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214

CALCULUS.

188. Proposed by A. H. HOLMES, Brunswick, Maine.

Required the perpendicular height of a right cone, radius of base being
unity, such that the maximum ellipse that can be cut from the cone shall equal
the base of the cone in area.

186. Proposed by Editor EPSTEEN.

ti i i /*°°sin my , /•"cos my ,

Evaluate I -dy, I -dy.

Joy "Joy *

GROUP THEORY.

6. Proposed by L. E. DICKSON, Ph. D„ The University oi Chicago.

Show that the binary substitutions oiif,,^,, the binary substitutions on
c 2 , r) 2 , and (?i£ 2 )('?,!?2) generate a maximal subgroup of the quaternary abelian
group.

MISCELLANEOUS.

146. Proposed by F. P. MATZ, Ph. D., Sc. D.

n . facos« + 6sina=c~l . ...

Glven {aeotf+ taiitf =cj to P™ethat

sin(a + /9)= — t, — n-i and cot«+cot/3=— --.

a? + b 2 c 2 —a

NOTES.

Mr. H. R. Willard has been appointed instructor in Mathematics in the
University of Maine.

Mr. C. A. Holden has been appointed assistant professor of Mathematics
in Dartmouth College.

Dr. C. Gunderson has been appointed instructor in Mathematics in the
Michigan Agricultural College.

Mr. C. H. Sisam has been appointed instructor in Mathematics at the U.

Mr. W. D. Cairns has been promoted to an associate professorship in
Mathematics at Oberlin College.

Prof. T. F. Nichols, of Hamilton College, has been promoted to a full
professorship of Applied Mathematics.

215

Miss M. E. Sinclair and Mr. C. Havemeyer have been appointed instruc-
tors in Mathematics in the University of Nebraska.

Dr. George H. Hallett has been promoted to an assistant professorship of
Mathematics in the University of Pennsylvania.

Mr. N. R. Wilson, lecturer in Mathematics in Wesley College, Winnipeg,
Manitoba, is doing advanced work at the University of Chicago.

Prof. T. E. Holgate of the department of Mathematics of Northwestern
University, has been appointed acting President of the University.

Dr. E. M. Blake, instructor in Mathematics in the University of Califor-
nia, has accepted the chair of Mathematics in the University of Arizona.

Professor Vining of Brandon College, Brandon, Manitoba, has been
granted a leave of absence for two years. His place is temporarily filled by Dr.
H. E. Jordan.

BOOKS.

Lehrbuch der Differenzenrechnung by D. Seliwanoff. B. G. Teubner, Leip-
zig, 1904. 92 pp.

At the request of the well known Leipzig publishers, B. G. Teubner, the author has
elaborated his article on Finite Differences in the Encyklopaedie der MathemaUschen Wis-
tenschaften, Vol. 1, pp. 918-937, to the dimensions of a book. Thus, while the encyclopaedia
gives but one page to the approximate evaluation of definite integrals and four pages to
the subject of difference equations, the book devotes six pages to the former and twenty-
nine pages to the latter. The gain in perspicuity over the encyclopaedia article is there-
fore considerable and indeed, although the author omits certain questions which might
well be taken up, the subjects which he treats are presented in a delightfully clear and
simple manner.

The books of Boole and Markoff are more corr.plete, but this work of Seliwanoff
should be regarded not as a handbook for one who is familiar with the subject, but as a
text book for the beginner who desires to learn the technique of computation, such as the
methods of interpolation, construction of tables, estimation of unavoidable errors.

Part I devotes thirty-two pages to the subject of Differences. After developing
some of the most important general theorems in Chapter 1, the question of Interpolation
is taken up in Chapter 2 where the author considers exact and approximate interpolation,
computation of the roots of numerical equations, and the computation of logarithms and
antilogarithms. The methods of evaluation of definite integrals in Chapter 3 are all very
elementary, culminating with Simpson's Formula.

In Part II, Chapter 1 treats the subject of Indefinite and Definite Summation. Ac-
cording to the conventional usage the symbol 2 is employed as the Calculus analog of
the sign of integration J*. In the opinion of the reviewer the symbol S would serve
the purpose somewhat better. First, the use of the Creek letter as a functional symbol,
where the (finite) integration is not possible, is a departure from its recognized meaning
in various domains of analysis ; second, the letter S corresponds somewhat closer to the

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