Auaust 11, 1899. ] 
connection with matters of principle are Kirch- 
hoff’s Vorlesungen uber mathematische Physik 
(Mechanik), Pearson’s Grammar of Science, and 
Mach’s Science of Mechanics. This last should 
be in the hands of all students who desire to 
follow the history of dynamical ideas.’’ We 
are still more interested to examine the book 
when we read in the introductory paragraph 
that ‘‘ Mechanics is a natural science ; its data 
are facts of experience ; its principles are gener- 
alizations from experience. The possibility of 
natural science depends on a principle which 
is itself derived from multitudes of particular 
experiences—the ‘ Principle of the Uniformity 
of Nature.’ This principle may be stated as 
follows: Natural events take place in invariable 
sequences.’’ 
From this classification of mechanics along 
with the natural sciences one may correctly in- 
fer that the work is more concerned with the 
facts than with the formulas of the subject. 
Indeed, the old notion, still held by many, that 
mechanics is simply a branch of applied mathe- 
matics whose data are as unquestionable as the 
data of Euclidean geometry, finds no tolerance 
here. On the contrary, one of the most impor- 
tant features of the work consists in its critical 
examination of the postulates and principles of 
mechanics and their range of applicability to 
matter as we know it. The doctrine of relativ- 
ity of motion, force, etc., so generally over- 
looked or ignored in works on dynamics, is 
here considered with much particularity ; well- 
known results are presented in clearer lights, 
and many new or less well-known results are 
to be found in every chapter. In short, the 
work isa thoroughly progressive and instruc- 
tive treatise which will bring pleasure and profit 
to any energetic student of mechanics. 
The book is divided into three parts embrac- 
ing in all thirteen chapters. The first part, in- 
eluding the first four chapters, deals with kine- 
matics; the first chapter being devoted to 
definitions, the second to vectors, the third to 
displacement, velocity and acceleration, and 
the fourth to applications of kinematical prin- 
ciples. A novelty of nomenclature introduced 
here with apparent advantage is the word 
‘frame,’ or the phrase ‘frame of reference,’ in 
place of ‘axes’ or ‘coordinate axes,’ though 
SCIENCE. 
181 
one may doubt the desirability of such a change 
of terms unless it can be made in other appli- 
cations of coordinate geometry as well. 
The second part, Chapters V. to VIII., is de- 
voted to the principles of dynamics. Herein 
there is a notable departure from the plan of 
treatment followed in most English texts. 
There is less of the appearance of formal de- 
duction and more of the reality of simple in- 
duction. This method leads, by an appeal to 
observation and experiment, to the essential 
concepts of mass and force, and thence to the 
equations of motion of a free particle. The 
laws of motion of Newton are not incorporated 
in the text, but are commented upon in a note 
at the end of Chapter V. General theorems 
concerning the motions of masses are consid- 
ered in Chapter VI.; systems of forces are 
treated in Chapter VII., and Chapter VIII. is 
devoted to work and energy. A new and 
commendable term, namely, ‘kinetic reaction,’ 
appears in this part for the first time, appar- 
ently, in a text-book. This may well replace 
the ‘expressed force,’ ‘ force of inertia,’ etc., of 
earlier writers. A critical note at the end of 
Chapter VIII. is well worth examination by 
advanced students of the science. 
The third part of the work, Chapters IX. to 
XIII, deals with methods and applications. 
These cover about 120 pages, and a large variety 
of solved and unsolved problems is set before 
the reader. Chapter IX. is occupied with free 
motions of particles, X. with constrained mo- 
tion, XI. with coplanar motions of a rigid body, 
XII. with miscellaneous methods, and XIII. 
with relative motion and gravitation. Much 
space is given in these chapters to impulsive 
motions and to the intricate questions of initial 
motions, and a considerable portion of Chapter 
XII. is devoted to the interesting subject of the 
motions of strings and chains. A short appen- 
dix deals with the questions of units and their 
dimensions. 
The work appears to be subject to the follow- 
ing minor criticisms: Too little space is given 
to kinetics in three dimensions, On p. 96 there 
is a definition of the Jaw of gravitation which 
will lead the incautious reader to adopt the 
common but erroneous notion that the gravita- 
tion constant is a mere number, that is, a quan- 
