182 
tity independent of the units of length, mass 
and time. And this leads to the remark that 
in didactic treatises it is best for the author as 
well as the student to make constant use of the 
theory of dimensions. On pp. 258, 260, 262, 
we find the phrase ‘impulsive pressure’ used 
as a synonym for momentum and impulse. 
This is plainly a slip of the pen, since the 
equally objectionable ‘impulsive force’ of the 
older writers finds no favor with the author. 
Here again, and also in the phrase ‘angular 
momentum,’ which the author seems to sanc- 
tion as the equivalent of ‘moment of momen- 
tum,’ the theory of dimensions points the way 
to precision of terminology. Lastly, a book so 
full of excellencies should have a much fuller 
index, some comparatively new terms like dis- 
sipative forces, motional forces and positional 
forces being omitted or given only indirectly, 
and the important name of Mach being over- 
looked altogether. 
With commendable admiration for their great 
master, the editors of the series of volumes to 
which the one before us belongs have under- 
taken to present in printed form the lectures 
on mathematical physics delivered by Helm- 
holtz in the later years of his life. In doing 
this they are doubtless fulfilling a pious duty, 
but they are also assuming a serious task, for 
no one short of a master is fitted to elaborate 
the lectures of a master. As regards the pres- 
ent volume, on the dynamics of discrete parti- 
cles, the task of the editor was not specially diffi- 
cult, since the subject has been pretty thoroughly 
wrought out during the past two hundred years. 
In fact, much of the matter in this volume 
would not be worth publishing at all in such a 
series if it did not possess here and there the 
impress of the master’s originality. 
The book is divided into four parts. The 
first part deals with the kinematics of a point, 
the second with the dynamics of a material 
point, the third with the dynamics of a material 
system, and the fourth is devoted to the general 
principles of dynamics, including statics as 
visualized in the principle of virtual displace- 
ments, and the methods of d’Alembert, La- 
grange and Hamilton in kinetics. 
The first part presents little that is novel, and 
SCIENCE, 
[N. S. Vou. X. No. 241. 
is quite insufficient for the needs of anything 
beyond elementary work in kinematics. The 
most important theorems of the subject are not 
even alluded to. The second. part establishes 
the equations of motion of a free particle by 
the aid of Newton’s laws, and devotes an un- 
due amount of space to the simplified case of a 
‘falling body’ without disclosing anything of 
its essential complexity. Then follow seventy- 
seven pages treating of oscillatory motions, in- 
cluding simple harmonie and damped vibra- 
tions and the theory of the simple pendulum 
moving ina plane or cone. Much of this space 
is rather dreary in its prolixity, but the physi- 
cist will find the sections treating of damped 
vibrations and forced vibrations well worth 
reading. 
The third part sets down the equations of 
motion of a system of masses by aid of the 
principle of equality of action and reaction 
whereby the internal forces of the system are 
seen to be self-balancing. Then follow the 
well-known theorems concerning the motion of 
translation of the centroid of the system and 
of its rotation about axes through the centroid. 
The notation used here is needlessly complex ; 
but the following section, which deals with the 
very important subject of moments of inertia, 
is rendered repulsive by reason of a violent and 
quite useless departure from current notation. 
Why should a subject so old (dating from Seg- 
ner and Euler) and so intrinsically difficult be 
encumbered by a strange notation when noth- 
ing new is presented ? 
The remainder of the third partis devoted to 
the principle of energy and to an elementary 
presentation of the theory of planetary motion. 
The forty pages allotted to the doctrine of 
energy are chiefly interesting for their historical 
matter and for the author’s physical concep- 
tions, while the thirty-six pages in which 
Newton’s problem of two bodies is treated 
afford an easy introduction to dynamical as- 
tronomy. 
For the advanced student of mechanics the 
fourth part of the book will be found most in- 
teresting and instructive. It is in this part 
that the editor presents the author’s latest 
views on the generalities of thescience. There 
is not much herein that is new ; but the student 
