SEPTEMBER 22, 1899. ] 
is regarded as ‘a quantity which becomes in- 
definitely small.’ According to the definition of 
limit, page 3, either of two variables, as — ' — 
mn increasing, may be the limit of the other. On 
page 10 we are told that when a point, moving 
continuously on a given curve, passes a speci- 
fied point of the latter, it tends at that instant 
to move on the tangent. There is, of course, 
no such tendency, and continuity is not defined 
till several pages later. On page 25 the con- 
clusion, ‘ Hence the first derivative, etc.,’ is, as 
stated, entirely unwarranted by the premises. 
‘Any finite constant’ is much too sweeping. 
It appears to be assumed throughout that con- 
tinuity implies derivability. The explanations 
of the differentials dy and dz, pp. 39, 40, are 
interesting and curious. It would be supere- 
rogatory to give here an exhaustive enumeration 
of the peculiarities encountered, the foregoing 
specimens, taken at random, being perhaps 
sufficient. 
The final three chapters present plainly and 
pleasantly an introduction to the practical 
phase of differential equations. The existence 
theorem, naturally not proved, is however 
tacitly assumed, and such fundamental questions 
as whether all modes and orders of elimination 
lead to the same equation are neither met nor 
propounded. 
Dr. Murray’s book is a simple, fresh, lumi- 
nous and suggestive presentation of the ele- 
mentary subject-matter of the integral calculus. 
While it was written primarily for engineering 
classes and particularly adapted to conditions 
prevailing at Cornell University, still the needs 
of others have been regarded and the work is 
not ill-suited asa guide to any one beginning 
the study of this branch of mathematics. The 
first two chapters, in particular, furnish an un- 
usually full account of fundamental concepts 
and operations. The two conceptions of inte- 
gration, as the inverse of differentiation, and as 
a process of summation, are shown to be one, 
On pages 9 and 11 and elsewhere, the symbol / 
is spoken of as denoting now a sum and again 
the limit of a sum, with seeming indifference. 
Chapter XII. deals briefly with the important 
subject of integral curves, and in the next 
SCIENCE. 
415 
chapter, which is final, we find a brief discus- 
sion of some common and important differential 
equations. 
For the convenience of any who may not 
have the time—several months, at least—neces- 
sary for the mastery of all the matter offered, 
a list of lessons for a shorter course is sug- 
gested. Many other minor features help to 
enhance the acceptability of the book. The 
exercises are numerous and many of them are 
not found in other works. A table of answers 
is appended as also a short table of integrals. 
Binding and paper are substantial and printing 
and proof-reading well done. There is no 
great pretense of rigor but there is life. The 
book was not stillborn. 
C. J. KEYSER. 
CoLUMBIA UNIVERSITY. 
GENERAL, 
THE Adjutant-General’s office of the War 
Department has undertaken the issue of a 
‘French-English Military Technical Diction- 
ary,’ compiled by Cornélis De Witt Willcox, first 
lieutenant of artillery, U.S. Army. The first 
part, which has just been issued, contains 160 
pages and reaches the word espace. The book 
is clearly printed with a judicious use of block 
and italic type. It will prove useful not only 
in the army and navy, but also to students of 
science in different directions. Many of the 
words translated will not be found in a good 
French dictionary as ‘Littré et Beaujean,’ yet 
they occur in scientific books. Not many 
Americans could give the equivalent of words 
such as abowement, abougri, abraquer, etc., and 
itis convenient to have at hand a dictionary in 
which they can be found. It is a matter for 
congratulation that there are in the army 
officers capable of such good scientific and 
literary work, and that it is encouraged by 
the authorities. 
THE Experiment station of West Virginia 
University has recently issued Bulletin, No. 56, 
prepared by Dr. Hopkins, summing up the 
work done by him as entomologist of the Station 
during the past eight or nine years. This isa 
large bulletin of over 360 pages, and contains 
much valuable data collected by the entomolog- 
ical department during the time named, as it 
