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U.S. Coast and Geodetic Survey 
Geodesy 



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n 






No. Ill J 

DEPARTMENT OF COMMERCE 

U. S. COAST AND GEODETIC SURVEY 

E. LESTER JONES, SUPERINTENDENT 



GEODESY 



iNERAL INSTRUCTIONS FOR PRECISE AND 
SECONDARY TRAVERSE 

U. S. COAST AND GEODETIC SURVEY 




PRICE, 10 CENTS 

old only by the Superintendent of Documents, Government Printing Office 
Washington, D. C. 



WASHINGTON 

GOVERNMENT PRINTING OFFICE 

1919 



Serial No. Ill 

DEPARTMENT OF COMMERCE 

U. S. COAST AND GEODETIC SURVEY 

E. LESTER JONES, SUPERINTENDENT 



GEODESY 



GENERAL INSTRUCTIONS FOR PRECISE AND 
SECONDARY TRAVERSE 

U. S. COAST AND GEODETIC SURVEY 



Special Publication No. 58 




PRICE, 10 CENTS 

Sold only by the Superintendent of Documents, Government Printing Offloe 
Washington, D. C. 



WASHINGTON 

GOVERNMENT PRINTING OFFICE 

1919 



r^i 



f(= %> ^'^.:. 




llL 



CONTENTS. 



Page. 

Introduction 5 

General statement 6 

Location of traverse stations 6 

Measurement of distances 7 

Check measurement 10 

Angle measurements 12 

Azimuth stations 14 

Marking stations 14 

Descriptions of stations 15 

Inclination corrections 16 

Records and computations 19 

Traverse measurement 20 

Check measurement 21 

Y levels over stakes 21 

Precise levels 22 

Sample computations and tables 23 

Computation of inclination correction 24 

Inclination correction table 25 

Inclination correction table for 50-meter tape lengths 28 

Computation of Savannah to Norfolk traverse line 33 

Certificate of standardization 34 

Temperature corrections 36 

Tape corrections for tape No. 552 when supported through- 
out. . ., 36 

Tape corrections for tape No. 552 for various methods of sup- 
port 37 

Projection computation 38 

Computation to close loops 39 

Computation of angle closure for loop 40 

Computation of distance for loop 40 

General instructions for secondary traverse 41 

Inclination correction table 42 

Factors for inclination correction 44 

Measurement of angles 45 

Azimuth stations 46 

Index 47 

3 



ILLUSTRATIONS. 

Page. 

Figure 1. Section of traverse line 19 

Figure 2, Diagram for projection computation, one offset sta- 
tion 37 

Figure 3. Diagram for projection computation, both stations 

offset on same side of track 38 

Figure 4. Diagram for projection computation, stations offset 

on opposite sides of track 39 

Figure 5. Diagram for loop computation 40 

4 . 



GENERAL INSTRUCTIONS FOR PRECISE AND SEC- 
ONDARY TRAVERSE, U. S. COAST AND GEO- 
DETIC SURVEY. 



INTRODUCTION. 

During the early part of 1917 the United btiiu-^ < un^t and (Jeodetic 
Survey started work on a system of precise traverse lines in Georgia 
and Florida, which have since been extended into other States along 
the Atlantic coast. This work was called for by the Corps of Engineers 
of the United States Army to give the necessary primary control for 
various military maps in that section of the country. Traverse was 
used instead of triangulation as the general lay of the land and the 
prevalence of high timber would have made high scaffold signals 
necessary to give clear lines for triangulation. The traverse lines 
followed the railroads, and so required but little signal building or 
cutting of timber. 

Although traverse has been used in place of triangulation by the 
United States Coast and Geodetic Survey at various times in the past 
it has never been used on so large a scale as in the recent work. The 
methods employed in the work were largely experimental at first, 
but they have been gradually changed and improved until they have 
become practically standard. 

It has been thought advisable to publish these general instructions 
in order to preserve the knowledge that has been gained, to standardize 
any future field work as much as possible, and to prevent the continued 
use of any methods which have been found inefficient or unwise. 

Wlien a precise traverse is to be run over country roads or along 
beaches, separate instructions supplementing these general instruc- 
tions will be issued to the officer in charge of the general operations. 

Changes iu these general instructions will undoubtedly be made 
from time to time as better methods are developed. The members 
of the field and office forces of the Survey engaged on the precise 
traverse and its computations are invited to offer suggestions which 
may make it possible to do the work more expeditiously without 
decreasing the accuracy or increasing the cost. 

5 



6 TT. S. COAST AND GEODETIC SURVEY. 

GENERAL STATEMENT. 

Precise traverse will, in general, be done in those sections of the coun- 
try where the topographic conditions make it impracticable to carry 
on primary triangulation. The work will supplement the primary 
triangulation in furnishing the fundamental control for the surveys and 
maps made by federal, State, or other organizations and by private 
individuals. The conditions which make it more desirable to carry 
on precise traverse than primary triangulation are flatness of the 
land and presence of timber. Under these conditions it is neces- 
sary to have comparatively short lines in the primary triangulation, and 
to erect high scaffold signals at the stations in order to make them inter- 
visible. 

These instructions are designed for the highest class of traverse, equal 
in accuracy to primary triangulation, and for secondary traverse com- 
parable in accuracy with secondary triangulation. Should it be 
necessary to carry on tertiary traverse for the control in local areas, 
special instructions will be furnished to officers in charge of the field 
work. 

LOCATION OF TRAVERSE STATIONS. 

1. In general the traverse will be run along a railroad track. The 
stations should usually be at the intersection of two contiguous tan- 
gents of the railroad. Occasionally when the tangent is particularly 
long and the profile of the road between its ends such that it would 
be difficult to get a line clear between the ends of the tangent, one or 
more intermediate stations should be placed at the side of the road. 
The profile of the road along the tangent will be the deciding factor in 
the location of the intermediate stations. If the ground is practically 
level along such a tangent, the stations may be placed almost anywhere, 
and should be located near a crossroad, if convenient. 

2. In general the stations along any tangent should not be more than 
4 or 5 miles apart, as delays caused by observing longer lines will more 
than offset the time gained by having fewer observations. It is also 
true that stations should be placed fairly close together, so as to be 
of the maximum benefit for public and private surveys. 

3. A traverse station should be placed near each railroad crossing or 
point where a branch line makes off from the line followed by the trav- 
erse. Also a traverse station should be located at or very near each 
town along the route of the traverse, and when at all practicable a 
second traverse station should be located ^vdthin 2 miles of the town 
in order to enable local engineers and surveyors to obtain an azimuth 
with little difficulty. 



GENERAL INSTRUCTIONS FOR TRAVERSE. 7 

4. When curves are numerous for any given distance and the tangents 
very short, it will be well to lay out comparatively long lines extending 
over several curves in order that the azimuth may be carried forward 
with greater strength than if it had to be carried through a number of 
short lines. The distance between the ends of such a long line can be 
carried by measurement and angles along the track. This latter work 
would be considered in the nature of a subsidiary scheme of angles. 
Care must be taken that each end of such a long line is carefully tied 
into the scheme running along the railroad between its ends. 

MEASUREMENT OF DISTANCES. 

6. The lengths in the traverse will depend on measurements made 
with 50-meter invar base tapes, standardized at the Bureau of Stand- 
ards before and after use in the field. 

6. The length should depend upon one measurement in one direction 
only, unless a blunder has been made. There should be three primary 
tapes in the party, two used in measurement and one used as a stand- 
ard. About one-half of the measurement of any considerable portion 
of the travei*se should be made with each of the working tapes. A com- 
parison should be made of the three tapes at intervals along the trav- 
erse in order to detect any changes that might occur in the length of one 
or both of the working tapes. No tape should be used ior more than 
15 kilometers of measurement without being recompared. The com- 
parison of the three base tapes can best be made on the stakes used in 
the traverse measurement between a point of tangency and a traverse 
station, A distance of at least 100 meters should be used in making the 
comparison. Metal strips should be used on the top of the stakes em- 
ployed for the comparison to prevent parallax in marking. The com- 
parison of the tapes with a record of temperatures, etc., should be 
entered in the traverse record. 

7. A tape should be sent to the office for restandardization if it differs 
by more than 1 part in 75 000 from the standard tape. 

8. As soon as a new tape has been received from the office a compari- 
son of this tape should be made with the standard tape and the other 
working tape or tapes. No actual field work should be done with the 
new tape until such a comparison has been made. 

9. Do not straighten out kinks in the tape. If such exist and the tape, 
in consequence, can not be used for measurement, send the tape to the 
office with a letter explaining in detail this condition, giving date on 
which the injury or injuries occurred. 



8 U. S. COAST AND GEODETIC SURVEY. 

10. The base tapes used in the field should have a tension applied 
of 15 kilograms, and this same tension will be used during the standardi- 
zation at the Bureau of Standards. 

11. Two thermometers should be attached to the tape, one at each 
end, during measurement, and they should be read and recorded at 
each tape length. Special centigrade thermometers, for use during 
traverse or base measurement, will be furnished by the office on appli- 
cation. In attaching the thermometers to the tape suitable cases 
should be used which will insure good contact with the tape and pre- 
vent the breaking of the thermometer. They should be attached to the 
tape beyond the end graduations in order to guard against any tendency 
to kink the working part of the tape. The cases can be fastened to 
the tape by means of adhesive tape, and this will make it possible to 
detach them easily when the tape is wound on the reel. 

12. A second measurement, with a primary tape, will be made over 
any section of the line of traverse which is to be used as a base line from 
which to start an arc of primary triangulation. 

13. When measuring along a railroad, the distances along the tan- 
gents will be measured with the 50-meter tape, supported throughout 
its length on top of a rail of the track. The distances from the points 
of tangency to the traverse stations at the intersection of tangents, 
should be measured over stakes especially set to support the tape. 

14. In measuring up to or away from a station the record should indi- 
cate clearly whether the tape was held on the station mark itself or on 
the bench or table built over the station mark. In this connection do 
not use the word "tablet" for the station mark, as it is easily confused 
with th e word ' ' table . ' ' 

15. In measuring the offset distance between the point on the rail 
and the station itself, for stations along tangents, the record should 
show whether the measurement was made horizontally or on an incline, 
and in the latter case the difference in elevation must be given, 

16. The record should also indicate clearly whether the traverse was 
measured to a rail station, to the rail opposite a station, or to the station 
itself. A rail station proper is one which is actually on the rail itself 
and is occupied with a theodolite for observations of the same degree 
of accuracy as for the regular scheme. A rail station is usually put in 
to aid in determining some point at some distance from the track. It 
is very rare that there will be another traverse station within one or two 
hundred meters of the rail station. 

17. ^\^lile measuring along the top of a rail, the position of the for- 
ward end of the tape can be transferred to the rail with an ordinary 
cheap glass cutter. In measuring over stakes, the forward end of the 



GENERAL INSTRUCTIONS FOR TRAVERSE. 9 

tape will be marked directly on the top of the stake by means of a 
knife cut or a mark Avith a glass cutter. If the top of the stake is badly 
battered, an ordinary pin may l^e driven in to mark the end of the 
tape. 

18. The rear contact man must use the same end of the small scratch 
on the rail as was used by the forward contact man. This will be 
brought about by the two contact men always standing on the same 
side of the tape. 

19. Great care must be exercised in counting and recording the 
number of tape lengths in a section. At least one other man in the 
party besides the recorder should count the tape lengths entirely 
independently. It is suggested that a system of counting tape lengths 
similar to the one used in ordinary surveying be tried out by the 
taping party. Small tin or aluminum rings or harness rings two or 
three inches in diameter could be used for the purpose. For each 
tape length one of these rings could be left beside the rail close to the 
mark on the rail by the forward contact man and later picked up by 
the rear contact man. Twenty one rings could be used and 20 of them 
passed to the forward contact man at the end of each kilometer. A 
piece of colored rag tied to the ring will enable the rear contact man 
to find it readily. The rings can be carried by means of a spring 
attached to the handle of each of the tape stretchers. 

20. To av(nd gross errors, all fractions of a tape length less than 
about 49.9 meters, which enter into a section, should be measured as 
set-ups. The set-ups will be measured with a standardized pocket 
steel tape or metal scale, except as provided for in paragraph 21. 

21. Wlien a fraction of a tape length is greater than 25 meters, it 
should be measured as two set-ups; the first one as half a tape length 
and the balance as a set-up to be measured with the pocket steel tape. 
A half tape length can easily be measured by placing a mark with a 
pencil or otherwise near the center of the base tape. Then the dis- 
tance from the stake ending the last full tape length to a point on a 
stake set approximately 25 meters can be measured twice, once with 
each half of the tape, and the error in marking the middle of the tape 
can thus be eliminated. 

22. In setting stakes on the prolongation of tangents it will be of 
advantage to begin at the station and work toward the rail in either 
direction, for this will bring the minimum number of set-ups on the 
stakes, and all half tape lengths on the stakes will be eliminated. 
When measuring by this method, ail necessary large set-ups will occur 
on the rail, where they are easily measured. 

114585' 19 2 



10 U. S. COAST AND GEODETIC SURVEY. 

23. A railroad curve often occurs in a deep cut, which makes it 
necessary to put the traverse station at the top of a high bank and 
renders the staking and taping difficult. If a saving of time can be 
made, it is permissible to compute the distance from the stake, 
beyond which the taping would be difficult, to the station by means 
of a triangle. A small base should be measured from this stake to 
another stake at some convenient point along the curve which will 
give a triangle with a good angle of intersection at the station. The 
angles should be measured with such accuracy as to insure against an 
error as great as one-half centimeter in the computed distance. The 
same method may be used in going ahead from the station. 

24. During the measurement with the base tape, indicate in the 
record the distance from the initial point of the section to crossroads, 
railroad stations, water towers, section houses, semaphores, bridges, 
culverts, mileposts, banks of rivers, State and county lines, decided 
changes of grade and possibly some other objects, in order that the 
traverse may be properly connected with the alignment of the rail- 
road, and thus make it possible to utilize the railroad surveys in 
making maps of the country through wliich the traverse runs. These 
measurements will also be utilized in making a determination of the 
geographic positions of some of the objects to which distances are 
measured. The record must show whether the taping is along the left- 
hand or right-hand rail. Instructions in regard to the angles to be 
measured to objects along the road are given on another page. 

25. The designations of the points of tangency and their distances 
from the initial station of the section should be carefully recorded; 
as, for example, P. T. 42=24-f-4. (24+4 means 4 meters beyond the 
end of the 24th tape length). In case the precise leveling precedes 
the taping, the designation of all permanent and temporary bench 
marks along the track, and their distances from the initial station, 
should also be recorded, as for example, 6+20=T. B. M. 115. 

26. No measurement should be made with the primary tape when 
the rail is wet, and when it is damp measurements should be made 
with caution. It is the experience of those engaged on measurement 
along railroad tracks that the tape tends to stick to the rail when the 
latter is wet, and therefore errors will result. 

CHECK MEASUREMENT, 

27. A single check measurement will be made of each section of 
the traverse with a 300-foot tape. The best means of recording the 
number of full tape lengths is to read and record the temperature each 
time. Only one thermometer need be used. Counters may be used 



GENERAL INSTRUCTIONS FOR TRAVERSE. 11 

as a check on the number of tape lengths. ^Tien measuring from the 
P. T. point to the station the tape may be supported on the stakes 
that were used for the invar tape, but no other regard should be 
given to these stakes. Plumb lines should be used at the ends of 
the tape, the same as in ordinary chaining, and the point marked 
on the ground with an iron pin. 

28. The 300-foot tape may be supported along the top of the rail 
or on the ties close to the rail while measuring between tangent 
points. The position of the forward end of the tape may be indi- 
cated on the top of the rail by a pencil mark. The location of the 
pencil mark may be indicated by a cross made with chalk or keel 
on the rail or a tie. The distances between the points of tangency 
and the traverse stations should be measured as in ordinary chain- 
ing without reference to the original stakes. 

29. A moderate pull only should be used with the 300-foot tape. It 
is believed that five kilograms is sufficient. The object of having a 
light pull is to make it possible to have the measurement made with 
a very small party. A heavy pull would require the use of stretchers 
at the forward and rear ends of the tape. The lengths of the tapes 
under the standard pull and temperature must be known. 

30. During the check measurement, distances should be indicated 
in the record from the traverse station at the beginning of the section 
to the country road and railroad crossings, to bridges, water tanks, 
mileposts, and other objects, as given in paragraph 24, in order that a 
check may be made on the determination of the distance of these 
objects from the traverse station. Designations of all points of tangency 
and all bench marks along the track and their distances from the 
initial station should be carefully recorded; as, for example, l-t-235= 
P. T. 42, and 11+135=T. B. M. 115. 

31. Measurements with the 300-foot tape may be made under any 
conditions of the weather. 

32. If the temperature is not recorded for each tape length, as smg- 
gested in paragraph 27, the approximate temperature of the tape should 
be entered in the record at least once for each section. 

33. If the measurement with the 300-foot tape differs by more than 
a few decimeters in any section from the distance given by the meas- 
urements with the 50-meter base tape, a second measurement with the 
300-foot tape will be made. If this second measurement agrees closely 
with the first one made with the 300-foot tape, then a second measure- 
ment will be made with the 50-meter tape. 



12 



IT. S. CX)AST AND GEODETIC SURVEY. 
ANGLE MEASUREMENTS. 



34. In general, the highest type of instrument will be used in meas- 
uring the angles of the main line of traverse stations. When a direction 
instrument is used which is read by micrometer microscopes, the 
angles will be measured in eight positions of the instrument. The 
initial settings for these positions are as follows: 



Position 
No. 



Reading. 



00 40 

30 01 60 

60 03 10 

90 04 20 

125 00 40 

155 01 50 

185 03 10 

215 04 20 



36. When the measurement of an angle in the main line of traverse 
stations is made with a 7-inch repeating theodolite, a sufficient number 
of observations should be made to obtain the same degree of accuracy 
as can be obtained by measuring the angle in eight positions with the 
direction theodolite. It is probable that about three sets, each con- 
sisting of six repetitions of the angle with the telescope direct and six 
repetitions of the explement with the telescope in the reversed posi- 
tion, will be needed to secure the degree of accuracy desired. 

36. A position for a direction instrument consists of a pointing on 
each object in the horizon, in both direct and reverse positions of the 
telescope, for one initial setting of the horizontal circle. 

37. Observations for angle measurements at the principal stations of 
the traverse should be made only when the conditions are favorable. 
To^an inexperienced observer this can be determined only by experi- 
ment. It will be found that a steady signal does not always mean that 
observing conditions are perfect, t<Sr it is possible that there may be 
lateral refraction under the conditions that obtain when the signal 
appears steady that might be absent when the signal is tremulous or 
jumpy. Excellent observations can be obtained on a signal that is 
moderately unsteady when a number of repetitions of the angle or 
direction is made. The amount of unsteadiness that will still permit 
good observations to be obtained can be determined approximately 
by the observer. He can observe some one direction under various 



GENERAL INSTRUCTIONS FOR TRAVERSE. 13 

weather conditions and note the agreement in the angle or direction 
obtained under each condition. 

38. The 7-inch repeating theodolite should be used in measuring all 
angles at subsidiary traverse stations which are not used for carrying 
the main azimuth ahead. One set of six repetitions of the angle with 
the telescope in the direct position, followed by a set of six repetitions 
of the explement of the angle with the telescope in the reversed posi- 
tion, is sufficient. 

39. The instrument and the object sighted upon should be accu- 
rately centered, or, if they are eccentric to the traverse stations, the 
eccentric distance and direction should be carefully measiured and 
entered in the records. The direction from the eccentric instrument 
station to the true station, or from the station to the eccentric object, 
should be entered in the list of directions and should be referred to 
the same initial station as the other directions from that station. 
Confusion is caused by recording the eccentric as "2.5 centimeters 
right." 

40. One of the greatest sources of error in triangulation or other angle 
measurements is what is known as phase. This is caused by uneven 
illumination of the object sighted on, thus causing the observer to 
point his cross wires to the right or left of the center of the object. 
When the sun is shining, a round or square pole \^'ill always have 
phase unless the sun is exactly in line with the instrument and the pole, 
except that a square pole will not have phase if one face of the pole is 
at right angles to the line to the observer. ^ Phase may be eliminated 
almost entirely by having a thin strip of board centered directly over 
the station mark. It is prt)bable that the signal on which the instru- 
ment will be mounted can be made in such a way that a pole 4 inches 
square can be set into the top of the tripod. This pole can be con- 
structed of two pieces of 2 by 4 inch material, and between the two 
pieces at the upper end can be placed the thin piece of board on which 
the observations are to be made. 

41. At each traverse station observe directions to such objects along 
the track as mileposts, water towers, semaphores, railroad stations, sec- 
tion houses, and any other objects that may be \isible. (See paragraph 
24.) With the angle or direction to these objects and the distances 
measured during the determination of the distances along each section, 
the geographic positions of a number of objects which may be of great 
geographic value may be determined. It is particularly important 
that angles or directions should be observed to objects distant from the 
railroad which may be determined by observations from several traverse 
stations. Each object of a more or less permanent nature whose geo- 



14 U. S. COAST AND GEODETIC SURVEY. 

graphic position can be computed from the angles and distance measure- 
ment made by the traverse increases the engineering and geographic 
value of the work. 

AZIMUTH STATIONS. 

42. Owing to the fact that errors in angle observations on a traverse 
tend to accumulate, it is necessary to observe frequent astronomic 
azimuths. The observations should be made on Polaris. 

43. In general, an azimuth station of primary accuracy will be 
established at intervals of about 30 or 35 traverse stations. Observa- 
tions for azimuth should be made only at main line traverse sta- 
tions (see par. 46). The locations of the Laplace azimuth stations 
will be given in the special instructions for each particular piece 
of work. 

44. The azimuths may be observed by the method of repetitions 
with a 7-inch theodolite. For any instrument double the number of 
obsei'vations should be made for azimuth as for a horizontal angle at a 
main traverse station. The probable error of a primary azimuth 
should not exceed 0.^^50 and for a Laplace station should not exceed 
0.^^30. 

45. At intervals of about 10 traverse stations secondary azimuth 
stations should be established between the primary azimuth stations. 
The accuracy of the secondary azimuths should be that represented by 
a probable error of about 6^\ 

46. In order that the geodetic azimuth may be carried along the 
traverse with a minimum ewor, it will be well to have stations on or 
off the road or railroad along which the traverse is measured which are 
intervisible for much longer distances than between the regular traverse 
stations. The azimuth can be carried through these extra stations; 
but whenever used, the extra stations should be connected in azimuth 
and distance with the regular traverse stations and should always be 
used instead of one of the regular stations for the azimuth observations. 
The angles measured at regular stations along any portion of the line 
where there are extra stations should be adjusted to the angles meas- 
ured at the extra stations. The extra stations, rather than the regular 
stations along the same piece of traverse, will be used in determining 
where an azimuth station will be located. 

MARKING STATIONS. 

47. The standard triangulation and reference marks should be used 
in marking the traveree stations. (See p. 42 of Special Publication 
No. 26.) They should be set into heavy blocks of concrete or stone to 
iiasure permanency. 



GENERAL INSTRUCTIONS FOR TRAVERSE. 15 

48. On the standard station and reference marks should be stamped 
the name of the traverse station, and, if the station mark is used as a 
bench mark, the letter and number designating the bench mark should 
also be stamped on the tablet. 

49. All traverse stations should be marked when each two contiguous 
stations are a mile or more apart. When the track along which the 
traverse is made has numerous curv'es and short tangents, some of the 
traverse stations need not be marked in a permanent manner. In 
general, there should be a permanently marked station at least every 
3 miles along the traverse, except, of course, when a section of the 
traverse along a tangent is more than 3 miles in length. Wlien a sta- 
tion is marked in a permanent manner, the next station back of it or 
ahead of it must be marked also in a permanent manner, in order that 
anyone using the traverse may be able to obtain an azimuth. The 
station should be marked with an underground as well as a surface 
m?,rk. The underground mark may be a bottle or some other object, 
preferably set in a small block of concrete. It is frequently the case 
that the underground mark will be left intact when the surface mark 
is destroyed . 

50. At each station marked in a permanent manner there should be 
placed a reference mark. This reference mark should consist of con- 
crete or rock, into which is set a standard inscriljed reference m'ark. 
It should be so accurately connected in distance and azimuth vnth the 
station mark that it may be used as the station mark if the latter should 
be destroyed. It should be placed in such a position that it will not 
be liable to be destroyed by the same agency that might destroy the 
station mark itself. 

51. Traverse stations which are not marked in a permanent manner 
should be marked temporarily with a suitable wooden or other kind 
f stake in order that the station may be available for several years 
after its establishment. Wood which resists decay, such as cedar or 
Georgia pine, should be used if it can be obtained easily. 

DESCRIPTIONS OF STATIONS. 

52. All stations of the traverse, whether marked permanently or in 
a temporary manner, should be described in such a way that they may 
be recovered easily. The descriptions should include the distance 
from the nearest milepost and railroad station and also the offset dis- 
tance from the nearest rail of the railroad track. The station mark and 
the reference mark should be described by notes, as given on pages 42 
and 43 of Special Publication No. 26. If a new type of station mark 
is used which is not covered by one of those notes, a new note should 



16 U. S. COAST AND GEODETIC SURVEY. 

be added and given a number. The Chief of the Division of Geodesy 
should be notified that a new note is being used, and the wording of the 
note and its number should be furnished him as soon as practicable 
after its adoption, 

63. It is often desirable in writing descriptions of stations to give 
approximate distances to various near-by objects which are not impor- 
tant or definite enough to justify an accurate measurement to them. 
Whenever possible, these distances should be paced, as gross errors are 
often made in estimating, and erroneous distances cause confusion 
when the station is recovered . 

54. The descriptions should be made on the cards furnished by the 
office for the descriptions of triangulation stations. The writer of the 
descriptions should have in mind that the descriptions will be pub- 
lished in the near future, and they should be in such a condition, there- 
fore, that the minimum amount of editing will be necessary in pre- 
paring the manuscript for the printer. Any facts essential to the re- 
covery of the station should be given, but those features of only a tem- 
porary nature should not bfe mentioned in the description. 

INCLINATION CORRECTIONS. 

66. In general, a line of precise levels will be run along the line of 
traverse at the same time that the traverse is measured. This leveling 
will be connected with such points of the traverse as will make it pos- 
sible to compute the inclination corrections of the measured distances. 
Precise leveling will be carried on in accordance with the general in- 
structions for precise leveling contained in Special Publication No. 22 
of the United States Coast and Geodetic Survey, or in later leveling 
publications, except as may be modified by the instructions for car- 
rying on primary traverse. 

66. There will be determined by the precise leveling party the 
elevations of any points of decided change in grade along a tangent. 
There will also be determined the elevation of the rail opposite all 
mileposts, water towers, section houses, railroad stations, and over all 
bridges and culverts. There will also be determined the elevation of 
all points of tangency which have been indicated by the traverse 
measuring party or which may be indicated by the leveling party, if 
the leveling precedes the measurement. Points of tangency should 
be marked on the rail or ties of the track by a cross, or otherwise. A 
designation or number should be given to the point of tangency as, 
for example, P. T. 42 ^in order that there may be no doubt as to the 
identification of the records of the measuring and leveling parties for 
any one section. 



GENERAL INSTRUCTIONS FOR TRAVERSE. 17 

57. The traverse stations which have been marked in a permanent 
manner will be used as the bench marks on the line of levels. In 
addition, the leveling party \v411 establish bench marks in each of the 
towns and cities through which the line passes, in order that the city 
surveyors and engineers may have sufficient bench marks to control 
the elevations of their various public works. 

58. None of the reference marks should be used as bench marks in 
the line of levels, as it has been found in the Office, when making the 
final computations, that the records are apt to be confusing when two 
bench marks are so close together as a traverse station and its reference 
mark. The precise leveling done in connection with the primary 
traverse along a railroad should follow the setting of the station marks 
of the traverse stations. This will make it possible to use the traverse 
stations as bench marks and mil avoid the necessity for setting other 
bench marks. If the leveling party should be held back at all on 
this account, the members of the leveling party can assist the traverse 
party in any way that is possible and work on their ovm records until 
the marking of the traverse stations has been carried ahead. The 
traverse party should do everything that is possible to keep the 
stations marked ahead of the leveling, in order that the leveling party 
may not be delayed. 

69. When carrying the line of levels from the railroad into a town 
for the purpose of connecting with the bench marks established on 
masonr>', brick, concrete, or other structures, the place where the 
leveling left the track should be indicated in the records. When the 
leveling has returned to the track, the rod should be held as nearly 
as possible on the same turning point that was last used when the line 
of levels left the track and a proper note should be made in the 
record. If this is done, it will be possible to get a continuous profile 
of the track over which the traverse is run, for use in computing the 
inclination corrections. 

60. Two rod readings should be taken on the rail opposite each trav- 
erse station or bench mark which has been established on the side 
of a tangent. One of those readings should be made from the instru- 
ment station just before getting to the point opposite the traverse sta- 
tion or bench mark, and the second rod reading should be made from 
the first instrument station after passing the traverse station or bench 
mark. This will make it possible for the computer to get a continuous 
profile between traverse stations and also obtain a rough check on the 
measured distances. It should be borne in mind that distances as 
well as elevations are computed from the precise levels. If the 

114.58.5" 19 3 



18 U. S. COAST AND GEODETIC SURVEY. 

leveling is done according to these instructions, gross errors in the 
taping will be discovered in computing the distances for the grade 
corrections. 

61. At all times when an extra rod reading is taken it should be 
indicated in the record by the letters F or B according to whether the 
reading was taken in front of the instrument or back of it. 

62. There should be noted in the record the points in the line of 
levels at which decided changes of grade occur. 

63. Care should be taken to show clearly in the record when 
readings are made opposite a railroad station if there is a traverse 
station near-by having the same name. 

64. In carrying on precise leveling one rod may be kept ahead for 
a whole section, and then for the next section the other rod can be 
kept ahead. By alternating the rods for successive sections no 
appreciable error will enter into the leveling, and in many cases the 
work will be expedited. This method should be used only if better 
progress can be made than by the usual method of ha\ing the same 
rod at a rod station for both the fore sight and the back sight. 

65. Except in special cases the inclination corrections for the 
distance from the points of tangency to the traverse stations should 
be determined by levels run especially for the purpose and separate 
from the precise leveling. The leveling over the stakes need have 
only such accuracy as is necessary to obtain the grade correction for 
any one tape length with an error not in excess of one millimeter or 
one part in 50 000. There should be both a forward and backward 
running with different instrument stations. 

66. In recording the levels over the stakes care should be used to 
give the stakes the same designation as in the traverse record. 

67. A leveling rod graduated to meters should be used for the Y 
levels in order to avoid the necessity for the conversions from feet to 
meters in joining the Y levels with the precise levels. It is recom- 
mended that a Y level equipped with stadia wii'es be used on this 
work in order to give an additional check on the distances measured 
over the stakes. The offset distance of each instrument station not 
in the line of stakes should be paced and noted in the record in order 
that proper allowance can be made in computing the check distances 
over the stakes. 



GENERAL INSTRUCTIONS FOR TRAVERSE. 19 

RECORDS AND COMPUTATIONS. 

68. There are given below samples of records, abstracts, computa- 
tions, and results in connection with primary traverse. These sam- 
ples should be followed unless authority has been given by the Super- 
intendent to deviate from them. 

69. The following samples of records and computations, with the 
exception of the computation of loop closure, are all for the same 
section of the traverse, namely, from station North to station Douglas 
of the Savannah-Norfolk traverse line. This makes it possible for 



Fig. 1. Section of traverse line. 

anyone desiring to do so to follow through the various steps of the 
computation and see how each value is obtained. The section 
selected is a typical one with one station at the intersection of two 
tangents and tho other an offset station on a long tangent. 

70. All angles of the traverse are measured and recorded as in 
triangulation, instructions for which have already been published in 
Special Publications Nos. 19 and 26. No samples of the angle 
measurements are included in this publication. 



20 



U. S. COAST AND GEODETIC SURVEY. 



71. Traverse measurement. 

From station North to station Douglas, forward measurement. 
Department op Commerce 

U. S. COAST AND GEODETIC SURVEY 

Form 590. 

[Date, 5-11-18; time, 10.30 a. m.; tape No. 552; bal. No. 266.] 



Section. 


Temp. 


Set-up. 


Setback. 


Tape 
sup- 
port. 




From 


To- 


For- 
ward. 


Rear. 


Remarks. 


Rail North. 


1 

2 

3 

4 

5 

6 

7 

8 

9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
24' 
25 
26 
Table Douglas. 

tid totals 


43.5 
41.3 
40.2 
39.1 
37.0 
36.1 
35.0 
36.8 
36.6 
36.4 
36.4 
37.3 
38.0 
38.6 
38.4 
38.4 
39.3 
39.2 
38.5 
39.2 
43.5 
41.4 
40.0 
40.0 


44.0 
41.0 
39.8 
38.9 
38.6 
38.5 
34.9 
.36.4 
36.1 
35.9 
34.9 
36.9 
37.1 
37.3 
38.4 
39.6 
39 7 
39.8 
39.9 
41.0 
44.3 
44.5 
43.9 
42.9 


Meters. 


Meters. 


aT 
T 
T 
T 
T 
T 
T 
T 
T 
T 
T 
T 
T 
T 
T 
T 
T 
T 
T 
T 
T 
T 
T 
T 
T 
3 
3 
3 

1 


Left-hand rail. 


1 








2 








3 








4 









5 






/6+20m.=T.B. 
t M. 115. 


6 






7 
8 






9 






fll-f7m-WR 


10 






X. (wagon- 


11 






12 






ing) 


13 








14 








15 








16 








17 








18 








19 








20 








21 








22 








23 






S. U.=55' 111" 
24+4 m.=P. 
^ T. 42 


24 


17.0565 




24' 


37.4 
36.7 
34.8 


34.8- 
35.1 
32.9 


0.0445 


25 




Chief of trav- 


26 


0.0110 










ing subparty: 
J Smook 


Means a 






17.0675 


0.0445 













o A "T" in this column means that the tape is supported throughout, a "3' 
'5" means the number of equally spaced supports. 



GENERAL INSTRUCTIONS FOR TRAVERSE. 



21 



72. Check measurement. 

From station Douglas to station North, backward measurement. 
[Date, 5-13-18; time, 9 a. m.; tape No. 251 (300-foot).] 



Section. 


Tem- 
pera- 
ture. 


Set- 
up. 


Set- 
back. 


Remarks. 


From 


To- 


Table Douglas. 


1 

2 

3 

4 

5 

6 

7 

8 

9 
10 
11 
12 
13 
14 
RaU north. 


"C. 

37.1 

36.5 

35.4 

35.0 

34.8 

34.6 

34.3 

34.1 

34.2 

34.6 

34.9 

35.2 

35.5 

36.1 

36.4 


Feet. 


Feet. 




1 






1-1-235'- P. T. 42. 


2 








3 








4 








5 








6 








7 








8 






8+257'- W R X. 


9 






(wagon road cross- 


10 






ing). 


11 






11+135' T. B. M. 115 


12 








13 








14 


284.8 







Totallengtli=44S4.8 fect= 1366.97 meters; original measuremcnt= 1367.02 meters. 
The check measurement may be recorded in the regular traverse book, Form 590, by 
making a few changes in the headings. 

73. Y levels over stakes. 

Station Douglas. 

[Date, 5-14-18; time, 11.30 a. m.; Y level, 93.J 





Forward running. 


Rod station. 


Backward running. 


Mean 


Rod station.a 


Back 
sight. 


Fore 
sight. 


Differ- 
ence of 
eleva- 
tion. 


Back 
sight. 


Fore 
sight. 


Differ- 
ence of 
eleva- 
tion. 


differ- 
once of 
eleva- 
tion . 


P. T. 42 


Feet. 
1.04 

y::::. 


Feet. 


Feet. 


P. T. 43 
3 
2 
1 
Mark at Doug- 
las 


Feet. 
6.75 


Feet. 


Feet. 


Feet. 


24' 
25 
26 
Table at Doug- 
las 


1.38 
1.20 
0.83 

2.84 


-0.34 

+0.18 
+0.37 

-2.01 


6.89 
5.80 
6.15 
3.54 


-0.14 
+1.09 
-0.35 

+2.61 


+ 0.16 

- 1.10 
+ 0.34 

- 2.60 


Mark at Doug- 
las 


} 


3.93 


-1.09 


Table at Doug- 
las. 




2.45 


+1.09 


- 1.09 


1 
2 
3 
P. T. 43 




6.52 
6.18 
7.29 
7.12 


-2.59 
+0.34 
-1.11 
+0.17 


26 

25 

24' 

P. T. 42 





0.43 
0.80 
0.98 
0.60 


+2.02 
-0.37 
-0.16 
+0.36 


- 2.02 
+ 0.37 
+ 0.17 

- 0.35 



a Y level readings should be recorded in the same order as the points sighted on actu- 
ally occur along the traverse line, in the direction of progress. 



V 



22 



17. S. COAST AND GEODETIC SURVEY. 



74. For convenience in printing, the backward and forward runnings 
of the Y levels over the stakes are given together in the preceding table. 
In the field the two runnings should be recorded on different pages, 
separated by a page or two in order to avoid duplication of errors by 
the recorder. A third running should be made if the first two fail to 
check. 

75. Precise levels. 

T. B. M. 115 to B. M, Aa (forward). 



Rail at T. B. M. 115 (B) 



42 3* 




^ 


t5 ^ 

Si -^ 

^ 1 




.a' bo 


% 1 




a o 


m f^ 




pq ^ 


223500000 




2003 


233600000 




2136 


243800000 




2269 


720 




70900000 


820 




84300000 


921 




97700000 


\1479Ha 




(153871 


h579?e 


Rail at A Douglas (F) 


hoQln 


U680 




(158471 


281 




. 128700000 


428 




140500000 


575 




152300000 


258200000 




1100 


273100000 




1219 


288000000 




1338 


256300000 




jl539 


271100000 


P. T, 43 (F) 


{1549W 


286000000 




ll5597 


504 




954 


651 




1025 


799 




1097 


814 




225400000 


962 




232700000 


1110 




240000000 


249300000 




j 148171 


264200000 


RaOatB.M. AaT) 


h552n 


279100000 




Il6237i 


120400000 
133700000 








4899828710 


147000000 


Difl. of siiTns= +20288 




2180 


Diff. of sums divided by 3 


=.- 


2328 


DifE. of elev.= +6762.7 




2476 






181871 






1890W 






,1963 







P. T. 42 (F) 



a AW numbers in this table marked with an "t?" are not included in the total, as 
they were put in the adding machine with the "non-add" key depressed. 



GENERAL INSTRUCTIONS FOR TRAVERSE. 23 

SAMPLE COMPUTATIONS AND TABLES. 

76. The various steps in making a traverse computation are as 
follows: 

(a) Checking list of directions from the original angle records. 

(6) Computation of gi-ade corrections and mean elevations of sections. 

(c) Computation of lengths on Form 589, including temperature, 
tape, and sea-level corrections. 

(d) Projection computation or computation of lengths between the 
true stations when the tape measures were made to a point on the 
rail opposite the station at either or both ends. 

(e) Closm-e of loops when the azimuth is carried through long lines 
extending past several stations. (See par. 46.) 

(/) Computation of geographic positions. As there is no check on 
this computation, it must be made in duplicate. 

(g) Final least square adjustment to make the traverse lines con- 
sistent with each other and with the triangulation with which they 
connect. 

77. Various tables which are useful in making the computations 
are given on the following pages just after the computation in each 
case for which they are needed. The first one of these tables giving 
the inclination correction for different lengths of section and differ- 
ences of elevation will be found on page 25. This is used for com- 
puting the inclination corrections when these corrections depend 
upon the precise levels. Following the computation of lengths on 
page 33 are several tables of tape corrections for tape No. 552 for 
various methods of support. These tables can be used only for this 
one standardization of this particular tape. Each tape and each 
new standardization requires new tables. Whenever a tape is used 
for any considerable length of time it will be found to save much 
work in the long run to construct tables similar to the ones published 
here. 



24 U. 8. COAST AND GEODETIC SURVEY. 

78. Computation of inclination correction. 

From station North to station Douglas. 



Bench mark. 


Differ- 
ence of 
eleva- 
tion. 


Dis- 
tance. 


Inclination 
correction.a 


Eleva- 
tion. 


Remarks. 


Rail North-.... 

-RailllS 

Rail 115- 

-P.T.42 


Meters. 
-0.01 
-0.59 
0.15 
+0.76 
-f-2.30 
+ 2.06 
+ 1.68 
-0.55 
-0.11 
+0.05 
+0.11 

-0.62 


Meters. 
16 
199 
102 
134 
197 
197 
198 
137 
13 
50 
50 

50 


Millimeters. 
0.0 
0.9 
0.1 
2.2 
13.4 
10.8 
7.1 
1.1 
0.5 
0.0 
0.2 

3.8 


Meters. 
103.051 

i62.'29J 

:::::::: 


107. 98 


Preciselevel record, Vol. 15 
{see page 22). 

Traverse record, Vol. 6 (see 
page 20) .and wye-levelrecord, 
Vol. I(epage21). 


2628. 


ao f Table 
^^'XDouglas.... 


Total . 


1343c 


40.1 








Meaneleva 


tion . . 


105.3 









a The corrections in this column were obtained from the table on page 25, except for 
the last part of the section, shown in italics, for which the corrections were obtained 
from the table on page 28. 

b The mean of these two elevations was used in computing the mean elevation for the 
whole section. 

c Due to the use of a convenient but slightly inaccurate value of the stadia constant 
for the precise level, this distance fails to check the measured distance. The percentage 
of error is qiute small, and by comparing several sections its value can be obtained 
quite accurately and allowance made for it. If the precise leveling has been done 
according to the instructions in this pubhcation, this check on the distance should 
locate any bluuder of a tape length in the tape measurement. 

79. With regard to the preceding computation it should be noted 
that the table on page 25 differs from the one on page 28 in this respect, 
that in the former the known measured distance, I, is the horizontal 
distance or leg of the right triangle, while in the latter it is the inclined 
distance or hypotenuse of the right triangle. This distinction should 
be kept in mind in computing any values which fall outside the limits 
of the tables. 

80. In computing inclination corrections outside the limits of the~ 
table on page 25 for the precise-leveling work it will be found that the 
first term only of the series formula at the top of the table, namely, 

^-j, will give sufficient accuracy. The same formula may also be used 

for the Y-level work when the lengths are other than the 25 or 50 
meters for which the table on page 28 is computed and when the 



GENERAL INSTRUCTIONS FOR TRA^T^RSE. 



25 



grades are under 5 per cent. Of course h must be expressed in meters 
instead of feet. Other values outside the limits of the tables can be 
obtained readily by actually computing -the right triangle. Barlow's 
tables of squares will be found useful in this connection. 

81. Inclination correction. 



^- . ,'h* 



[Correction=i Vp+^^= iT~+i7i (always negative).] 



Length 
of sec- 








Difference of elevation in meters. 








tion in 
meters. 


0.0 


0.. 


0.2 


0.3 


0.4 


0.5 


0.6 


0.7 


0.8 


0.9 


1.0 


10 


mm. 
0.0 


mm. 
0.5 
0.2 
0.2 
0.1 

0.1 
0.1 
0.1 
0.1 
0.1 

0.0 


mm. 
2.0 
1.0 
0.7 
0.5 

0.4 
0.3 
0.3 
0.2 
0.2 

0.2 
0.2 
0.2 
0.2 
0.1 

0.1 
0.1 
0.1 
0.1 
0.1 


mm. 


mm. 


mm. 


mm. 


mm. 


mm. 


mm. 


mm. 


20 


2.2 
1.5 
1.1 

0.9 
0.8 
0.6 
0.6 
0.5 

0.4 
0.4 
0.4 
0.3 
0.3 

0.3 
0.3 
0.3 
0.2 
0.2 


4.0 
2.7 
2.0 

1.6 
1.3 
1.1 
1.0 
0.9 

0.8 
0.7 
0.7 
0.6 
0.6 

0.5 
0.5 
0.5 
0.4 
0.4 














3o:.... 




4.2 
3.1 

2.5 
2.1 

1.8 
1.6 
1.4 

1.2 
1.1 
1.0 
1.0 
0.9 

0.8 
0.8 
0.7 
0.7 
0.7 


6.0 
4.5 

3.6 
3.0 
2.6 
2.2 
2.0 

1.8 
L6 
1.5 
1.4 
1.3 

1.2 
1.1 
1.1 
1.0 
0.9 


8.2 
6.1 

4.9 
4.1 
3.5 
3.1 
2.7 

2.4 
2.2 

2.0 
1.9 
L7 

1.6 
L5 
1.4 
1.4 

1.3 


10.7 
8.0 

6.4 
5.3 
4.6 
4.0 
3.6 

3.2 
2.9 
2.7 
2.5 
2.3 

2.1 
2.0 
1.9 

1.8 
1.7 






40 




10.1 

8.1 
6.8 
5.8 
5.1 
4.5 

4.0 
3.7 
3.4 
3.1 
2.9 

2.7 
2.5 
2.4 
2.2 

2.1 


12.5 


.50 .. 




10 


60 




8.3 


70 




7.1 


80..... 




6 2 


90 




5.6 


100 




5 


110 




4.5 


120 




4 2 


130 


i 


3 8 


140 


i 


3 6 


150 


' 


33 


ICO 




3.1 
2.9 

2 8 


170... . 






180 


.. 




190 






2 6 











200 






0.1 
0.1 
0.1 
0.1 
0.1 

0.1 
0.1 
0.1 
0.1 
0.1 

0.1 


0.2 
0.2 
0.2 
0.2 
0.2 

0.2 
0.2 
0.2 
0.2 
0.2 

0.2 


0.4 
0.4 
0.4 
0.3 
0.3 

0.3 
0.3 
0.3 
0.3 
0.3 

0.3 


0.6 
0.6 
0.6 
0.5 
0.5 

0.5 
0.5 
0.5 
0.4 
0.4 

0.4 


0.9 
0.9 
0.8 
0.8 
0.7 

0.7 
0.7 
0.7 
0.6 
0.6 

0.6 


1.2 
1.2 
1.1 
1.1 
1.0 

1.0 
0.9 
0.9 
0.9 
0.8 

0.8 


1.6 
1.5 
1.5 
1.4 
1.3 

1.3 
1.2 
1.2 
LI 
1.1 

LI 


2.0 
1.9 
1.8 
1.8 
L7 

L6 
L6 
L5 
1.4 
L4 

1.3 


2 5 


210 

220 






2.4 
2.3 
2 2 


230 







240 






2.1 
2 


250 






260... . 






1 


270. 






1.8 
L7 

L7 


280 






290 

300 













26 U. S. COAST AND GEODETIC SURVEY. 

Inclination correction Continued . 



Length 






Difference of elevation in meters. 








of sec- 






















tion in 






















meters. 


1.1 


1.2 


1.3 


1.4 


1.5 


1.6 


1.7 


1.8 


1.9 


2.0 




mm. 


mm. 


mm. 


mm. 


mm. 


mm. 


mm. 


mm. 


mm. 


mm. 


40 


15.1 


18.0 


















50 . 


12.1 


14.4 


16.9 


19.6 


22.5 


25.6 










60 


10.1 


12.0 


14.1 


16.3 


18.8 


21.3 


24.1 


27.0 


30.1 


33.3 


70 


8.6 


10.3 


12.1 


14.0 


16.1 


18.3 


20.6 


23.1 


25.8 


28.6 


80 


7.6 


9.0 
8.0 


10.6 
9.4 


12.2 
10.9 


14.1 
12.5 


16.0 
14.2 


18.1 


20.2 


22.6 
20.1 


25.0 
22.2 


90 


6.7 






100 


6.0 


7.2 


8.4 


9.8 


11.2 


12.8 


14.4 


16.2 


18.0 


20.0 


110 


5.5 


6.5 


7.7 


8.9 


10.2 


11.6 


13.1 


14.7 


16.4 


18.2 


120 


5.0 


6.0 


7.0 


8.2 


9.4 


10.7 


12.0 


13.5 


15.0 


16.7 


130 


4.7 


5.5 


6.5 


7.5 


8.7 


9.8 


11.1 


12.5 


13.9 


15.4 


140 


4.3 


5.1 


6.0 


7.0 


8.0 


9.1 


10.3 


11.6 


12.9 


14.3 


150 


4.0 


4.8 


5.6 


6.5 


7.,5 


8.5 


9.6 


10.8 


12.0 


13.3 


160 


3.8 


4.5 


5.3 


6.1 


7.0 


8.0 


9.0 


10.1 


11.3 


12.5 


170 


3.6 


'i.2 


5.0 


5.8 


6.6 


7.5 


8.5 


9.5 


10.6 


11.8 


180 


3.4 


4.0 


4.7 


5.5 


6.3 


7.1 


8.0 


9.0 


10.0 


11.1 


190 


3.2 


3.8 


4.4 


5.2 


5.9 


6.7 


7.6 


8.5 


9.5 


10.5 


200 


3.0 


3.6 


4.2 


4.9 


5.6 


6.4 


7.2 


8.1 


9.0 


10.0 


210 


2.9 


3.4 


4.0 


4.7 


6.4 


6.1 


6.9 


7.7 


.8.6 


9.5 


220 


2.7 


3.3 


3.8 


4.5 


6.1 


6.8 


6.6 


7.4 


8.2 


9.1 


230 


2.6 


3.1 


3.7 


4.3 


4.9 


5.6 


6.3 


7.0 


7.8 


8.7 


240 


2.5 


3.0 


3.5 


4.1 


4.7 


5.3 


6.0 


6.7 


7.5 


8.3 


250 


2.4 


2.9 


3.4 


3.9 


4.5 


6.1 


5.8 


6.5 


7.2 


8.0 


280 


2.3 


2.8 


3.2 


3.8 


4.3 


4.9 


5.6 


6.2 


6.9 


7.7 


270 


2.2 


2.7 


3.1 


3.6 


4.2 


4.7 


5.4 


6.0 


6.7 


7.4 


280 


2.2 


2.6 


3.0 


3.6 


4.0 


4.6 


5.2 


6.8 


6.4 


7.1 


290 


2.1 


2.5 


2.9 


3.4 


3.9 


4.4 


6.0 


5.6 


6.2 


6.9 


300 


2.0 


2.4 


2.8 


3.3 


3.7 


4.3 


4.8 


5.4 


6.0 


6.7 



GENERAL INSTRUCTIONS FOR TRAVERSE. 
Inclination correction Continued. 



27 



Length 
of sec- 
tion in 
meters. 



Difference of elevation in meters. 



2.1 



2.2 



2.3 



2.4 



2.5 



2.6 



2.7 



2.8 



2.0 



3.0 



70 
80 
90 

100 
110 
120 
130 
140. 

150, 

160, 
170 
ISO 
190, 

200, 
210, 
220, 
230, 
240. 

250 

260, 
270, 
280, 
290. 

300. 



mm. 
31.5 
27.6 
24.5 

22.0 
20.0 
18.4 
17.0 
15.7 

14.7 
13.8 
13.0 
12.2 
11.6 

11.0 
10.5 
10.0 
9.6 
9.2 

8.8 
8.5 
8.2 
7.9 

7.6 



mm. 
34.6 
30.2 
26.9 

24.2 
22.0 
20.2 
18.6 
17.3 

16.1 
15.1 
14.2 
13.4 
12.7 

12.1 

11.5 
11.0 
10.5 
10.1 

8.7 

9.3 
9.0 
8.7 
8.3 

8.1 



mm. 
37.8 
33.1 
29.4 

2S.4 

24.0 
22.0 
20.3 
18.9 

17.6 
16.5 
15.6 
14.7 
13.9 

13.2 

12.6 
12.0 
11.5 
11.0 

10.6 
10.2 
9.8 
9.4 
9.1 

8.8 



mm. 
41.1 
36.0 
32.0 

28.8 
26.2 
24.0 
22.1 
20.6 

19.2 

18.0 
16.9 
16.0 
15.2 

14.4 
13.7 
13.1 
12.5 
12.0 

11.5 
11.1 
10.7 
10.3 
9.9 

9.6 



34 



31.2 
28.4 
26.0 
24.0 
22.3 



ly.o 
18.4 
17.4 
16.5 

15.6 
14.9 
14.2 

13.6 
13.0 

12.5 
12.0 
11.6 
11.2 

10. S 



42.2 
37.6 

33.8 
30.7 
28.2 
26.0 



22.5 
21.1 
19.9 

18.8 
17.8 

16.9 
16.1 
15.4 
14.7 

14.1 

13.5 
13.0 
12.5 
12.1 
11.7 



10.4 11.3 



45.6 
40.5 

36.4 
33.1 
30.4 
28.0 
26.0 

24.3 
22.8 
21.5 
20.2 
19.2 

18.2 
17.4 
16.6 
15.8 
15.2 

14.6 
14.0 
18.5 
13.0 
12.8 

12.1 



49.0 
43.8 

39.2 
35.6 
32.7 
30.2 
28.0 

26.1 
24.5 
23.1 
21.8 
20.6 

19.6 
18.7 
17.8 
17.0 
16.3 

15.7 
15.1 
14.5 
14.0 
13.5 

13.1 



46.7 

42.0 
3<S.2 
35.0 
32.3 
30.0 

28.0 
26.3 
24.7 
23.4 
22.1 

21.0 
20.0 
19.1 
18.3 
17.5 

16.8 
16.2 
15.6 
15.0 
14.5 

14.0 



50.0 

45.0 
40.9 
37.5 
34.6 
32.1 

30.0 
2<<.l 
26.5 
25.0 
23.7 

22.5 
21.9 
20.5 
19.6 

18.7 

18.0 
17.3 
16.7 
16.1 
15.5 

15.0 



28 



U. S. COAST AND GEODETIC SURVEY. 



82. Inclination corrections for 50-meter tape lengths. - 

[Cor. = .01h2 .OOOOOlh*.] 



Difference in 


Correc- 


Difference in 


Correc- 


Difference in 


Correc- 


elevation. 


tion. 


elevation. 


tion. 


elevation. 


tion. 


Meters. 


Feet. 


mm. 


Meters. 


Feet. 


mm. 


MeUrs. 


Feet. 


mm. 


0.00 


0.000 


0.0 


0.50 


1.640 


2.5 


1.00 


3.281 


10.0 


.01 


.033 


.0 


.51 


1.673 


2.6 


1.01 


3.314 


10.2 


.02 


.066 


.0 


.52 


1.706 


2.7 


1.02 


3.346 


10.4 


.03 


.098 


.0 


.53 


1.739 


2.8 


1.03 


3.379 


10.6 


.04 


.131 


.0 


.54 


1.772 


2.9 


1.04 


3.412 


10.8 


.05 


.164 


.0 


.55 


1.804 


3.0 


1.05 


3.445 


11.0 


.06 


.197 


.0 


.56 


1.837 


3.1 


1.06 


3.478 


11.2 


.07 


.230 


.0 


.57 


1.870 


3.2 


1.07 


3.510 


11.4 


.08 


.262 


.1 


.58 


1.903 


3.4 


1.08 


3.543 


11.7 


.09 


.295 


.1 


.59 


1.936 


3.5 


1.09 


3.676 


11.9 


.10 


.328 


.1 


.60 


1.968 


3.6 


1.10 


3.609 


12.1 


.11 


.361 


.1 


.61 


2.001 


3.7 


1.11 


3.642 


12.3 


.12 


.394 


.1 


.62 


2.034 


3.8 


1.12 


3.675 


12.5 


.13 


.427 


.2 


.63 


2.067 


4.0 


1.13 


3.707 


12.8 


.14 


.459 


.2 


.64 


2.100 


4.1 


1.14 


3.740 


13.0 


.15 


.492 


.2 


.65 


2.133 


4.2 


1.15 


3.773 


13.2 


.16 


.525 


.3 


.66 


2.105 


4.4 


1.16 


3.806 


13.5 


.17 


.558 


.3 


.67 


2.198 


4.5 


1.17 


3.839 


13.7 


.18 


.591 


.3 


.68 


2.231 


4.6 


1.18 


3.871 


13.9 


.19 


.623 


.4 


.69 


2.264 


4.8 


1.19 


3.904 


14.2 


.20 


.656 


.4 


.70 


2.297 


4.9 


1.20 


3.937 


14.4 


.21 


.689 


.4 


.71 


2.329 


5.0 


1.21 


3.970 


14.6 


.22 


.722 


.5 


.72 


2.362 


5.2 


1.22 


4.003 


14.9 


.23 


.755 


.5 


.73 


2.395 


5.3 


1.23 


4.035 


15.1 


.24 


.787 


.6 


.74 


2.428 


5.5 


1.24 


4.068 


15.4 


.25 


.820 


.6 


.75 


2.461 


5.6 


1.26 


4.101 


15.6 


.26 


.853 


.7 


.76 


2. 493 


5.8 


1.26 


4.134 


15.9 


.27 


.886 


.7 


.77 


2. 526 


6.9 


1.27 


4.167 


16.1 


.28 


.919 


.8 


.78 


2.559 


6.1 


1.28 


4.199 


16.4 


.29 


.951 


.8 


.79 


2.592 


6.2 


1.29 


4.232 


16.6 


.30 


.984 


.9 


.80 


2.625 


6.4 


1.30 


4.265 


16.9 


.31 


1.017 


1.0 


.81 


2.657 


6.6 


1.31 


4.298 


17.2 


.32 


1.050 


1.0 


.82 


2.690 


6.7 


1.32 


4.331 


17.4 


.33 


1.083 


1.1 


.83 


2.723 


6.9 


1.33 


4.3&4 


17.7 


.34 


1.115 


1.2 


.84 


2.756 


7.1 


1.34 


4.396 


18.0 


.35 


1.148 


1.2 


.86 


2.789 


7.2 


1.35 


4.429 


18.2 


.36 


1.181 


1.3 


.86 


2.822 


7.4 


1.36 


4.462 


18.5 


.37 


1.214 


1.4 


.87 


2.854 


7.6 


1.37 


4.495 


18.8 


.38 


1.247 


1.4 


.88 


2.887 


7.7 


1.38 


4.528 


19.0 


.39 


1.280 


1.5 


.89 


2.920 


7.9 


1.39 


4.560 


19.3 


.40 


1.312 


1.6 


.90 


2.953 


8.1 


1.40 


4,593 


19.6 


.41 


1.345 


1.7 


.91 


2.986 


8.3 


1.41 


4.626 


19.9 


.42 


1.378 


1.8 


.92 


3.018 


8.5 


1.42 


4.659 


20.2 


.43 


1.411 


1.8 


.93 


3.051 


8.6 


1.43 


4.692 


20.4 


.44 


1.444 


1.9 


.94 


3.084 


8.8 


1.44 


4.724 


20.7 


.45 


1.476 


2.0 


.95 


3.117 


9.0 


1.45 


4.757 


21.0 


.46 


1.509 


2.1 


.96 


3.150 


9.2 


1.46 


4.790 


21.3 


.47 


1.542 


2.2 


.97 


3.182 


9.4 


1.47 


4.823 


21.6 


.48 


1.575 


2.3 


.98 


3.215 


9.6 


1.48 


4.856 


21.9 


.49 


1.60P 


2.4 


.99 


3.248 


9.8 


1.49 


4.888 


22.2 



GENERAL INSTRUCTIONS FOR TRAVERSE. 29 

Inclination corrections for 50-meter tape lengths Continued. 



Difference in 


Correc- 


Difference in 


Correc- 


Difference in 


Correc- 


elevation. 


tion. 


elevation. 


tion. 


elevation. 


tion. 


Meters. 


Feet. 


mm. 


Meters. 


Feet. 


mm. 


Meters. 


Feet. 


mm. 


1.50 


4.921 


22.5 


2.00 


6.562 


40.0 


2.50 


8.202 


62.5 


1.51 


4.954 


22.8 


2.01 


6.594 


40.4 


2.51 


8.235 


63.0 


1.52 


4.9S7 


23.1 


2.02 


6.627 


40.8 


2.52 


8.208 


63.5 


1.53 


* 5.020 


23.4 


2.03 


6. 600 


41.2 


2.53 


8.301 


64.0 


1.54 


5.052 


23.7 


2.04 


6.693 


41.6 


2.54 


8.333 


64.6 


1.55 


5.085 


24.0 


2.05 


6.726 


42.0 


2.55 


8.366 


65.1 


1.56 


5.118 


24.3 


2.06 


6.759 


42.5 


2.56 


8.399 


65.6 


1.57 


5.151 


24.6 


2.07 


6.791 


42.9 


2.57 


8.432 


66.1 


1.58 


5.184 


25.0 


2.08 


6.824 


43.3 


2.58 


8.465 


66.6 


1.59 


5.217 


25.3 


2.09 


6.857 


43.7 


2.59 


8.497 


67.1 


1.60 


5.249 


25.6 


2.10 


6.890 


44.1 


2.60 


8.530 


67.6 


1.61 


5.282 


25.9 


2.11 


6.923 


44.5 


2.61 


8.563 


68.2 


1.62 


5.315 


26.2 


2.12 


6.955 


45.0 


2.62 


8.596 


68.7 


1.63 


5.348 


26.6 


2.13 


6.988 


45.4 


2.63 


8.629 


69.2 


1.64 


5.381 


20.9 


2.14 


7.021 


45.8 


2.64 


8.661 


69.7 


1.65 


5.413 


27.2 


2.15 


7.054 


46.2 


2.65 


8.694 


70.3 


1.66 


5.446 


27.6 


2.16 


7.087 


46.7 


2.66 


8.727 


70.8 


1.67 


5.479 


27.9 


2.17 


7.119 


47.1 


2.67 


8.760 


71.3 


1.68 


5.512 


28.2 


2.18 


7.152 


47.5 


2.68 


8.793 


71.9 


1.69 


5.545 


28.6 


2.19 


7.185 


48.0 


2.69 


8.825 


72.4 


1.70 


5. -.77 


28.9 


2.20 


7.218 


48.4 


2.70 


8.858 


73.0 


1.71 


5.6iO 


29.2 


2.21 


7.251 


48.9 


2.71 


8.891 


73.5 


1.72 


5.643 


29.6 


2.22 


7.283 


49.3 


2.72 


8.924 


74.0 


1.73 


5.676 


29.9 


2.23 


7.316 


49.8 


2.73 


8.957 


74.6 


1.74 


5.709 


30.3 


2.24 


7.349 


60.2 


2.74 


8.989 


75.1 


1.75 


5.741 


30.6 


2.25 


7.382 


50.7 


2.75 


9.022 


75.7 


1.76 


5.774 


31.0 


2.26 


7.415 


51.1 


' 2.76 


9.055 


76.2 


1.77 


5.807 


31.3 


2.27 


7.447 


61.6 


2.77 


9.088 


76.8 


1.78 


5.840 


31.7 


2.28 


7.480 


52.0 


2.78 


9.121 


77.3 


1.79 


5.873 


32.0 


2.29 


7.513 


62.5 


2.79 


9.14 


77.9 


1.80 


5.906 


32.4 


2.30 


7.546 


52.9 


2.80 


9.186 


78.5 


1.81 


5.938 


32.8 


2.31 


7.579 


53.4 


2.81 


9.219 


79.0 


1.82 


5.971 


33.1 


2.32 


7.612 


53. 9> 


2.82 


9.252 


79.6 


1.83 


0.004 


33.5 


2.33 


7.644 


54.3 


2.83 


9.285 


80.2 


1.84 


6.037 


33.9 


2.34 


7.677 


54.8 


2.84 


9.318 


80.7 


1.85 


6.070 


34.2 


2.3.5 


7.710 


55.3 


j 2.85 
2.86 


9.350 


81.3 


1.86 


6.102 


34.6 


2.3^^ 


7.743 


65.7 


9.383 


81.9 


1.87 


6.135 


35.0 


2.37 


7.776 


56.2 


2.87 


9.416 


82.4 


1.88 


6.168 


35.3 


2.38 


7.808 


56.7 


2.88 


9.449 


83.0 


1.89 


6.201 


35.7 


2.39 


7.841 


57.2 


2.89 


9.482 


83.6 


1.90 


6.234 


36.1 


2.40 


7.874 


57.6 


2.90 


9.514 


84.2 


1.91 


6.266 


36.5 


2.41 


7.907 


68.1 


2.91 


9.547 


84.8 


1.92 


6.299 


36.9 


2.42 


7.940 


68.6 


2.92 


9.580 


85.3 


1.93 


6.332 


37.2 


2.43 


7.972 


59.1 


2.93 


9.613 


85.9 


1.94 


6.365 


37.6 


21.44 


8.905 


59.6 


2.91 


9.646 


86.5 


1.95 


6.398 


38.0 


2.45 


8.038 


60.1 


2.95 


9.678 


87.1 


1.96 


6.430 


38.4 


2.46 


8.071 


60.6 


2.96 


9.711 


87.7 


1.97 


6.463 


38.8 


2.47 


8.104 


61.0 


2.97 


9.744 


88.3 


1.98 


6.496 


39.2 


2.48 


8.136 


61.5 


2.98 


9.777 


88.9 


1.99 


6.529 


39.6 


2.49 


8.169 


62.0 


2.99 


9.810 


89.5 



30 U. S. COAST AND GEODETIC SURVEY. 

Inclination corrections for 50-meter tape lengths Continued . 



:::: 

Difference in 


Correc- 


Dlflerence in 


Correc- 


Difference in 


COTrec- 


elevation. 


Uon. 


elevation. 


tion. 


elevation. 


tion. 


Meters. 


Fed. 


mm. 


Meters, 


Feet. 


mm. 


Meters. 


Feet. 


mm. 


3.00 


9.842 


90.1 


3.50 


11.483 


122.7 


4.00 


13.123 


160.3 


3.01 


9.875 


90.7 


3.51 


11.516 


123.4 


4.01 


13. 156 


161.1 


3.02 


9.908 


91.3 


3.52 


11.549 


124.1 


4.02 


13. 189 


161.9 


3.03 


9.941 


91.9 


3.53 


11.581 


124.8 


4.03 


13. 222 


162.7 


3.04 


9.974 


92.5 


3.64 


11.614 


125.5 


.4.04 


13. 255 


163.6 


3.05 


10.007 


93.1 


3.55 


11.647 


126.2 


4.05 


13. 287 


164.3 


3.06 


10.039 


93.7 


3.56 


11. 680 


126.9 


4.06 


13.320 


165.1 


3.07 


10.072 


91.3 


3.57 


11.713 


127.6 


4.07 


13.353 


165.9 


3.03 


10.105 


95.0 


3.58 


11.745 


128.3 


4.08 


13.386 


166.7 


3.09 


10.138 


95.6 


3.59 


11.778 


129.0 


4.09 


13. 419 


167.6 


3.10 


10.171 


96.2 


3.60 


11.811 


129.8 


4.10 


13. 451 


168.4 


3.11 


10.203 


96.8 


3.61 


11.844 


130.5 


4.11 


13. 484 


169.2 


3.12 


10.236 


97.4 


3.62 


11.877 


131.2 


4.12 


13.517 


170.0 


3.13 


10. 2G9 


98. 1 


3.63 


11.909 


131.9 


4.13 


13.550 


170.9 


3.14 


10.302 


98.7 


3.64 


11.942 


132.7 


4.14 


13.583 


171.7 


3.15 


10.335 


99.3 


3.65 


11.975 


133.4 


4.15 


13.615 


172.5 


3.16 


10.367 


100.0 


3.66 


12.008 


134.1 


4.16 


13.648 


173.4 


3.17 


10.400 


100.6 


3.67 


12.041 


131.9 


4.17 


13.681 


174.2 


3.18 


10.433 


101.2 


3.68 


12.073 


135.6 


4.18 


13.714 


175.0 


3.19 


10. 466 


101.9 


3.69 


12. 106 


136.3 


4.19 


13.747 


176.9 


3.20 


10.499 


102.5 


3.70 


12.139 


137.1 


4.20 


13.780 


176.7 


3.21 


10.531 


103. 1 


3.71 


12. 172 


137.8 


4.21 


13.812 


177.6 


3.22 


10.564 


103.8 


3.72 


12. 205 


138.6 


4.22 


13.845 


178.4 


3.23 


10.597 


104.4 


3.73 


12. 238 


1.39.3 


4.23 


13.878 


179.2 


3.24 


10.630 


105.1 


3.74 


12. 270 


140.1 


4.24 


13.911 


180.1 


3.25 


10.663 


105.7 


3.75 


12.303 


140.8 


4.25 


13.944 


181.0 


3.26 


10.696 


106.4 


3.76 


12.336 


141.6 


4.28 


13.976 


181.8 


3.27 


10.728 


107.0 


3.77 


12.369 


142.3 


4.27 


14.009 


182.7 


3.28 


10.761 


107.7 


3.78 


12. 402 


143.1 


4.28 


14.042 


183.5 


3.29 


10.794 


108.4 


3.79 


12. 434 


143.8 


4.29 


14.075 


184.4 


3.30 


10.827 


109.0 


3.80 


12.467 


144. 6 


4.30 


14.108 


185.2 


3.31 


10.860 


109.7 


3.81 


12.500 


145.4 


4.31 


11.140 


186.1 


3.32 


10.892 


110.3 


3.82 


12.533 


146.1 


4.32 


11.173 


187.0 


3.33 


10.925 


111.0 


3.83 


12.566 


146.9 


4.33 


1 !. 206 


187.8 


3.34 


10.958 


111.7 


3.84 


12.598 


147.7 


4.34 


14.239 


188.7 


3.35 


10.991 


112.4 


3.85 


12.631 


148.4 


4.35 


14.272 


189.6 


3.36 


11.024 


113.0 


3.86 


12.664 


149.2 


4.36 


14.304 


190.5 


3.37 


11.056 


113.7 


3.87 


12. 697 


150.0 


4.37 


14.337 


191.3 


3.38 


11.089 


114.4 


3.88 


12.730 


150.8 


4.38 


14.370 


192.2 


3.39 


11.122 


115.1 


3.89 


12.762 


151.6 


4.39 


14.403 


193.1 


3.40 


11.155 


115.7 


3.90 


12.795 


152.3 


4.40 


14.436 


194.0 


3.41 


11.188 


116.4 


3.91 


12.828 


153.1 


4.41 


14.468 


194.9 


3.42 


11.220 


117.1 


3.92 


12.861 


153.9 


4.42 


14.601 


195.7 


3.43 


11.253 


117.8 


3.93 


12. 894 


154.7 


4.43 


14.534 


196.6 


3.44 


11.286 


118.5 


3.94 


12.926 


155.5 


4.44 


14.567 


197.5 


3.45 


11.319 


119.2 


3.95 


12.959 


156.3 


4.45 


14.600 


198.4 


3.46 


11.352 


119.9 


3.96 


12.992 


157.1 


4.46 


14.633 


199.3 


3.47 


11.384 


120.6 


3.97 


13.025 


157.9 


4.47 


14.665 


200.2 


3.48 


11.417 


121.3 


3.98 


13.058 


158.7 


4.48 


14.698 


201.1 


3.49 


11.450 


122.0 


3.99 


13.091 


159.5 


4.49 


14.731 


202.0 



GENERAL INSTRUCTIONS FOR TRAVERSE. 31 

Inclination corrections for 50-meter tape lengths Continued. 



Difference in 


1 Corree- 


Difference in 


Correc- 


Difference in 


Correc- 


elevation. 


! tion. 


elevation. 


tion. 


elevation. 


tion. 


Meters. 


Feet. 


mm. 


Meters. 


FeeL 


mm. 


llfeters. 


FeeL 


mm. 


4.50 


14.764 


202.9 


5.00 


16. 404 


250. 6 


i 5.50 


18.045 


303.4 


4.51 


14.797 


203.8 


5.01 


16.437 


251.6 


1 5.51 


18.077 


304.5 


4.52 


14.829 


204.7 


5.02 


16.470 


252.6 


5.52 


18,110 


305.6 


4.53 


14.862 


205.6 


5.0;? 


16.503 


253.6 


5.53 


18.143 


306.7 


4.54 


14.895 


206.5 


5.04 


16.535 


254.7 


5.54 


18.176 


307.9 


4.55 


14.928 


207.5 


5.05 


16.568 


255.7 


5.55 


18.209 


309.0 


4.56 


14.961 


208.4 


5.06 


16.601 


256.7 


5.56 


18.241 


310.1 


4.57 


14.993 


209.3 


5.07 


16.634 


257.7 


5-57 


18.274 


311.2 


4.58 


15.026 


210.2 


5.08 


16.607 


258.7 


5.58 


18.307 


312.3 


4.59 


15.059 


211.1 


5.09 


16.699 


259.8 


5.59 


18.340 


313.5 


4.60 


15.092 


212.0 


6.10 


16.732 


260.8 


6.60 


18.373 


314.6 


4.61 


15.125 


213.0 


5.11 


16.765 


261.8 


5.61 


18.405 


315.7 


4.62 


15.157 


213.9 


6.12 


16.798 


262.8 


5.62 


18.438 


316.8 


4.63 


15.190 


214.8 


6.13 


16.831 


263.9 


5.63 


18.471 


318.0 


4.64 


15.223 


215.8 


6.14 


16.863 


264.9 


5.64 


18.504 


319.1 


4.65 


15.256 


216.7 


5.15 


16.896 


265.9 


5.65 


18.537 


320.2 


4.66 


15.289 


217.6 


5.16 


16.929 


267.0 


5.66 


18.570 


321.4 


4.67 


15.321 


218.6 


5.17 


16.962 


268.0 


5.67 


18.602 


322.5 


4.68 


15.354 


219.5 


5.18 


16.995 


269.0 


5.68 


18.635 


323.7 


4.69 


15.387 


220.4 


5.19 


17.028 


270.1 


6.69 


18.668 


324.8 


4.70 


15.420 


221.4 


5.20 


17.060 


271.1 


5.70 


18.701 


326.0 


4.71 


15.453 


222.3 


5.21 


17.093 


272.2 


6.71 


18.734 


327.1 


4.72 


15.486 


223.3 


5.22 


17.128 


273.2 


6.72 


18. 766 


328.3 


4.73 


15.518 


224.2 


o.Zi 


17.159 


274.3 


5.73 


18.799 


329.4 


4.74 


15.551 


225.2 


5.24 


17.192 


276.3 


5.74 


18.832 


330.0 


4.75 


15.584 


226.1 


5.25 


17.224 


276.4 


5.75 


18.865 


331.7 


4.76 


15.617 


227.1 


5.26 


17.257 


277.4 


5.76 


18.898 


332.9 


4.77 


15.650 


228.0 


5.27 


17.290 


278.5 


6.77 


18.930 


334.0 


4.78 


15.682 


229.0 


5.2S 


17.323 


279.6 


5.78 


18.963 


335.2 


4.79 


16.715 


230.0 


5.29 


17.356 


280.6 


5.79 


18.996 


836.4 


4.80 


15.748 


230.9 


6.30 


17.388 


281.7 


6.80 


19.029 


337.5 


4.81 


15.781 


231.9 


6.31 


17.421 


282.8 


5.81 


19.062 


338.7 


4.82 


15.814 


232."9 


5.32 


17.454 


283.8 


5.82 


19.094 


339.9 


4.83 


15.846 


233.8 


5.33 


17.487 


284.9 


5.83 


19.127 


341.0 


4.84 


15.879 


234.8 


5.34 


17.620 


286.0 


5.84 


19.160 


342.2 


4.85 


15.912 


235.8 


6.35 


17.652 


287.0 


5.85 


19.193 


343.4 


4.86 


15.945 


236.8 


5.36 


17.585 


288.1 


5.86 


19.226 


344.6 


4.87 


15.978 


237.7 


5.37 


17.618 


289.2 


5.87 


19.268 


345.8 


4.88 


16.010 


238.7 


6.38 


17.651 


290.3 


5.88 


19.291 


346.9 


4.89 


16.043 


239.7 


5.39 


17.684 


291.4 


5.89 


19.324 


348.1 


4.90 


16.076 


240.7 


5.40 


17.716 


292.5 


5.90 


19.357 


349.3 


4.91 


16.109 


241.7 


5.41 


17. 749 


293.5 


5.91 


19.390 


350.5 


4.92 


16. 142 


242.7 


5.42 


17.782 


294.6 


5.92 


19.423 


351.7 


4.93 


16.175 


243. 6 


5.43 


17.815 


295.7 


5,93 


19.465 


a52.9 


4.94 


16.207 


244.6 


6.44 


17.848 


296.8 


5.94 


19.488 


364.1 


4.95 


16.240 


245.6 


6.45 


17.881 


297.9 


6.95 


19.521 


355.3 


4.96 


16.273 


246.6 


5.46 


17.913 


299.0 


5.96 


19.554 


356.5 


4.97 


16.306 


247.6 


5.47 


17.946 


300.1 


5.97 


19.587 


357.7 


4.98 


16.339 


248.6 


5.48 


17.979 


301.2 


5.98 


19.619 


358.9 


4.99 


16.371 


249.6 


5.49 


18.012 


302.3 


5.99 


19.652 


360.1 



32 U. S. COAST AND GEODETIC SURVEY. 

Inclination corrections for 50-meter tape lengths Continued. 



Difference in 


Correc- 


Difference in 


Correc- 


Difference in 


Correc- 


elevation. 


tion. 


elevation. 


tion. 


elevation. 

1 


tion, 


Meters. 


Feet. 


mm. 


Meters. 


Feet. 


mm. 


Meters. 


Feet. 


mm. 


6.00 


19.083 


361.3 


6.50 


21.325 


424.3 


7.00 


22. 966 


492.4 


6.01 


19.718 


362.5 


6.51 


21.358 


425.6 


7.01 


22. 999 


493.8 


6,02 


19. 751 


363.7 


6.52 


21.391 


426.9 


7.02 


23.031 


495.2 


6.03 


19.783 


364.9 


6.53 


21.424 


428.2 


7.03 


23.064 


496.6 


6.04 


19.816 


366.1 


6.64 


21.457 


429.5 


7.04 


23.097 


498.1 


6.05 


19.849 


367.4 


6.55 


21.489 


430.9 


7.05 


23.130 


499.5 


6.06 


19.882 


368.6 


6.56 


21.522 


432.2 


7.06 


23.163 


500.9 


6.07 


19.915 


369.8 


6.57 


21.555 


433.5 


7.07 


23.195 


502.3 


8.08 


19.947 


371.0 


6.58 


21.588 


434.8 


7.08 


23.228 


503.8 


6.09 


19.980 


372.3 


6.59 


21.621 


436.2 


7.09 


23.261 


505.2 


6.10 


20.013 


373.5 


6.60 


21.654 


437.5 


7.10 


23.294 


506.6 


6.11 


20.046 


374.7 


6.61 


21.686 


438.8 


! 7.11 


23.327 


508.1 


6.12 


20.079 


375.9 


6.62 


21.719 


440.2 


1 7.12 


23.360 


509.5 


6.13 


20.112 


377.2 


6.63 


21.752 


441.5 


7.13 


23.392 


511.0 


6.14 


20.144 


378.4 


6.64 


21.785 


442.8 


7.14 


23.425 


512.4 


6.15 


20.177 


379.7 


6.65 


21.818 


444.2 


7.15 


23.458 


513.8 


6.16 


20.210 


380.9 


6.66 


21.850 


445.5 


7.16 


23.491 


615.3 


6.17 


20.243 


382.1 


6.67 


21.883 


446.9 


7.17 


23.524 


616. 7 


6.18 


20.276 


383.4 


6.68 


21.916 


448.2 


7.18 


23.556 


518.2 


6.19 


20.308 


384.6 


6.69 


21.949 


449,6 


7.19 


23.589 


619.6 


G.20 


20.341 


385.9 


6.70 


21.982 


450.9 


7.20 


23.622 


521.1 


6.21 


20.374 


387.1 


6.71 


22. 014 


452.3 


7.21 


23.655 


622.5 


(5.22 


20.407 


388.4 


6.72 


22.047 


453.6 


7.22 


23.688 


524.0 


6.23 


20.440 


389.6 


6.73 


22.080 


455.0 


7.23 


23.720 


525.5 


6.24 


20.472 


390.9 


6.74 


22. 113 


456.3 


7.24 


23.753 


526.9 


6.25 


20.505 


392.2 


6.75 


22.146 


457.7 


7.25 


23.786 


528.4 


6.26 


20.538 


393.4 


6.76 


22. 178 


459. 1 


7.26 


23.819 


529.9 


6.27 


20.571 


394.7 


6.77 


22.211 


460.4 


7.27 


23.852 


531.3 


6.28 


20.604 


395.9 


6.78 


22.244 


461.8 


7.28 


23.884 


532.8 


6.29 


20.636 


397.2 


6.79 


22.277 


463.2 


7.29 


23.917 


634.3 


6.30 


20.669 


398.5 


6.80 


22.310 


464.5 


7.30 


23.950 


535.7 


6.31 


20.702 


399.7 


6.81 


22.342 


465.9 


7.31 


23.983 


637.2 


6.32 


20.735 


401.0 


6.82 


22.375 


467.3 


-7.32 


24.016 


538.7 


6.33 


20.768 


402.3 


6.83 


22.408 


468.7 


7.33 


24.049 


540.2 


6.34 


20.800 


403.6 


6.84 


22.441 


470.0 


7.34 


24.081 


541.7 


0.35 


20.833 


404.9 


6.85 


22.474 


471.4 


7.35 


24.114 


643.1 


6.36 


20.866 


406.1 


6.86 


22.507 


472.8 


7.36 


24.147 


644.6 


6.37 


20.899 


407.4 


6.87 


22.539 


474.2 


7.37 


24.180 


546.1 


6.38 


20.932 


408.7 


6.88 


22.572 


475.0 


7.38 


24.213 


547.6 


6.39 


20.965 


410.0 


6.89 


22.605 


477.0 


7.39 


24.245 


549.1 


6.40 


20.997 


411.3 


6.90 


22.638 


478.4 


7.40 


24.278 


550.6 


6.41 


21.030 


412.6 


6 91 


22.671 


479.8 


7.41 


24.311 


552.1 


6.42 


21.063 


413.9 


6.92 


22.703 


481.2 


7.42 


24.344 


553.6 


6.43 


21.096 


415.2 


6.93 


22.736 


482.6 


7.43 


24.377 


655.1 


6.44 


21. 129 


416.5 


6.94 


22.769 


484.0 


7.44 


24.409 


656.6 


6.45 


21.161 


417.8 


6.95 


22.802 


485.4 


7.45 


24.442 


558.1 


6.46 


21.194 


419.1 


6.96 


22.835 


486.8 


7.46 


24.475 


559.6 


6.47 


21.227 


420.4 


6.97 


22.867 


488.2 


7.47 


24.508 


561.1 


6.48 


21.260 


421.7 


6.98 


22.900 


489.6 


7.48 


24.541 


562.6 


6.49 


21.293 


423.0 


6.99 


22.933 


491.0 


7.49 
7.50 


24. 573 
24.606 


564.1 
565.7 



GENERAL INSTRUCTIONS FOR TRAVERSE. 



33 



P 



IS 



&I 



CO 

02 

O 

o 

I 

I 

o 



is 



1.5 






^ in to Pico Ci o* Oi ^ 

Coo to to ceo r t~ 

IS! iS O O ^M 00 

^iS SoS8 

^ I I I I I I I I 

t ii s IS s i 

^ o 

"' I I I I Mil 



liii 

" + + 



=18 

0*000 

I ++ 



^?A 



+ 1 I 



+ + 






o8S 



io S8 



'+I+ + + + 



+ I I 



88l 



+ + + + + 



III + 1 









it>.e> t>-o 



g2 gis53^ rl^ 



:ssi 8i 8;5S s 



8^^^ 



u5>cu5 uStfiio tS>iiu5 u6>o 



^iHp^ Pht^ft, a<&M(zi fc[ii 



3 >.o 

1^ 



S 






a tco 
i,o eg 



O O 



Isq ^Is 



cb22 

SCQOQ 



ii 

: 

go 

si 



2 



o i3 
o p. 

1^ 

1^1 

Sot? 
** 'Sb^ 

02 .r-1 g> 

fe s ^ 

lis 

tag 

2 fl.o 
o w o ^ 

a ^|2 



d o "^^ 

2 "'f 

S >H s 
fl a e 

"-" o <y T: 

^ ^^ Ph 

If o M .2 

g ^^ 

7. S ' 



CO 



s. 



^ 



0) 00 






CJ 



00 



25 

5 .^3 









'is ^ 



si 

II 



^ " ^ . 

r* 2 fl d t:' 

^ :2 .2 o -S 

II * 



O 0) 

1 



zl 






8 2 S 



ill 



a a ^ 
^ - i a a 



03 ?Q ^ 

S =2 03 0) 

rt u g ^ 

M -^ ^ ?^ 



01 

-CI '^ a 



11 O) 0) -fJ 

till 



34 U. S. COAST AND GEODETIC SURVEY. 

(6) For the tape correction see the certificate of standardization 
below and the tape-standardization tables on page 36. The caten- 
ary correction is included in the tape correction, as the tapes are 
supported in the field in the same manner as when standardized. 

(c) For the inclination correction, see page 24. 

(d) The sea-level correction or the correction for reducing the 
length to sea level is computed by the formula, 

Sea level cor.= 
r 

in which J.=the length of section in meters, imcorrected except for 
set-up or setback to the nearest meter, /t=mean elevation of section to 
nearest meter (see p. 24) and r=mean radius of the earth. Log r is 
obtained from the tables on pages 55-60 of Special Publication No. 26. 
The arguments for use in these tables are obtained by estimating the 
mean latitude and azimuth for each part of the traverse line in which 
the various sections have the same general direction. For the com- 
putation above, log r was computed for that part of the traverse line 
extending from the Savannah River to Columbia, as the line is prac- 
tically straight for that whole distance. Log r=G. 80312. 

86. Certificate of standardization (invar base tape No. 552.) 

December 5, 1910. 
Supported horizontally at 0, 25, and 50 meter points under tension 
of 15 kilograms: 

(0 to 50 m.)=50 m. -2.815 mm.+(i-27.4 0.) 0.0282 mm. 
(probable errors) 0.020 mm. 0.0008 mm. 

Supported horizontally at 0, 12.5, 25, 37.5, and 50 meter points under 
tension of 15 kilograms: 

(0 to 50 m.)=50 m. +0.113 mm.+(i-27.3 C.) 0.0282 mm. 
(probable errors) 0.019 mm. 0.0008 mm. 

Mass per meter=25.8 grams. ;; 



GENERAL INSTRUCTIONS FOR TRAVERSE. 35 

86. Additional computed values of tape corrections (invar base tape 
No. 652.) 

AL=the amount the tape is shortened by supporting it at 
equidistant intervals instead of supporting it through- 
out. 
n=number of sections into which the tape is divided by 

equidistant supports. 
/=Iength of such section. 
w;= weight of tape per unit of length. 
f=the applied tension. 

Supported throughout under tension of 15 kilograms: 

(0 to 50 m.)=50 m. +1.060 mm.+(-27.4 0.) 0.0282 mm. 

Supported horizontally at and 50 meter points under tension of 
15 kilograms: 

(0 to 50 m.)=50 m.-14.:^71 mm.-f (-27.4 C.) 0.0282 mm. 

87. To obtain the tape correction when a part of the tape is supported 
on stakes and the remainder is supported throughout, use combinations 
of the proper fractional parts of the corresponding corrections given 
above. For example, if the tape is supported horizontally at the 
and 25 meter points and throughout from the 25 to 50 meter points under 
a tension of 15 kilograms, the tape correction is computed as follows: 

Taperor. = i (-2.815 mm.)+H+l 060 mm. )= -0.878 mm. 

and the formula for the length becomes 

(0 to 50 m.)=50 m. -0.878 mm.+(t-27.4 C.) 0.0282 mm. 



36 



TJ. S. COAST AND GEODETIC SUR^^:Y. 



88. Temperature corrections, tape No. 662. 

[Cor.=+(f-27.*'4 C.) 0.0000282 meters per tape length.] 



Tem- 
perature. 


Correction. 


Tem- 
perature. 


Correction. 


Tem- 
perature. 


Correction. 


Proportional 
parts. 


"C. 




"C. 




"C. 




2S 29 





-0.000773 

744 


15 
16 


-0.000350 
321 


30 
31 


+0.000073 




1 


102 








2 


716 


17 


293 


32 


130 


1 


3 


3 


3 


688 


18 


265 


33 


158 


2 


6 


6 


4 


660 


19 


237 


34 


186 


3 


8 


9 


5 


631 


20 


209 


35 


214 


4 


11 


12 


6 


603 


21 


180 


36 


243 


5 


14 


14 


7 


575 


22 


152 


37 


271 


6 


17 


17 


8 


547 


23 


124 


38 


299 


7 


20 


20 


9 


519 


24 


96 


39 


327 


8 


22 


23 


10 


491 


25 


68 


40 


355 


9 


25 


26 


11 


462 


26 


40 


41 


384 


10 


28 


29 


12 


434 


27 


-0.000011 


42 


412 




13 


406 


28 


+0.000017 


43 


440 




14 


-0.000378 


29 


+0.000045 


44 
45 


468 
+0.000496 





89. Tape corrections for tape No. 662 when supported throughout. 



Tape 


Correc- 


Tape 


Correc- 


Tape 


Correc- 


Tape 


Correc- 


lengths. 


tion. 


lengths. 


tion. 


lengths. 


tion. 


lengths. 


tion. 




Meters. 




Meters. 




Meters. 




Meters. 


1 


+0.0011 


26 


0.0276 


51 


0.0541 


76 


0.0806 


2 


.0021 


27 


.0286 


52 


.0551 


1 77 


.0816 


3 


.0032 


28 


.0297 


53 


.0562 


! 78 


.0827 


4 


.0042 


29 


.0307 


54 


.0572 


1 79 


.0837 


5 


.0063 


30 


.0318 


55 


.0583 


' 80 


.0848 


6 


.0064 


31 


.0329 


56 


.0594 


81 


.0859 


7 


.0074 


32 


.0339 


57 


.0604 


82 


.0869 


8 


.0085 


33 


.0350 


58 


.0615 


83 


.0880 


9 


.0095 


34 


.0360 


59 


.0625 


84 


.0890 


10 


.0106 


35 


.0371 


60 


.0636 


85 


.0901 


11 


.0117 


36 


.0382 


61 


.0647 


86 


.0912 


12 


.0127 


37 


.0392 


62 


.0657 


87 


.0922 


13 


.0138 


38 


.0403 


63 


.0668 


88 


.0933 


14 


.0148 


39 


.0413 


64 


.0678 


89 


.0943 


15 


.0159 


40 


.0424 


65 


.0689 


90 


.0954 


16 


.0170 


41 


.0435 


66 


.0700 


91 


.0965 


17 


.0180 


42 


.0445 


67 


.0710 


92 


.0975 


18 


.0191 


43 


.04.56 


68 


.0721 


93 


.0986 


19 


.0201 


44 


.0466 


69 


.0731 


94 


.0996 


20 


.0212 


45 


.0477 


70 


.0742 


95 


.1007 


21 


.0223 


46 


.0488 


71 


.0753 


96 


.1018 


22 


.0233 


47 


.0498 


72 


.0763 


97 


.1028 


23 


.0244 


48 


.0509 


73 


.0774 


98 


.1039 


24 


.0254 


49 


.0519 


74 


.0784 


99 


.1049 


25 


0.0265 


50 


0. 0530 


75 


0.0795 


100 


0.1060 



GENERAL INSTRUCTIONS FOR TRAVTJRSE. 37 

90. Tape corrections for tape No. 552 for various methods of support. 









Correction, tape supported 












at and 


at 0, 121, 


at 0, 25, 




Tape 
lengths. 








25 m. 


and 25 m. 


and 37i 




at 0, 25, 

and 50 m. 

points. 


at0,12i, 

25,37i, 

and 50 m. 


at 0, 25. 


points 

and 

through- 


points 

and 

through- 


m. points 

and 
through- 


at and 
50 m. 
points. 




points. 


points.o 


out from 


out from 


out from 










25 to 50 


25 to 50 


37J to 50 












m.b 


m.c 


m.d 






.\feter8. 


^^eters. 


MettTs. 


Meiers. 


Meters. 


Meters. 


Meters. 


1 


-0.0028 


+0.0001 


-0.0014 


-0.0009 


+0.0006 


-0.0011 


-0.0144 


2 


.0056 


.0002 


.0027 


.0018 


.00i2 






3 


.0084 


.0003 


.0041 


.0026 


.0018 






4 


.0113 


.0005 


.0054 


.0035 


.0023 






5 


.0141 


.0006 


.006S 


.0014 


.0029 






6 


.0169 


.0007 


.0081 


.0053 


.0035 






7 


.0197 


.0008 


.0095 


.0061 


.0041 






8 


.0225 


.0009 


.0108 


.0070 


.0047 






9 


.0253 


.0010 


.0122 


.0079 


.0053 






10 


-0.0282 


+0.0011 


-0.0135 


-0.0088 


+0.0059 







o Equivalent to tape supported at 0, 12* , 25, and 50 meter points. 

b F.quivalent to tape supported at 25 and 50 meter points and tliroughout from to 25 
meters. 

c Equivalent to tape supported at 25, 37J, and 50 meter points and throughout from 
to 25 meters. 

d Equivalent to taue supported at 12*, 25, and 60 meter points and throughout from 
to 12i meters. 



t(S3 metjsra 




OougUs 



Fig. 2. Diagram for projection computation, one olTset station. 



38 TJ. S. COAST AND GEODETIC SURVEY. 

91. Projection computation, North to Douglas. 

(See fig. 2.) 

log 7.169=0. 8554586 
log sin 92 15^ 45^^= 9.9996613 -10 
log dist. North to X=0. 8551199 

log 7.169=0. 8554586 
log cos 92 15^ 45^^= 8.5963531 -10 
log dist. Rail North to X=9. 4518117 

Dist. Rail North to X= 0. 2830 meters 

Dist. Rail North to Dougla8= 1366. 9858 meters 

Dist. Douglas to X=1367. 2688 meters 

log. dist. North to X =0.8551199 
log. dist. Douglas to X= 3. 1358539 

log tan a=7. 7192660-10 
log sec. a=0. 0000060a 
log dist. Douglas to X= 3. 1358539 
log dist. North to Douglas=3. 1358599 

Dist. North to Douglas=1367. 2877 meters 

^ Raitxl^ ,8069.fl80 ffietera J^ Rail Rlncpo 



Fig. 3. Diagram for projection computation, both stations offset on same side of track . 

92. If both stations involved are offset from the measured line, a 
computation similar to the first half of the computation above must 
be made for each end of the line. The distance between the two 
"X " points can thus be obtained and will give the length of the base 
of the long, slender right triangle by which the final length between 
stations is computed. The short side of this right triangle is obtained 
by adding together the distances from the ''X" points to the stations 

o It is not necessary to take out the value of angle . Find in the log tables the log 
tan a just computed, and then on the same page in the corresponding column and line 
under the heading of cosine will be found log cos a. The colog of this cosine is the log 
secant a desired. The logarithms of the cosine and secant change very slowly for such 
small angles and can be obtained readily with little interpolation. 



GENERAL INSTRUCTIONS FOR TRAVERSE. 



39 



in case the stations are on opposite sides of the track or by subtracting 
the smaller distance from the larger in case the stations are on the same 
side of the track. (See figs. 3 and 4.) 




Ra.iCievcianci 



Fig. 4. Diagram for projection computation, stations offset on opposite sides of track. 

93. In making the projection computations it is very essential that 
a diagram similar to one of the figures 2 to 5 be made for each computa- 
tion. Much confusion will thus be avoided and gross errors elimi- 
nated. As the offset distance is small as compared with the distance 
between stations, it is well in making these diagrams to exaggerate 
very considerably the distances at right angles to the track and also 
to exa^erate the angles when it is necessary for the sake of clearness. 

Computation to close loops. 

94. As stated in pars^aph 4, it is desirable in hilly or rolling country 
where the railroad has numerous curves and short tangents to carry 
the azimuth through long lines, extending past several intermediate sta- 
tions which are necessarily near together, in order that the resulting 
azimuth may have greater accuracy. The loop thus formed gives a 
good check on the angle measurements. It also gives a rough check on 
the distance measurements, for if an error has been made in the taping 
the departures or perpendiculars for the loop will not sum up to zero 
unless the error was made on a line very nearly parallel to the long line 
through which the azimuth is carried. The error will show up also 
in the position computations if they are made both through the long 
line and through the short lines. 

95. The manner of computing the loop and making the projections 
to the main line is shown in the following computation. See also 
figure 5. The computation of the departures or perpendiculars men- 
tioned in the paragraph above is made in the same manner as the com- 
putation of distance for the loop as shown in the table on the following 
page except that in column 4 log sin azimuth should be used in place 
cf log cos azimuth. The sign of the function must be taken into 
account. 



40 U. S. COAST AND GEODETIC SURVEY. 

96. Computation of angle closure for loop. 



Liv^mgston A 

L;vlo|ston ^-~ ^~ l^33'^5~7'36r3l 

807'I9"99-^ ^C" "^^iS^'ae'DS. /u |65''2S'35"60 

Livingston s'l^Wct^ra.T, /-"- \- 

825'"0I-' Xivings+on C 




311 
!?^eO-3535l'l7"6l) 



Fig. 5. Diagram for loop computation. 



Angles and 
azimuths. 



Correction 

for 

closure. 



Assumed azimuth Livingston-North . 
Angle at Livingston 

Azimuth Livingston-Livingston A . . . 

Azimuth Livingston A-Livingstou. . . 

Angle at Livingston A 

Azimuth Livingston A-Li^ingston ]> . 

Azimuth Livingston B -Livingston h . 

Angle at Livingston B 

Azimuth Livingston B-Livingston C. 

Azimuth Livingston C-Livingston B 

Angle at Livingston C 

Azimuth Livingston C-North 

Azimuth North-Livingston C 

Angle at North 

Azimuth North-Livingston 

Error of closure 

Eri-or of closure per angle 



- 8 


07 


19. 99 1 


351 
171 
222 


52 
52 
04 


40.01 ! 
40.01 1 
56. 30 1 


33 
213 
154 


57 
57 
28 


36. 31 i 
36.31 j 
05. 70 1 


8 
188 
165 


25 
25 
25 


42.01 

42.01 : 

35.60 1 


353 

173 
6 


51 

51 

08 


17.61 ! 
17.61 
46. 10 j 



180 



00 03.71 

03.71 

0.74 



Final 
corrected 
seconds. 



00 00 00.00 

-0.74 



-0.74 



-0.74 



I -0. 74 



-0.75 



00.00 
20.73 



39.27 
39.27 
55. 56 



34. S3 
34.83 
04.96 

39.79 
39.79 
34. 86 



14.65 
14.65 
45.35 



00.00 



97. Computation of distance for loop. 



Section. 



Length. 



Azimuth, a 



Log cos 
azimuth. 



Log 
length. 



Log 

projected 

length. 



Projected 
length. 



Livingston . . . 
Livingston A . 
Livingston A . 
Livingston B . 
Livingston B . 
Livingston C . 
Livingston C . 
North.. 



Meters. 
1247. 9212 

1074. 4132 

1152. 3746 

536. 1025 



351 52 39.27 

33 57 34.83 

8 25 39.79 

353 51 14.65 



9.9956214 
9. 9187803 
9.9952848 
9. 9974966 



3. 0961872 
3. 0311713 



3. 0918086 
2. 9499516 



3.0615936 3.0568784 



3. 7432041 



Computed distance Livingston-Nort 
Log distance Livingston-North 



3. 7407007 



Meters. 
1235. 4028 

891. 1516 

1139. 9304 

5504. 2823 



8770. 7671 
3. 9430376 



a These are the azimuths computed in the preceding computation. They are referred 
to the line Livingston-North, which was assumed to have the azimuth 00' 00.00", 
and the convergence of the meridians was not taken into account. Consequently they 
are not true azimuths. 



GENERAL INSTRUCTIONS FOR TRAVERSE. 41 

GENEBAL INSTBUCTIONS FOR SECONDARY TRAVERSE. 

98. Secondary traverse will be used in those areas where secondary 
triangulation would ordinarily be carried on except for the configura- 
tion of the ground, presence of heavy woods, and extensive swamps 
which make triangulation excessively expensive. 

99. In general, secondary triangulation and secondary traverse or a 
combination of the two, depending on the country to be controlled, 
will be used instead of primar>^ triangulation or precise traverse when 
the distance between terminal points of the line or arc is less than 150 
miles. These classes of work must always be joined at each end of an 
arc or line with pre\'iously adjusted horizontal control, 

100. The probable error of the length of a line of secondar>' traverse 
should, in general, be not greater than 1 part in 25 000. This accuracy 
will be obtained if the error of closure in position is less than about 1 
part in 10 000 of the distance run. 

101. The general instructions for precise traverse will apply to 
secondary traverse. ox<"opt whoro thoy conflict \vith the following 
considerations, 

102. One measurement will ])e made of each section of a line of 
traverse with a 50-meter invar tape under the same conditions as 
obtained during standardization, except as to temperature. It may be 
found desirable to read and record the temperature for each tape length 
in order to keep count of the number of tape lengths. Otherwise the 
temperature will be read and recorded three times on each section 
once near the beginning, once near the end, and once near the middle 
of the section. These readings are nece8sar\' to avoid uncertainty in 
case one temperature is erroneously read or recorded. 

103. The temperature may be read from only one thermometer; but, 
should this be done, the thermometer should be carefully examined 
and be compared with a standard thermometer once each day in order 
to detect any break in the thread of mercury which might have occurred. 

104. When measuring along a country road, the forward end of the 
tape may be marked by a nail driven into the ground or by a wooden 
peg, on which the end of the tape may be indicated by a small nail 
driven into the peg. A piece of paper laid on the ground and weighted 
down, by a stone or earth, near the peg or nail will enable the rear tape 
man to find the nail or peg easily. 

106. If any part of the tape is unsupported, a note to this effect should 
be made in the record book and a correction for sag or catenary will be 
computed and applied when the office computation is made. 

106. For measurements along a rail of a railroad no inclinations will 
be computed for separate tape lengtlis where the slope is approximately 



42 



U. S. COAST AND GEODETIC SURVEY. 



the same from one end of the section to the other. Under this condition 
the inclination correction for the distance mil be taken from the 
inclination correction table which follows. There will be computed 
for each tape length the inclination correction for portions of a section 
which are measured over stakes. This is necessary because the grade 
is frequently steep when measuring from a point of tangency on a rail- 
road to the station at the end of the section. 
107. Inclination correction (see p. 25). 



Distance 


Difference of elevation in meters. 


in meters. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


100 


mm. 
5 
2 


mm. 
20 

5 


mm. 
45 
22 
15 
11 
9 
8 
6 


mm. 


mm. 


mm. 


mm. 


mm. 


mm. 


mm. 


mm. 


mm. 


mm. 


mm. 


200 


40 
27 
20 
16 
13 
11 
10 
9 
8" 


62 
42 
31 
25 
21 
18 
16 
14 
12 
11 
10 


90 
60 
45 
36 
30 
26 
23 
20 
18 
16 
15 
14 
13 


















300.... 


82 
61 
49 
41 
35 
31 
27 
24 
22 
20 
19 
18 
16 
15 


107 

80 
64 
53 
46 
40 
36 
32 
29 
27 
25 
23 
21 
20 
19 

B 


135 

101 
81 
67 
58 
51 
45 
40 
37 
34 
31 
29 
27 
25 
24 
22 
21 
20 












400 




125 
100 
83 
71 
63 
56 
50 
45 
42 
38 
36 
33 
31 
29 
28 
26 
25 


151 
121 
101 
86 
76 
67 
60 
55 
50 
46 
43 
40 
38 
36 
34 
32 
30 


180 
144 
120 
103 
90 
80 
72 
65 
60 
55 
51 
48 
45 
42 
40 
38 
36 






500.... . 




169 
141 
121 
106 
94 
84 
77 
70 
65 
60 
56 
53 
50 
47 
44 
42 


196 


600.... 






163 


700 






140 


800.... 






123 


900 








109 


1000 








98 


1100 . 








89 


1200 










82 


1300.. 










75 


1400 












70 


1500... 












65 


1600. 














61 


1700 














58 


1800 
















54 


1900 






1 








?>f,- 


2000 






.... 








49 






i 1 






1 





Distance in 


15 


16 


17 


Difference of elevation in meters. 




meters. 


18 


19 


20 


21 


22 


23 


24 


25 


26 


27 


500 


mm. 

225 

187 

161 

141 

125 

112 

102 

94 

86 

80 

75 

70 

66 

62 

59 

56 


mm. 


mm. 


mm. 


mm. 


mm. 


mm. 


mm. 


mm. 


mm. 


mm. 


t 
mm. 


mm. 


600 


213 

183 

160 

142 

128 

116 

107 

98 

91 

85 

80 

75 

71 

67 

64 


241 

206 

181 

161 

144 

131 

120 

111 

103 

96 

90 

85 

80 

76 

72 


270 

231 

203 

180 

162 

147 

135 

125 

116 

108 

101 

95 

90 

85 

81 





















700 


258 
226 
201 
180 
164 
150 
139 
129 
120 
113 
106 
100 
95 
90 


286 
250 
222 
200 
182 
167 
154 
143 
133 
125 
118 
111 
105 
100 


315 

276 
245 
220 
200 
184 
170 
157 
147 
138 
130 
122 
116 
110 














800 


303 
269 
242 
220 
202 
186 
173 
161 
151 
142 
134 
127 
121 


331 

294 
264 
240 
220 
203 
189 


360 
320 
288 
262 
240 
222 
206 








900 


347 
312 
284 
260 
240 
223 
208 
195 
184 
174 
164 
156 


376 
338 
307 
282 
260 
241 
225 
211 
199 
188 
178 
169 


405 


1000 


364 


1100 . . . 


331 


1200. 


304 


1300 


280 


1400 


260 


1500 


176 
165 
156 
147 
139 
132 


192 
180 
169 
160 
152 
144 


?43 


1600 


228 


1700 


214 


1800 


20?, 


1900 


^n 


2000 


182 







GENERAL INSTRUCTIONS FOR TRAVERSE. 43 

Inclination correction Continued. 





Difference of elevation in meters. 








Distance in 




meters. 


28 


29 


30 


31 


32 


33 


34 


35 


36 


37 


38 


39 


40 


1000 


mm. 
392 
356 
327 
302 
280 
261 
245 
231 
218 
206 
196 


mm. 
420 
382 
350 
323 
300 
280 
263 
247 
234 
221 
210 


mm. 
450 
409 
375 
346 
321 
300 
281 
265 
250 
237 
225 


mm. 


mm. 


mm. 


mm. 


mm. 


mm. 


mm. 


mm. 


mm. 


mm. 


1100 


437 
400 
370 
343 
320 
300 
283 
267 
253 
240 


465 
427 
394 
366 
341 
320 
301 
284 
269 
256 


495 
454 
419 
389 
363 
340 
320 
302 
287 
272 
















1200 


482 
445 
413 
385 
361 
340 
321 
304 
289 


610 
471 

438 
408 
383 
360 
340 
322 
306 


540 
498 
463 
432 
405 
381 
360 
341 
324 










1300 


527 
489 
456 
428 
403 
380 
360 
342 


555 
516 
481 
451 
425 
401 
380 
361 


585 
543 
507 
475 
447 
422 
400 
380 




1400 


571 


1500 


533 


1600 


.son 


1700 


471 


1800 


444 


1900 


421 


2000 


400 







108 . In taking the inclination correction from the tables the difference 
in elevation of the two points of tangency of a section can be obtained 
from the Y leveling over the stakes at the ends of a section. The 
record should show clearly what are the differences in elevation between 
the ends of the section and the points of tangency, and there should 
be no doubt whatever as to the sign of each difference. These differ- 
ences applied to the difference in elevation of the ends of the section 
as furnished by the precise leveling will give the difference in elevation 
of the points of tangency, which is one of the arguments in obtaining 
the correction from the table. The other ailment is the distance 
between the tangent points. In most cases the grade corrections 
obtained from the table will be too small, owing to irregularities in the 
slope of the line, but the error mil in nearly all cases bo less than i part 
in 100 000, and therefore may be neglected. 

109. Should the grade change decidedly in a section, the distance 
of the change or changes from one of the ends of the section should be 
noted in the record of tape measurement, and the slope may be meas- 
ured by a small transit or theodolite. The correction will be 

D (l-cos^), 

where D is the measured distance and A is the angl( of inclination. 
The foUomng table gives values of 1 cos A for various slopes. 



44 U. S. COAST AND GEODETIC SURVEY. 

110. Factors for inclination correction. 

rCorrection=D (1 cos A).] 



Angle 




Angle 




Angle 




Ajigle 




ofincli- 


1 cos^. 


ofincli- 


1 oos^. 


of incli- 


1 cos^. 


ofincli- 


1-cos^. 


nation. 




nation. 




nation. 




nation. 




00 


0.0000000 


r 

50 


0.0001058 


o r 

1 40 


0.0004230 


2 30 


0.0009518 


01 


0.0000000 


51 


1100 


41 


4315 


31 


9645 


02 


0002 


52 


1144 


42 


4401 


32 


9773 


03 


0004 


53 


1188 


43 


4488 


33 


0.0009902 


04 


0007 


54 


1234 


44 


4576 


34 


0. 0010032 


05 


0011 


55 


1280 


45 


4664 


35 


0163 


06 


0015 


56 


1327 


46 


4753 


36 


0294 


07 


0021 


57 


1375 


47 


4843 


37 


0427 


08 


0027 


58 


1423 


48 


4934 


38 


0560 


09 


oa34 


59 


1473 


49 


5026 


39 


0694 


10 


0.0000042 


1 00 


0.0001523 


1 50 


0.0005119 


2 40 


0.0010829 


11 


OOol 


01 


1574 


51 


5212 


41 


0965 


12 


0061 


02 


1626 


52 


5307 


42 


1101 


13 


0072 


03 


1679 


53 


5402 


43 


. 1239 


14 


00S3 


04 


1733 


54 


5498 


44 


1377 


15 


0095 


05 


1788 


55 


5595 


45 


1516 


16 


0108 


06 


1843 


56 


5692 


46 


1656 


17 


0122 


07 


1899 


57 


5791 


47 


1797 


18 


0137 


08 


1956 


58 


5890 


48 


1939 


19 


0153 


09 


2014 


59 


5991 


49 


2081 


20 


0.0000169 


1 10 


0.0002073 


2 00 


0.0006092 


2 50 


0.0012224 


21 


0187 


11 


2133 


01 


6194 


51 


2369 


22 


0205 


12 


2193 


02 


6296 


52 


2514 


23 


0224 


13 


2254 


03 


6400 


53 


2660 


24 


0244 


14 


2317 


04 


6505 


54 


2806 


25 


0264 


15 


2380 


05 


6610 


55 


2954 


26 


0286 


16 


2144 


06 


6716 


56 


3103 


27 


0308 


17 


2508 


07 


6823 


57 


3252 


28 


X)332 


18 


2574 


08 


6931 


58 


3402 


29 


0356 


19 


2640 


09 


7040 


59 


3553 


30 


0.0000381 


1 20 


0.0002708 


2 10 


0.0007149 


3 00 


0.0013705 


31 


0407 


21 


2776 


11 


7260 






32 


0433 


22 


2845 


12 


7371 






33 


0461 


23 


2914 


13 


7483 






34 


0489 


24 


2985 


14 


7596 






35 


0518 


25 


3057 


15 


7710 






36 


0548 


26 


3129 


16 


7824 






37 


0579 


27 


3202 


17 


7940 






38 


0611 


28 


3276 


18 


8056 






39 


0644 


29 


3351 


19 


8173 






40 


0.0000677 


1 30 


0. 0003427 


2 20 


0.0008291 






41 


0711 


31 


3503 


21 


8410 






42 


0746 


32 


3581 


22 


8530 






43 


0782 


33 


3659 


23 


8650 






44 


0819 


34 


3738 


24 


8772 






45 


0857 


35 


3818 


25 


8894 






46 


0895 


36 


3899 


26 


9017 






47 


0935 


37 


3980 


27 


9141 






48 


0975 


38 


4063 


28 


9266 






49 


1016 


39 


4146 


29 


9391 







GENERAL INSTRUCTIONS FOR TRAVERSE. 45 

111. When measuring distances of a secondary traverse along a 
country road, slopes may be measured as angles of inclination with a 
small transit or theodolite, or the differences in elevation of the tape 
ends may be obtained by a single line of ordinary leveling. In order 
that there may be no uncertainty as to the identification of the tape 
ends, it may be advisable to have the leveling follow just behind the 
measuring party. 

112. ^^^len measuring over a country road where the ground is nearly 
level or where the slopes are low with very small changes in grade, it 
will not be necessary to determine the difference in elevation of the 
ends of each tape length. Under such conditions it will be best to 
measure inclinations as angles. 

113. A second measurement must be made of each section of a sec- 
ondary traverse with a 300 or 200 foot tape. This measurement made 
with a tape of a different unit from that of the tape used in the first 
measurement will make it reasonably certain that no tape length has 
been dropped or added in the first measurement and will also guard 
against a blunder in measuring a set-up. The second measurement is 
made only as a check, and no grade, temperature, sag, or other correc- 
tions will be made to the distance measured. A second check meas- 
urement should be made with the foot tape if the first check measiu*e- 
ment does not agree within one part in 1500 with the measurement, 
uncorrected for grade, made with the meter tape. If the error was 
made in the meter-tape measurement, a second measurement should 
be made with that tape. The record must indicate clearly the 
accepted length. 

Measurement of angles. 

114. In general, the angles of the traverse will be measured with a 
7-inch theodolite, using the method of repetitions. The requisite 
accuracy will probably be obtained if the angle is measured by 6 repe- 
titions of the angle and 6 repetitions of the explement of the angle. 
The telescope should be reversed in the middle of the set to eliminate 
the effect of the coUimation error. If the angles are measured with a 
direction theodolite, three or four measures, with the initial readings 
equally spaced on the circle, will be sufficient. The angle should be 
measured clockwise from the back station. 

116. The greatest care should be used to make sure that the pole on 
which the angle observations are made is straight, accurately centered 
over the station, and vertical. If the line is of such length that the 
pole can not be distinctly seen, one face of the signal pole or of any 
target used should be placed at right angles to the line of sight to avoid 
the effect of phase. 



46 U. S. COAST AND GEODETIC SURVEY. 

Azlmutli stations. 

116. Azimuth stations on secondary traverse lines will be estab- 
lished at intervals of from 15 to 20 traverse stations. These azimuths 
should have an accuracy represented by a probable error not greater 
than 1/^5. This accuracy can probably be obtained by making 
double the number of observations that is used in measuring a horizontal 
angle of the secondary traverse. Instructions for azimuth observations 
will be foimd on page 14. 



INDEX 



Accuracy: Paragraph. 

Angle observations 35, 114 

Azimuth obser^-ations 44, 45, 116 

Check measurement 33 

Secondary traverse 100 

Angle: 

Inclination of tape Ill, 112 

Measurements 34-46, 70, 114 

Observations, secondar>' traverse. 114 

Angles to additional points 41 

Azimuth: 

Accuracy 116 

Long lines 4, 46 

Observations 44, 45 

Stations 42,116 

Stations, location 43, 45, 46 

Base line, second precise measure- 
ment 12 

Base tapes. See Invar tapes. 

Bench marks: 

In towns 57 

O n traverse stations 57, 68 

Bench over station mark 14 

Cards for descriptions 54 

Catenary 84,105 

Catenary correction formula 86 

Centering of instnmient and object. . 39 

Changes of grade 62 

Check measurement: 

300-foot tape 27,72 

Second 33 

Secondary traverse 113 

Closure of loop 94, 95, 96 

Computations, sample. . 76-so, S3-87, 91-97 
Counters for tape lengths 19, 27 

Description cards 54 

Descriptions of stations 52-54 

Designation: 

Points of tangencv 25, 30, 56 

Stakes ". 66 

Direction instrument 34, 36 

Direction Instrument, definition of 

position 36 

Distances: 

Approximate for descriptions 53 

Between azimuth stations 43,45,46 

Between traverse stations 2 

By precise leveling 60 

Computation of final 84 

For loop 97 

Measurement for secondary trav- 
erse 102 

Measurement of check 27, 72 

Measurement of precise 5, 71 

Offset 15 

To points of tangency 25,30 

BocentricItIs 39, 115 



Elevations: Paragraph. 

Additional, by precise leveling 56 

Points of tangency 56 

Rail opposite stations and bench 

marks 60 

Reference marks 58 

Extra fore sights 61 

Factors for inclination correction... 110 
Fore sights, extra 61 

Grade changes 62 

Grade correction. See Inclination 
correction. 

Inclination: 

Angle 111,112 

Correction 55-67, 78-80, 106 

Correction tables 79-82, 107-110 

Injury to tapes 9 

Instrument , centering 39 

Instruments 34, 67 

Invar tapes, 50-meter 5-11, 102 

Kinks in tape 9 

Length.*!. See Distances. 

Level rods: 

Alternating 64 

For Y levels 67 

Leveling: 

Preci.5e 55,56,75 

Precise, distances 60 

Precise, extra fore sights 61 

Y, over stakes 65,67,73,74 

Y.rods 67 

Location: 

Azimuth stations 43,45,46 

Permanent station marks 49 

Traverse stations 1, 2, 3 

Loop: 

Closure 94,95,96 

Distance 97 

Lines to form 4, 46 

Marks: 

At station 47-51 

For tape lengths 17,18,104 

Reference, elevation 68 

Measurement: 

Check , secondary traverse 113 

Distances , check 27, 72 

Distances , precise 5, 71 

Distances, second check 33 

Distances , secondary traverse 102 

Taping in rain 26, 31 

To additional points 24, 30 

Notes on description of stations 52 

Object, centering 39 

47 



48 



INDEX. 



Observations: Paragraph. 

Angle, secondary traverse 114 

Angle, subsidiary stations 38 

Angle, weather conditions 37 

Azimuth 44 

Number required for angle 35 

On Polaris for azimuth 42 

Offset distances 15 

Phase 40,115 

Points: 

Angles to additional 41 

Measurements to ad ditiona ! 24 , 30 

Points of tangency 25, 30 

Elevations 56 

Polaris observations for azimuth 42 

Position, definition, dirootion instru- 
ment 36 

Precise leveling 55, 56, 75 

Distances 60 

Extra fore sights 61 

Profile of track 59 

Projection, rail to true station ... 91, 92, 93 

Rail elevations, opposite stations 

and bench marks 60 

Rail station, projection to true 

station 91, 92, 93 

Rail stations 16 

Railway stations, name 63 

Records, sample 68-75 

Reference marks 50 

Elevations 58 

Restandardization of tapes 7, 8 

Rods, level: 

Alternating 64 

Y levels 67 

Sample computations. . . 76-80. 83-87, 91-97 

Sample records 68-75 

Secondary traverse 98-116 

Setbacks 20, 21 

Set-ups 20, 21 

Stadia readings, Y levels 67 

Stake setting 22 

Stakes: 

Designation 66 

Y 1 e veling 65, 67, 73, 74 

Stand over station mark 14 

Standard mark for station 47, 48, 50 

Standard notes, descriptions of sta- 
tions 52 

Standardization: 

Of tapes 7, 8, 85 

Tension of tapes 10 

Station marking 47-51 

Station stand or bench 14 

Stations: 
Angle observations at subsidiary . 38 

Angles to additional 41 

t. Azimuth 42, 116 

'^^ Descriptions , 52-54 



Stations Continued. Paragraph. 

Distances between 2 

In towns 3 

Location of 1-3 

Measurements to additional 24, 30 

Projection from rail to true 91-93 

Rail 16 

Railway, name 63 

Traverse, as bench marks 57, 58 

Support: 

For tapes 13, 28, 105 

Tape correction tables, for various 
methods of 90 

Tables: 

Explanation 77 

Inclination correction 79-82, 107-110 

Tape correction 89, 90 

Temperature correction 88 

Tangents, location of stations along . 1,2 
Tape correction: 

Computed values 86,87 

Tables 89, 90 

Tape lengths: 

Counter- 19, 27 

Marks 17, 18, 104 

Tapes: 

50-meter invar 5-11 

300-foot 27 

Checking lengths in field 6 

Kinks 9 

Number used 6 

Standardization 7, 8, 85 

Support for 13, 28, 105 

Temperature 11, 27, 32 

Tension 10, 29 

Tapmg: 

On wet rails 26, 31 

Triangle to avoid 23 

Temperature correction tables 88 

Temperature of tapes .... 11, 27, 32, 102, 103 

Temporary marks 49, 51 

Tension for tapes 10, 29 

Theodolite 35 

Thermometer attachment 11 

Thermometers 11, lOa 

Towns: 

Bench marks in 57 

Stations in , 3 

Triangle to avoid taping . . . , 23 

Weather conditions for observing 

angles 37 

Weather, taping in rain ...... , 26, 31 

Y level 67 

Y leveling: 

Over stakes 65,67,73,74 

Rods 67 

Stadia readings 67 



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