammar, etc. ..20 
Caron's First French Class-Book ..20 

First French Reading- Book. .20 

French Grammar 20 

Chambaud's Fables Choisies 18 

Christison's French Grammar 20 

Fables et Contes Cboisis 20 

Fleury's History of France. .20 

French New Testament IS 

Gibson's Le Petit Fablier 18 

Hallard's French Grammar 20 

Schneider's First French Course.. .18 

Conversation- Grammar.lS 

French Reader 18 

French Manual 18 

ficrin Littdraire 16 



Surenne's Dictionaries P. 19 

New French Manual, etc.. .19 

New French Dialogues 19 

French Classics 19,20 

French Reading Instructor 20 

Wolski's French Extracts '20 

French Grammar .20 ' 



Latin and Greek. 

Ainsworth's Latin Dictionary 23 

Cicero's Orationes Selectee 24 

Cato Major, De Officii8....24 

Clyde's Greek Syntax 21 

Dymock's Csesar and Sallust 22 

Edin. Academy Class-Books: — 
Rudiments of Latin Language... 21 

Latin Delectus 21 

Rudiments of Greek Language.. .21 

Greek Extracts 21 

Ciceronis Opera Selecta 21 

Selecta e Poetis 21 

Ferguson's (Prof.)Gram. Exercises 24 

.....<r. Latin Delectus, 24 

Ovid's Metamorphoses24 

Fergussou's (Dr) Xenophon^s Ana- 
basis 23 

Greek Gram. Exercises 23 

Homer's Iliad, witli Vocab. 23 

Geddes' (Prof.) Greek Grammar.. .21 

Greek Testament, by Duncan 23 

Hunter's Ruddiman's Rudiments .22 

Sallust, Virgil, & Horace 22 

Livy, Books 21 to 25 22 

Latin Testament, by Beza 23 

Macgowan's Latin Lessons 22 

Mair's Introduction, by Stewart... 23 
Massie's Latin Prose Composition 22 

M'Dowall's Csesar and Virgil 22 

Melville's Lectiones Selectae 22 

Neilson's Eutropius 22 

Stewart's Cornelius Nepos 23 

Veitch's Homer's Iliad 23 

German. 
Fischart's New German Reader... 24 

Logic. 
Port-Royal Logic (Prof, Bayne6')24 

School Registers. 
Pupil's Daily Register of Marks. 17 
School Register of Attendance, 

Absence, and Fees 17 

Geometrical Drawing. 
Kennedy's Grade Geometiy 17 



Messrs Oliver and Boyd were awarded Medals for their Educa- 
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ENGLISH BEADING, GEAMMAE, ETC. 

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DR M'CULLOCH'S SERIES OF CLASS-BOOKS. 

These Books are intended for the use of Schools where the general 
mental culture of the pupil, as well as his proficiency in the art of reading, 
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They form, collectively, a progressional Series, so constructed and 
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the way for those of greater difficulty. 

The subject-matter of the Books is purposely miscellaneous. Yet it is 
always of a character to excite the interest and enlarge the knowledge of 
the reader. And with the design of more effectually promoting his mental 
growth and nurture, the various topics are introduced in an order con- 
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usually developed. 

That the moral feelings of the pupil may not be without their proper 
stimulus and nutriment, the lessons are pervaded throughout by the 
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DR MCCULLOCH'S READING-BOOKS FOR SCHOOLS. 

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THIRD READING- BOOK, containing simple Pieces in 

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COURSE OF ELEMENTARY READING in Science 
and LiTEEATURE, compiled from popular Writers, 39 Woodcuts, 3s. 

MANUAL OF ENGLISH GRAMMAR, Philosophical 
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By James Colvillk, M.A., En;?lish Master, Glasgow Academy; late Eng- 
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Part I., embracing Standards 1 and 2. 36 pages. 2d. — Answers, 3d. 
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REID'S RUDIMENTS OF MODERN GEOGRAPHY, with 36 

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DOUGLAS'S PROGRESSIVE GEOGRAPHY, a New Work, 
LENNIE'S GRAMMAR, with Analysis of Sentences, 
DOUGLASS GRAMMAR, with Analysis of Sentences, . 
REID'S GRAMMAR, with Analysis of Sentences, 
HUNTER'S SCHOOL SONGS, with Music, 



THE PRINCIPLES OF ENGLISH GRAMMAR; with a 

Series of Progressive Exercises, and a Supplementary Treatise on 
Analysis of Sentences. By Dr James Douglas, lately Teacher of 
English, Great King Street, Edinburgh. Is. 6d. 

DOUGLAS'S INITIATORY GRAMMAR, for Junior 
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DOUGLAS'S PROGRESSIVE ENGLISH READER. 

. A New Series of English Reading-Books. The Earlier Books are illus- 
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First Book. 2d. I Third Book. Is. I Fifth Book. 2s. 
Second Book. 4d. | Fourth Book. Is. 6d. | Sixth Book. 2s. 6d. 

DOUGLAS'S SELECTIONS FOR RECITATION, with 

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DOUGLAS'S SPELLING AND DICTATION EXERCISES. 

144 pages, price Is. 

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DOUGLAS'S ENGLISH ETYMOLOGY: A Text-Book of 
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SHAKESPEARE'S KING RICHARD 11, With Historical 

and Critical Introductions; Grammatical, Philological, and other Notes, 
etc. Adapted for Training Colleges. By Rev. Canon Rodinson, M.A., 
late Principal of the Diocesan Training College, York. 2s. 

WORDSWORTH'S EXCURSION. THE WANDERER. 

With Notes to aid in Analysis and Paraphrasing. By Canon Robinson. 
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6 ENGLISH READING, GRAMMAR, ETC. 

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Comprising the Substance of all the most approved English Grammars, 
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ANALYSIS OF SENTENCES: Being the Appendix to 
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DALGLEISH'S PROGRESSIVE ENGLISH GRAMMAR, 

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Instruction and Use of Schools. By lingo Reid, Member of the College 
of Preceptors. With 65 Wood Engravings. 3s. 

REID'S ELEMENTS OF PHYSICAL GEOGRAPHY; 

with Outlines of Geology, Mathematical Geography, and Astrox- 
OMY, and Questions for Examination. With numerous Illustrations, 
and a large coloured Physical Chart of the Globe. Is. 



SCHOOL ATLASES. 

A GENERAL ATLAS OF MODERN GEOGRAPHY; 29 

Maps, Coloured. By Thomas Ewing. 7s. 6d. 

WHITE'S ELEMENTARY ATLAS OF MODERN GEO- 
GRAPHY. 4to, 10 Maps, Coloured. 2s. 6d. 

Contents.— 1. The W^orld; 2. Europe; 3. Asia; 4. Africa; 5. Nortli 
America; 6. South America; 7. Euglaud; 8. Scotland; 9. Ireland; 10. 
Palestine. 

A SCHOOL ATLAS OF MODERN GEOGRAPHY. 4to, 
16 Maps, Coloured. By Alexander Reid, LL.D., late Head Master of 
the Edinburgh Institution, etc. 5s. 

REID'S INTRODUCTORY ATLAS OF MODERN GEO- 
GRAPHY. 4to, 10 Maps, Coloured. 2s. 6d. 

Contents.— 1. The World; 2. Europe; 3. Asia; 4. Africa; 5. North 
America; 6. South America; 7. England; 8. Scotland; 9. Ireland; 10. 
Palestine. 

MURPHY'S BIBLE ATLAS of 24 Maps, with Historical 

Descriptions. Is. 6d. coloured. 

Witness. — " We recommend this Atlas to teachers, parents, and indi- 
vidual Christians, as a comprehensive and cheap auxiliary to the intelli- 
gent reading of the Scriptures." 



12 



HISTOEY. 



The works in this department have been prepared with the greatest care. 
They will be found to include Class-books for Junior and Senior Classes in 
all the branches of History generally taught in the best schools. While 
the utmost attention has been paid to accuracy, the narratives have in 
every case been rendered as instructive and pleasing as possible, so as to 
relieve the study from the tediousness of a mere dry detail of facts, 

A CONCISE HISTORY OF ENGLAND IN EPOCHS. 

By J. F. CoRKRAN. With Maps and Genealogical and Chronological 

Tables, and comprehensive Questions to each Chapter. New Edition, 

with the History continued. 2s. 6d. 

The writer has endeavoured to convey a broad and full impression of 
the great Epochs, and to develop with care, but in subordination to the 
rest of the narrative, the growth of Law and of the Constitution. 

HISTORY OF ENGLAND FOR JUNIOR CLASSES; with 

Questions for Examination. Edited by Henry White, B.A. Trinity 

College, Cambridge, M.A. and Ph.D. Heidelberg. Is. 6d. 

Athenceum. — " A cheap and excellent history of England, admirably 

adapted for the use of junior classes. The various changes that have 

taken place in our constitution are briefly but clearly described. It is 

surprising how successfully the editor has not merely avoided the obscurity 

which generally accompanies brevity, but invested his narrative with an 

interest too often wanting in larger historical works. The information 

conveyed is thoroughly sound; and the utility of the book is much 

increased by the addition of examination questions at the end of each 

chapter." 

HISTORY OF GREAT BRITAIN AND IRELAND; with 

an Account of the pi*esent State and Resources of the United Kingdom 
and its Colonies. With Questions and a Map. By Dr White. 3s. 
Athenceum. — " A carefully compiled history for the use of schools. The 
writer has consulted the more recent authorities: his opinions are liberal, 
and on the whole just and impartial ; the succession of events is developed 
with clearness, and with more of that picturesque effect which so delights 
the young than is common in historical abstracts." 

HISTORY OF SCOTLAND FOR JUNIOR CLASSES; 

with Questions for Examination. Edited by Dr White. Is. 6d. 

HISTORY OF SCOTLAND FOR SENIOR CLASSES; 

Avith Questions for Examination. Edited by Dr White. 3s. 6d. 

HISTORY OF FRANCE; with Questions for Examination, 

and a Map. Edited by Dr White, 3s. 6d. 

Athenceum. — " Dr White is remarkably happy in combining convenient 
brevity with sufficiency of information, clearness of exposition, and interest 
of detail. He sliows great judgment in apportioning to each subject its 
due amount of consideration." 

OUTLINES OF UNIVERSAL HISTORY. Edited by Dr 

White. 2s. 

Spectator.— '•'■'DisUnct in its arrangement, skilful in its selection of 
leading features, close and clear in its narrative." 



HISTORY. 13 



DR WHITE'S ELEMENTS OF UNIVERSAL HISTORY, 

On a New and Systematic Plan. In Thbeb Parts. Part I. Ancient 
History; Part II. History of the Middle Ages; Part III. Modem 
History. With a Map of the World. 7s. ; or in Parts, 2s. 6d. each. 

This work contains numerous synoptical and other tables, to guide the 
researches of the student, with sketches of literature, antiquities, and 
manners during each of the great chronological epochs. 

OUTLINES OF THE HISTORY OF ROME; with Ques- 
tions for Examination. Edited by Dr White. Is. 6d. 

London Bcview .—" This abridgment is admirably adapted for the use of 
schools,— the best book that a teacher could place in the hand of a youthful 
student." 

SACREO HISTORY, from the Creation of the World to the 
Destraction of Jerusalem. With Questions for Examination. Edited by 
Dr White. Is. 6d. 

ELEMENTS OF GENERAL HISTORY, Ancient and 
Modem. To which are added, a Comparative View of Ancient and 
Modern Geography, and a Table of Chronology. By Alex. Fraseb 
Tytlee, Lord Woodhouselee, formerly Professor of History in the 
University of Edinburgh. New Edition, with the History continued. 
With two large Maps, etc. 3s. 6d, 

WATTS' CATECHISM OF SCRIPTURE HISTORY, and 

of the Condition of the Jews from the Close of the Old Testament to the 
Time of Christ. With Inteoddction by W. K. Tweedib, D.D. 28. 

SIMPSON'S HISTORY OF SCOTLAND; with an Outline 
of the British Constitution, and Questions for Examination at the end ol 
each Section. 3s. 6d. 

SIMPSON'S GOLDSMITH'S HISTORY OF ENGLAND; 

With the Narrative brought down to the Middle of the Nineteenth 
Century. To which is added an Outline of the British Constitution. 
With Questions for Examination at the end of each Section. 3s. 6d. 

SIMPSON'S GOLDSMITH'S HISTORY OF GREECE. 

With Questions for Examination at the end of each Section. 3s. 6d. 

SIMPSON'S GOLDSMITH'S HISTORY OF ROME. With 

Questions foi Exaninatim at the end of each Section. 3s. 6d. 



14 WRITING, ARITHMETIC, AND BOOK-KEEPING. 



WKITHTG, AKITHMETIO, AND BOOK-KEEPINa. 

This section will be found to contain works in extensive use in many of the 
best schools in the United Kingdom. The successive editions have been 
carefully revised and amended. 

ARITHMETIC ADAPTED TO THE NEW CODE, in 

Three Parts. By Alexander Trotter, Teacher of Mathematics, etc., 
Edinburgh. Parts I. and IL, embracing the first four Standards^ are now 
Beady. Each containing 36 pages, 2d., stifif wrapper. Answers to 
Parts I. and II., price 3d. each. Part III. in Preparation, 

PRACTICAL ARITHMETIC FOR JUNIOR CLASSES. 

By Henry G. C. Smith, Teacher of Arithmetic and Mathematics in 
George Heriot's Hospital. 64 pages, 6d. stiff wrapper. Answers, 6d. 

From the Rev. Philip Kelland, A.M., F.R.SS. L. & E., late Fellow oj 
Queens^ College, Cambridge, Professor of Mathematics in the University of 
Edinburgh. 

"I am glad to learn that Mr Smith's Manual for Junior Classes, the MS, 
of which I have examined, is nearly ready for publication. Trusting that 
the Illustrative Processes which he has exhibited may prove as efficient in 
other hands as they have proved in his own, I have great pleasure in 
recommending the work, being satisfied that a better Arithmetician and a 
more judicious Teacher than Mr Smith is ndt to be found." 

PRACTICAL ARITHMETIC FOR SENIOR CLASSES; 

Being a Continuation of the above. By Henry G. C. Smith. 2s. 

Answers, 6d. Key, 2s. 6d. 

*** The Exercises in both works, which are copious and original, have been 
constructed so as to combine interest with utility. They are accompanied by 
illustrative processes. 

LESSONS IN ARITHMETIC FOR JUNIOR CLASSES. 

By James Trotter. 66 pages, 6d. stiff wrapper; orSd. cloth. Answers,6d. 

This book was carefully revised, and enlarged by the introduction of 
Simple Examples of the various rules, worked out at length and fully 
explained, and of Practical Exercises, by the Author's son, Mr Alexander 
Trotter, Teacher of Mathematics, etc., Edinburgh ; and to the present 
edition Exercises on the proposed Decimal Coinage have been added. 

LESSONS IN ARITHMETIC for ADVANCED CLASSES; 

Being a Continuation of the Lessons in Arithmetic for Junior Classes. 
Containing Vulgar and Decimal Fractions; Simple and Compound 
Proportion, with their Applications; Simple and Compound Interest; 
Involution and Evolution, etc. By Alexander Trotter. New Edition, 
with Exercises on the proposed Decimal Coinage. 76 pages, 6d. in stiff 
wrapper ; or 8d. cloth Ansioers, 6d. 

Each subject is also accompanied by an example fully worked out and 
minutely explained. The Exercises are numerous and practical. 



WRITING, ARITHMETIC, AND BOOK-KEEPING. 15 

A COMPLETE SYSTEM OF ARITHMETIC, Theoretical 

and Pi'actical; containing the Fundamental Rules, and their Application 
to Mercantile Computations; Vulgar and Decimal Fractions; Involution 
and Evolution; Series; Annuities, Certain and Contingent. By Mr 
Tbottee. 8s. Key, 4s. 6d. 

*^* All the 3400 Exercises in this work are new. They are applicable to the 
tusiness of real life, and are framed in such a way as to lead the pupil to 
reason on the matter. There are upwards of 200 Examples wrought out at 
lengtlt and minutely explained. 

INGRAM'S PRINCIPLES OF ARITHMETIC, and their 
Application to Business explained in a Popular Manner, and clearly 
Illustrated by Simple Rules and Numerous Examples. Remodelled and 
greatly Enlarged, with Exercises on the proposed Decimal Coinage. By 
Alkxandeb Teotteb, Teacher of Mathematics, etc., Edinburgh. Is. 
Key, 2s. 

Each rule is followed ty an example wrought out at length, and is illustrated 
by a great variety of practical questions applicable to business. 

MELROSE'S CONCISE SYSTEM OF PRACTICAL 

ARITHMETIC ; containing the Fundamental Rules and their Applica- 
tion to Mercantile Calculations; Vulgar and Decimal Fractions; Ex- 
changes; Involution and Evolution; Progressions; Annuities, Certain 
and Contingent, etc. Re-arranged, Improved, and Enlarged, with Exer- 
cises on the proposed Decimal Coinage. By Alexander Trotter, 
Teftcher of Mathematics, etc., in Edinburgh. Is. 6d. Key, 2s. 6d. 

Each Rule is followed hy an example worked out at length, and minutely 
explained, and by numerous practical Exercises. 

HUTTON'S ARITHMETIC AND BOOK-KEEPINa. 2s. 6d. 

BUTTON'S BOOK-KEEPING, by Trotter. 2s. 

Suts of Ruled Writing Books, — Single Entry, per set, Is. 6d. ; Double 
Entry, per set, Is. 6d. 

STEWART'S FIRST LESSONS IN ARITHMETIC, for 

Jimior Classes ; containing Exercises in Simple and Compound Quantities 
arranged so as to enable the Pupil to perform the Operations with the 
greatest facility and correctness. With Exercises on the proposed 
Decimal Coinage. 6d. stifif wrapper. Answers, 6d. 

STEWART'S PRACTICAL TREATISE on ARITHMETIC, 

Arranged for Pupils in Classes. With Exercises on the proposed Decimal 
Coinage. Is. 6d. This work includes the Answers ; with Questions for 
Examination. Key, 2s. 

GRAY'S INTRODUCTION TO ARITHMETIC ; with 

Exercises on the proposed Decimal Coinage. lOd. bound in leather. 
Key, 28. 



16 COPY-BOOKS, MATHEMATICS, ETC. 

LESSONS IN ARITHMETIC FOR JUNIOR CLASSES. 
By James Maclaren, Master of the Classical and Mercantile Academy, 
Hamilton Place, Edinburgh. 6d. stiff wrapper. 

The Answers are annexed to the several Exercises. 

MACLAREN'S IMPROVED SYSTEM OF PRACTICAL 

BOOK-KEEPING, arranged according to Single Entry, and adapted to 
General Business. Exemplified in one set of Books. Is. 6d. 
A Set of Ruled Writing Books, expressly adapted for this work, Is. Qd. 

SCOTT'S FIRST LESSONS IN ARITHMETIC. 6(1 

stiff wrapper. Answers, 6d. 

SCOTT'S MENTAL CALCULATION TEXT -BOOK. 

Pupil's Copy, 6d. Teacher's Copy, 6d. 



COPY BOOKS, in a Progressive Series, 

By R. SCOTT, late Writing-Master, Edinburgh. 

Each containing 24 pages. Price : Medium Paper, M. ; Post Paper, 4i. 

SCOTT'S COPY LINES, in a Progressive Series, 4d. each. 



THE PRINCIPLES OF GAELIC GRAMMAR; With the 
Definitions, Rules, and Examples, clearly expressed in English and 
Gaelic : containing copious Exercises for Reading the Language, and for 
Parsing and Correction. By the Rev. John Foebks, late Minister of 
Sleat. 3s. 6d. 



MATHEMATICS, NATUKAL PHILOSOPHY, ETC. 

INGRAM'S CONCISE SYSTEM OF MATHEMATICS, 

Theoretical and Practical, for Schools and Private Students. Improved 
by James Trotter. With 340 Woodcuts. 4s. 6d. Key, 3s. 6d. 

TROTTER'S MANUAL OF LOGARITHMS AND PRAC- 
TICAL MATHEMATICS, for Students, Engineers, Navigators, and 
Surveyors. 3s. 

A COMPLETE SYSTEM OF MENSURATION; For 

Schools, Private Students, and Practical Men. By Alex. Ingram. 
Improved by Jambs Trotter. 2s. 

INGRAM AND TROTTER'S EUCLID. Is. 6d. 

INGRAM AND TROTTER'S ELEMENTS op ALGEBRA, 

Theoretical and Practical, for Schools and Private Students. 3s. 



MUSIC, DRAWING, SCHOOL REGISTERS. 17 

INTRODUCTORY BOOK OF THE SCIENCES. By 
James Nicol, F,R.S.E.,F.G.S., Professor of Natural History in the Uni- 
versity of Aberdeen. With 106 Woodcuts. Is. 6d. 



SCHOOL SONGS WITH MUSIC, 

By T. M. HuNTEB, Director to the Association for the Revival of Sacred 

Music in Scotland. 

ELEMENTS OF VOCAL MUSIC: An Introduction to the 
Art of Reading Music at Sight. Price 6d. 

*** This Work has been prepared with great care, and is the result of long 
practical experience in teaching. It is adapted to all ages and classes, 
and will he found considerably to lighten the labour of both teacher and 
pupil. The exercises are printed in the standard notation, and the notes are 
named as in the original Sol-fa System. 

Contents. — Music Scales. — Exercises in Time. — Syncopation. — The 
Chromatic Scale.— Transposition of Scale. — The Minor Scale.— Part 
Singing. — Explanation of Musical Terms. 

HUNTER'S SCHOOL SONGS. With Preface by Rev. 
James Currie, Training College, Edinburgh. 

FOR JUNIOR CLASSES : 60 Songs, principally set for two 

voices. 4d. — Second Series : 63 Songs. 4d. 
FOR ADVANCED CLASSES : 44 Songs, principally set for three 
voices. 6d.—Seco}id Series : 4:6 Songs. 6d. 



SCHOOL PSALMODY ; containing 58 Pieces arranged for 
three voices. 4d. 

GEOMETRICAL DRAWING-. 
THE FIRST GRADE PRACTICAL GEOMETRY. In- 
tended chiefly for the use of Drawing Classes in Elementary Schools 
taught in connexion with the Department of Science and Art. By John 
Kennedy, Head Master of Dundee School of Art. 6d. 



SCHOOL REGISTER. Pupil's Daily Register op Marks. 
Improved Edition. Containing Spaces for 48 Weeks ; to which are added , 
Spaces for a Summary and Order of Merit for each Month, for each 
Quarter, and for the Year. For Schools in general, and constructed to 
furnish information required by Government. 2d. 

SCHOOL REGISTER OF ATTENDANCE, ABSENCE, 

AND FEES: adapted to the Provisions of the Revised Code, by 
MoBRis F. Myron. Each folio will serve 50 pupils for a Quarter. Is. 



18 FRENCH. 



CLASS-BOOKS BY CHAS. HENRI SCHNEIDER, F.E.I.S., M.C.P., 

Senior French Master in the Edinburgh High School, the Merchant 
Company's Educational Institution for Young Ladies, the School of 
Arts and Watt Institution, etc. ; French Examiner to the Educational 
Institute of Scotland, etc. 

SCHNEIDER'S FIRST YEAR'S FRENCH COURSE. 

Is. 6d. 

*** This work forms a Complete Course of French for Beginners, 
and comprehends Grammatical Exercises, with Rules; Reading Lessons, 
with Notes; Dictation; Exercises in Conversation; and a Vocabulary of 
all the Words in the Book. 

THE EDINBURGH HIGH SCHOOL FRENCH CONVER- 

SATION-GRAMMAR, arranged on an entirely New Plan, with Ques- 
tions and Answers. Dedicated, by permission, to Professor Max Miiller. 
3s. 6d. Key, 2s. 6d. 

THE EDINBURGH HIGH SCHOOL NEW PRACTICAL 
FRENCH READER : Being a Collection of Pieces from the best French 
Authors. With Questions and Notes, enabling both Master and Pupil 
to converse in French. 3s. 6d. 

THE EDINBURGH HIGH SCHOOL FRENCH MANUAL 

of CONVERSATION and COMMERCIAL CORRESPONDENCE. 
2s. 6d. 

In this work, Phrases and Idiomatic Expressions which are used most 
frequently in the intercourse of every-day life have been carefully collected. 
Cai-e has been taken to avoid what is trivial and obsolete, and to introduce 
all the modem terms relative to railways, steamboats, and travelling in 
general. 

]j]CRIN LITT^RAIRE : Being a Collection of Lively Akec- 

DOTEs, Jeux de Mots, Enigmas, Charades, Poetry, etc., to serve as 

Readings, Dictation, and Recitation. 3s. 6d. 

Letter from Professor Max Mijller, University of Oxford, May 1867. 

"My dear Sir, — I am very happy to find that my anticipations as 
to the success of your Grammar have been fully realized. Your book 
does not require any longer a godfather; but if you wish me to act as 
such, I shall be most happy to have my name connected with your 
prosperous child. — Yours very truly, Max MUller. 

" To Mons. C. H. Schneider, Edinburgh High School." 



THE FRENCH NEW TESTAMENT. The most approved 
Protestant Version, and the one in general use in the French 
Reformed Churches. Pocket Edition, roan, gilt edges. Is. 6d. 

CHAMBAUD'S FABLES CHOISIES. With a Vocabulary 

containing the meaning of all the Words. By Scot and Wells. 2s. 

LB PETIT FABLIER. With Vocabulary. For Junior 
Classes. By G. M. Gibson; late Rector of the Bathgate Academy. Is. 6d. 



FRENCH. 19 



STANDARD PRONOUNCING DICTIONARY OF THE 
FRENCH AND ENGLISH LANGUAGES. In Two Parts. Part I. 
French and English. — Part II. English and French. By GABRiEii 
SuREXNE, late Professor in the Scottish Naval and Military Academy, 
etc. The First Part comprehends Words in Common Use, Terms con- 
nected with Science and the Fine Arts, Historical, Geographical, and 
Biographical Names, with the Pronunciation according to the French 
Academy and the most eminent Lexicographers and Grammarians. The 
Second Part is an ample Dictionary of English words, with the Pronun- 
ciation according to the best Authorities. The whole is preceded by 
a Practical and Comprehensive System of French Pronunciation. 7s. 6d., 
strongly bound. 

The Pronunciation is shown ly a different spelling of the Words. 

SURENNE'S FRENCH-ENGLISH and ENGLISH-FRENCH' 
DICTIONARY, without the Pronunciation. 3s. 6d., strongly bound. 

SURENNE'S FENELON'S TELEMAQUE. 2 vols, Is. each, 
stiff wrapper ; or bound together, 2s. 6d. 

SURENNE'S VOLTAIRE'S HISTOIRE DE CHARLES XIL 

Is. stiff wrapper; or Is. 6d. bound. 

SURENNE'S VOLTAIRE'S HISTOIRE DE RUSSIE SOUS 
PIERRE LE GRAND. 2 vols, Is. each, stiff wrapper ; or bound together, 
2s. 6d. 

SURENNE'S VOLTAIRE'S LA HENRIADE. Is. stiff wrap- 
per; or Is. 6d. bound. 

SURENNE'S NEW FRENCH DIALOGUES; With an In- 
troduction to French Pronunciation, a Copious Vocabulary, and Models 
of Epistolary Correspondence. Pronunciation marked throughout. 2s. 

SURENNE'S NEW FRENCH MANUAL AND TRAVEL- 
LER'S COMPANION. Containing an Introduction to French Pro- 
nunciation; a Copious Vocabulary; a very complete Series of Dialogues 
on Topics of Every-day Life ; Dialogues on the Principal Continental 
Tours, and on the Objects of Interest in Paris; with Models of Epistol- 
ary Correspondence. Intended as a Class-book for the Student and a 
Guide to the Tourist. Map. Pronunciation marked throughout. 3s. 6d. 

SURENNE'S PRONOUNCING FRENCH PRIMER. Con- 
taining the Principles of French Pronunciation, a Vocabulary of easy 
and familiar Words, and a selection of Phrases. Is. 6d. stiff wrapper. 

SURENNE'S MOLIERE'S L'AVARE : Come'die. Is. stiff wrap- 
per; or Is. 6d. bound. 

SURENNE'S MOLIERE'S LE BOURGEOIS GENTIL- 
HOMME : Comddie. Is. stiff wrapper; or Is. 6d. bour.d. 



20 FRENCH. 



SURENNE'S MOLIERE'S LE MISANTHROPE : Comedie., 
LE MARIAGE FORCE : ComMie. Is. stiff wrapper; or Is. 6d. bound. 

SURENNE'S FRENCH READING INSTRUCTOR, Reduced 

to 2s. 6d. 

HALLARD'S FRENCH GRAMMAR. 3s. 6d. Key, 3s. 6d 

GRAMMAR of the FRENCH LANGUAGE. By Auguste 
Beljame, B.A., LL.B., Vice-Principal of the Paris International 
College. 2s. 

BELJAME'S FOUR HUNDRED PRACTICAL EXER- 
CISES. Being a Sequel to Beljame's French Grammar. 2s. 

*^* Both Books bound together, Bs. 6d. 
The whole work haw been composed with a view to conversation, a great 

number of the Exercises being in the form of questions and answers. 

FIRST FRENCH CLASS-BOOK, or a Practical and Easy 
Method of learning the French Language, consisting of a Series of 
French and English Exercises, progressively and gi'ammatically ar- 
ranged. By Jules Caron, F.E.I.S,, French Teacher, Edin. Is. Key, Is. 
This work follows the natural mode in which a child learns to speak its 
own language, by repeating the same words and phrases in a great variety 
of forms until the pupil becomes familiar with their use. 

CARON'S FIRST FRENCH READING-BOOK: Being 
Easy and Interesting Lessons, progressively arranged. With a Copious 
Vocabulary of the Words and Idioms in the text. Is. 

CARON'S PRINCIPLES OF FRENCH GRAMMAR. With 

numerous Exercises. 2s. Key, 2s. 

Spectator.—" May be recommended for clearness of exposition, gradual 
progression, and a distinct exhibition to the mind through the eye by means 
of typographical display : the last an important point where the subject 
admits of it." 

AN EASY GRAMMAR OF THE FRENCH LANGUAGE. 

With Exercises and Dialogues. By John Christison, Teacher of 
Modern Languages. Is. 4d. Key, 8d. 

CHRISTISON'S RECUEIL DE FABLES ET CONTES 

CHOISIS, h rUsage de la Jeunesse. Is. 4d. 
CHRISTISON'S FLEURY'S HISTOIRE DE FRANCE, 

Racontee h la Jeunesse. With Translations of the difficult Passages. 
2s. 6d. 

FRENCH EXTRACTS FOR BEGINNERS. With a Voca- 
bulary and an Introduction By F. A. Wolski, Master of the Foreign 
Language Department in the High School of Glasgow. 2s. 6d. 

WOLSKI'S NEW FRENCH GRAMMAR. With Exercises. 

3d. 6d. 



LATIN AND GREEK. 21 

EDINBURGH ACADEMY CLASS-BOOKS. 

The acknowledged merit of these school-books, and the high reputation of 
the seminary from Trhich they emanate, almost supersede the necessity 
of any recommendation. The " Latin " and " Greek Rudiments " form an 
introduction to these languages at once simple, perspicuous, and compre- 
hensive. The "Latin Rudiments" contain an Appendix, which renders 
the use of a separate work on Grammar quite unnecessary; and the list of 
anomalous verbs in the " Greek Rudiments" is believed to be more extensive 
and complete than any that has yet appeared in School Grammars of the 
language. In the " Latin Delectus " and " Greek Extracts " the sentences 
have been arranged strictly on the progressive principle, increasing in 
difficulty with the advancement of the Pupil's knowledge; while the 
Vocabularies contain an explanation not only of every word, but also ol 
every difficult expression which is found in the works,— thus rendering the 
acquisition of the Latin and Greek languages both easy and agreeable. 
The Selections from Cicero embrace the portions of his works which are 
best adapted for Scholastic tuition. 

1. RUDIMENTS OF THE LATIN LANGUAGE. 2s. 

%* This work forms an introduction to the language, at once simple^ 
perspicuous, and comprehensive. 

2. LATIN DELECTUS; with a Vocabulary containing an 
^Explanation of every Word and Difficult Expression which occurs in 
the Text. 33. 6d. 

3. RUDIMENTS OF THE GREEK LANGUAGE, with the 

Syntax entirely re-written, and witli Accent and Quantity treated of 
according to their mutual relations. 3s. 6d. 

4. GREEK EXTRACTS; with a Vocabulary containing an 
Explanation of every Word and of the more Difficult Passages in the 
Text. 8s. 6d. 

5. SELECTIONS FROM CICERO. Ss. 

6. SELECTA E POETIS LATINIS. 3s. 



GREEK SYNTAX ; with a Rationale of the Constructions, by 
Jas. Clyde, LL.D., one of the Classical Masters of the Edin. Academy. 
With Prefatory Notice by John S. Blackie, Professor of Greek in the 
University of Edinburgh. Uh Edition, entirely rc-written, and enlarged 
by a Summary for the use of Learners and a chapter on Accents. 4s. 6d. 

G;REEK GRAMMAR for the Use of Colleges and Schools. 

By Professor Geddes, University of Aberdeen. 4s. 

The author has endeavoured to combine the elearnesa and conciseness of 
the older Greek Grammars with the accuracy and fulness of more recent ones. 



22 LATIN AND GREEK. 



DB HUNTEE'S CLASSICS. 

1. HUNTER'S RUDDIMAN'S RUDIMENTS. Is. 6d. 

2. HUNTER'S SALLUST; with Footnotes and Translations. 

ls.6d. 

3. HUNTER'S VIRGIL, with Notes and other Illustrations. 

28. 6d. 

4. HUNTER'S HORACE. 2s. 

5. HUNTER'S LIVY. Books XXI. to XXV. With Critical 

and Explanatory Notes, lieduced to 3s. 



LATIN PROSE COMPOSITION: The Construction of Clauses, 

with Illustrations from Cicero and Cajsar ; a Vocabulary containing an 
Explanation of every "Word in the Text ; and an Index Verborum. By 
John Massie, A.M. 3s. 6d. 

DYMOCK'S C^SAR ; with Illustrative Notes, a Historical and 
Geographical Index, and a Map of Ancient GauL 4s. 

DYMOCK'S SALLUST; with Explanatory Footnotes and a 
Historical and Geographical Index. 28. 

C-iESAR; with Vocabulary explaining every Word in the Text, 
Notes, Map, and Historical Memoir. By William M 'Dow all, late 
Inspector of the Heriot Foundation Schools, Edinburgh. 3s. 

M'DOWALL'S VIRGIL; with Memoir, Notes, and Vocabulary 
explaining every Word in the Text. 3s. 

NEILSON'S EUTROPIUS ET AURELIUS VICTOR; with 

Vocabulary containing the meaning of every Word that occurs in the 
Text. Revised by Wm. M'Dowall. 2s. 

LECTIONES SELECTS : or, Select Latin Lessons in Morality, 
History, and Biography : for the use of Beginners. With a Vocabulary 
explaining every Word in the Text. By C. Melville, late of the 
Grammar School, Kirkcaldy. Is. 6d. 

MACGOWAN'S LESSONS IN LATIN READING. In Two 

Parts. Part I., Improved by H. Feaser Halle, LL.D. 23. 17th 
Edition. Part II. 2s. 6d. The two Courses furnish a complete Latin 
Library of Reading, Grammsir, and Composition for Beginners, con- 
sisting of Lessons wliich advance in difficulty by easy gradations, 
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LATIN AND GREEK. 28 

M AIR'S INTRODUCTION TO LATIN SYNTAX: with 

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XENOPHON'S ANABASIS, BOOKS I. AND XL; with 

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Athenceum. — " The text of this admirable little work is that of Dindorf, 
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difficult passages, with exact information upon points of antiquities derived 
from the best and most modern authorities." 

GRAMMATICAL EXERCISES ON THE MOODS, 

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*#* This work is intended to follow the QreeTc Rudiments, 

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24 LATIN AND GREEK. 



LATIN ELEMENTARY WORKS AND CLASSICS. 

Etlited by George Ferguson, LL.D., lately Professor of Humanity !n 

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ITALIAN. 
THEORETICAL AND PRACTICAL ITALIAN GRAM- 
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A NEW GERMAN READER, in Pkose and Verse ; with a 
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PUBLISHED PY OLIVER AND BOYD, EDINBURGH; ^ 

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