510 Notices respecting New Books. 
quantity so denoted by Weierstrass, atid =K—H. We thus 
have 
—_ cin 0+ 5 sin 36+ esin SO + 5 L resin 70 
2 
ee 2 faiSBee Z 8 Laee BE . my sin 130+ &e, 
ee = sin 6—5 sin 564. ? sin 59-2 oy. sin 70 
2 92 2 
ae Bast 99— 52 peaed > sin 116+ tS a >, sin 130— &e. 
LVIII. Notices respecting New Books. 
An Elementary Treatise on Dynamics, containing Applications to 
Thermodynamics. By B. Wiurtamson, M.A., ge, and F. A. 
Tarzteton, LL.D. London: Longmans, Green, and Co. 459 pp. 
yale is uuquestionably an important work on Dynamics, com- 
prising within the compass of 459 pages the Dynamics of a 
Particle (218 pp.), the Kinematics and Kinetics of a Rigid Body 
(207 pp ), including two chapters on Energy (40 pp.) and one on 
Small Oscillations (43 pp.), anda final chapter on Thermodynamics 
(29 pp.). Except for a few applications to elastic material and 
some to the thermodynamics of gases (as illustrations of the 
Theory of Energy), the work is confined to the Motion of Rigid 
Bodies, and is on the whole a most carefully thought-out treatise 
on so large a subject. 
It professes to “ start from the most elementary conceptions, so 
that any student who is acquainted with the Calculus can commence 
the Treatise without requiring the previous study of any other 
work on the subject.” (see preface). It is perhaps a natural result 
of this that the early parts are easy and in considerable detail, 
whilst the later parts are difficult from their conciseness. It may, 
indeed, be doubted whether any student could really read this 
Treatise through (and work out the examples) without external 
help in the later parts. The examples have been chosen with 
great care so as to form excellent illustrations of the text; of a 
great many, however, it must be said that they are rather mstruc- 
tive problems which have been solved by accomplished mathema- 
ticians than exercises for students ; more or less full details of the 
working of these are given :—e.g. Ex. 15 to 27, on Kinetics of a 
Rigid Body, are ‘“ the substance of Prof. MacCullagh’s Lectures on 
Rotation.” 
It is singular that though the work bears the names of two 
mathematicians on the titlepage, and seems to have received at 
least partial revision from a third (see preface), a decided looseness 
