DECEMBER 29, 1899. ] 
The contents of the book are: 
Chapters I: to IV., Genera] Principles of 
Alternating Waves and Measurements. 
Chapters V. to VII., Inductive Circuits, Par- 
allel and Series Connection. 
Chapters VIII. to XV., Alternators, Trans- 
formers, Synchronous Motors, Converters, In- 
duction Motors, Transmission Lines. 
The book is based on college experience and 
intended as a text-book for colleges, and fulfills 
this object admirably, better than any other 
book on these subjects that I know, not only 
by what it gives but also by what it omits. It 
does not give design of alternating apparatus 
except in a few isolated cases, which would 
preferably have been omitted also. The de- 
signing data and methods in the present state 
of the electrical industry form one of the most 
valuable assets of a few large manufacturing 
companies, and thus are practically inaccessible 
to the public, so that any book claiming to 
teach design of alternating apparatus can im- 
mediately be recognized as an intentional or 
unintentional fraud. 
In electrical engineering, as in most branches 
of science, two methods of investigation exist. 
The differential method compounds the equa- 
tions of the phenomena taking place in the 
time differential. It is the only exact method, 
and the method which has given broad results 
of universal importance in the hands of men 
such as Maxwell and Heavyside, but in the 
hands of anybody but a mathematical genius, 
this method is absolutely barren of results. In 
engineering practice to integrate the differential 
equations, such assumptions have to be made 
that ultimately the result, derived by excessive 
labor, applies to phantom apparatus only, as a 
hysteresis-less transformer, or an induction mo- 
tor without self-induction, or any such monster. 
In the integral method, the time differential 
and to a large extent, the time as variable has 
altogether disappeared, the alternating wave is — 
represented by its quadratic mean and its phase, 
the E.M.F of self-induction finds its expression 
in a constant ohmic reactance, and even the 
hysteretic loop has disappeared and is repre- 
sented by an angle of advance of the phase of 
magneto-motive force with regard to the mag- 
netic flux. 
SCIENCE, 
965 
This method is naturally an approximation 
only, and after the problem has been solved 
the results have to be discussed regarding their 
accuracy, and corrections applied to allow for 
secondary effects, as higher harmonics, etc., 
just as in astronomy the preliminary orbit of a 
comet has to be corrected for the disturbances 
caused by the planets. 
But the integral method is the only method 
which is of practical utility, whether as graph- 
ical or trigometrical, or symbolic treatment in 
complex quantities. — 
Unfortunately in our colleges, usually, too 
much preponderance is still given to the differ- 
ential method, starting from Green’s theorem 
and leading into the nowhere, and further time 
wasted by spreading misinformation in the at- 
tempt to teach apparatus design, although, 
fortunately, a reaction is setting in now by re- 
placing the teaching of apparatus design by 
that of a thorough understanding and study of 
the actions and internal reactions of the appa- 
ratus, and differential methods by engineering 
methods. 
I believe, however, that these differential 
methods might better be dropped altogether 
from the curriculum of our colleges, and the 
time saved thereby distributed between the 
teaching of engineering methods, for which the 
above discussed book forms a very suitable 
text-book, and is especially intended, and dif- 
ferential calculus pure and simple, endeavoring 
in the latter to give the student a thorough un- 
derstanding and intuition into the fundamental 
principles rather than to load his memory with 
a lot of useless, because immediately forgotten, 
formalism. There appears to me no branch of 
science more tedious than mathematical physics. 
Mathematically, it has neither the interest nor 
the elegance of pure mathematics, and physic- 
ally, it is, with very few exceptions, barren of 
results. 
CuHas. P. STEINMETZ. 
Kinematics of Machinery. By JoHn H. Barr, 
M.S., M.M.E., Professor of Machine Design, 
in Sibley College, Cornell University. New 
York, Wiley & Sons. London, Chapman & 
Hall. 1899. 8vo., pp. v + 247, 213 illustra- 
tions, cloth. $2.50. 
