Avueust 18, 1899. ] 
due to surface and line distributions of mass. 
The fourth and fifth are occupied with the 
function of Green and the problem of Dirichlet. 
The sixth gives an exposition of the potential 
theory as applied to double strata (double 
couches) ; that is, two infinitely near surface or 
stratum distributions of equal but opposite 
densities. The seventh and eighth continue 
the consideration of the problem of Dirichlet, 
the former by means of the process of Green’s 
equivalent stratum (here called La methode du 
balayage), and the latter by the method of 
Neumann. The ninth chapter is devoted to an 
extension of the method of Neumann to the 
case of simply connected regions, and to certain 
functions (called Fonctions fondamentales) 
which conform to the conditions of the poten- 
tial function due to a simple surface distribution 
of mass. 
The treatment of the subject, except for the 
few final pages in which the ‘fonctions fonda- 
mentales’ are discussed, is very precise from 
the purely mathematical point of view. ‘‘J’ai 
cherché,’’ the author says, p. 348, ‘‘& donner 
partout 4 mes raisonnements un charactére de 
parfait rigueur.’’ For this reason the work 
will doubtless prove most interesting to the 
mathematician and most instructive to the 
physicist. But the latter can hardly conceal 
the regret that his demands for precision are 
not equally met. Thus, to cite some illustra- 
tions, the Newtonian potential is defined by 
the equation 
y m 
Te = 
n 
’ 
where m is any element mass and r its distance 
from the attracted mass ; and we are told that 
the components of attraction in the coordinate 
directions are 
OY <  SOY 
ES B50 eel RES 
but not a word is said about the gravitation 
constant nor of the difficulties a reader who 
may know the dimensions of force may have in 
interpreting 0V/dx, ete. Again, how do ‘ poten- 
tiel newtonien d’une surface sphérique homo- 
gene’ and ‘potentiel logarithmique d’une cir- 
conférence’ sound to one whose imagination is 
always shocked by the suggestion of surface 
and line distributions of real matter? Again, 
SCIENCE. 
215 
on p. 215, £,7,¢ figure as components of a 
velocity, but on p. 217 the author says: ‘‘Sup- 
posons maintenant que le vecteur §, 7, ¢ soit, en 
chaque point, normal a la surface, ¢c’est-a-dire 
que |’on ait: 
Sa= Oh (= |th C4 
a,B,y désignant les cosinus directeurs de la 
normale au point 2, y, z.’’ The reader will find 
out, of course, sooner or later, how to remove 
these inconsistencies, but it would have been 
very easy to avoid them entirely and to have thus 
fulfilled the requirements of the physicist as 
well as those of the mathematician. 
English students of the theory of the potential 
will be glad to find good French authority for 
the term Laplacian as applied to the sum of the 
three second derivatives of the potential with 
respect to the coordinate directions. Thus, for 
example, the author writes, p. 118, ‘‘Le la- 
placien AV, more commonly written 4?V or y?V. 
by English writers, ‘ fait unsaut brusque. . .”’ 
The most important technical features of the 
book are to be found in the investigations of 
the potential of single and double surface dis- 
tributions, in the considerable space devoted to 
the logarithmic potential, and in the thorough 
though tedious treatment of the problems of 
Green and Dirichlet. 
The volume on kinematics, potential and hy- 
dromechanics presents an unusual though not 
incongruous combination of subjects. A good 
knowledge of kinematics and a considerable 
acquaintance with the potential theory are, in 
fact, necessary preliminaries to the study of the 
mechanics of fluids. 
Over half of the book, 200 pp., is devoted to 
kinematics and mechanism. Beginning with 
the elements of the subject, Chapter I treats 
of the rectilinear and curvilinear motions of a 
point, Chapter II of the coplanar motion of 
an invariable figure, Chapter III of the mo- 
tions of a rigid body, Chapter IV of helicoidal 
motions (theory of screws), Chapter V of the 
relative motion of a point, and Chapter VI of 
the motions of various forms of mechanisms, 
including belts, gearing, links, etc. In the de- 
velopment of the purely kinematical principles 
the author supplies both geometrical and ana- 
lytical proofs. Many of the former and some 
of the latter appear to follow new lines in this 
