214 
in the days of Laplace and Gauss, for one mind 
to possess a working knowledge of the entire 
group of the mathematico-physical sciences. 
An idea of the comprehensive scope of this 
Cours may be gained by the following list of 
titles to the preceding ten numbers of the series : 
1°, Théorie mathématique de la lumiére, I., 1 
Vol. ; 2°, Blectricité et Optique, 2 Vol. ; 3°, 
Thermodynamique, 1 Vol. ; 4°, Legons sur la 
Théorie de 1’Elasticité, 1 Vol.; 5°, Théorie 
mathématique de la lumiére, II., 1 Vol.; 6°. 
Théorie des Tourbillons, 1 Vol. ; 7°, Les oscil- 
lations électriques, 1 Vol.; 8°, Capilarité, 1 
Vol. ; 9°, Théorie analytique de la propagation 
de la chaleur, 1 Vol. ; 10°, Calcul des probabili- 
tés, 1 Vol. These, together with the two 
works announced above, which are Nos. 11° 
and 12° of the series, make a total of thirteen 
octavo volumes devoted to at least ten fairly 
distinct subjects of mathematical physics. All 
of these volumes have appeared within a period 
of about ten years, during which the indefat- 
igable author has found time also for many re- 
searches in pure mathematics and for important 
contributions to dynamical astronomy.* 
The reader who is not already acquainted 
with this important series of works will natu- 
rally enquire what are its characteristic features 
and what are the advantages to be gained by a 
study of this rather formidable aggregate of 
three to four thousand pages of intensely math- 
ematical literature. 
In the first place, it should be said that the 
works are in no sense treatises. They assume, 
in general, a considerable knowledge of the 
subject on the part of the student, and do not 
attempt, as a rule, to give that degree of detail 
which is essential in an elementary presenta- 
tion. Secondly, it must be said that these 
works are much more mathematical than phys- 
ical. Indeed, it will doubtless appear to some 
that the title of the series ought to be Cours de 
mathématique physique; for the ease with 
which the author substitutes mathematical ab- 
stractions for physical realities is often painful 
to one who is at all conscious of the obstinate 
properties of matter. In many cases, also, the 
formulas dealt with are entirely divested of the 
* Especially his ‘ Nouvelles théories de mécanique 
céleste.’ 
SCIENCE. 
[N.S. Vor. X. No. 242. 
factors which are indispensable to their use by 
the physicist; so that while the mathematical ar- 
gument may proceed unimpeachably the results 
attained are often quite unsuited for the phys- 
ical laboratory or the computer’s mill. But let 
nomathematician who has the slightest liking 
for physical applications and no physicist who 
has a fondness for mathematical methods of re- 
search be deterred by such trifling matters of 
detail from an attentive study of these volumes. 
For the mathematician will find in them a 
wealth of beautiful analysis satisfying all the 
canons of modern precision and at the same 
time not obtrusively technical and practical ; 
while the physicist, on the other hand, will be 
delighted and instructed by the luminous expo- 
sitions of obscure questions, by the fresh and 
rigorous proofs of old theorems, by the more 
refined processes of modern analytical pro- 
cedure, and by the sharper limitations of the 
fields explored. In short, it is one of the prime 
merits of these works that they afford a com- 
mon ground on which the pure and applied 
mathematicians may meet to their mutual ad- 
vantage. Of course, there must be some con- 
cessions. The pure mathematician must admit, 
while reading the Cours, at any rate, that the 
phenomena of nature present intricate though 
special and perhaps grossly utilitarian illustra- 
tions of his general theorems ; and the physicist 
must own, with due contrition, that it is not 
uninteresting and profitless, occasionally, to 
free one’s self from the restrictions of matter, 
or even to investigate the imaginary properties 
of hypothetical mediums. 
The volume devoted to the Théorie du poten- 
tiel Newtonien is chiefly concerned with the 
properties and application of the function de- 
pendent on the law of the inverse square of the 
distance, but considerable attention is given also 
to the logarithmic potential, which has come to 
play an important role in some physical prob- 
lems. The book is divided into nine chapters. 
The first deals with the potential at a point ex- 
ternal to the attracting mass, with the equation 
of Laplace and with the harmonic developments 
of the potential function. The second is con- 
cerned with the potential at a point internal to 
the attracting mass, and with the equation of 
Poisson. The third is devoted to the potential 
