216 
well gleaned field. This work does not seem 
to be, asa whole, very satisfactory, however, in 
view of the heavy drafts which kinetics and 
some branches of applied mechanics now make 
on kinematics. A more condensed and a more 
analytical treatment would have been clearer, 
we think, and would have left room for some 
important generalities omitted, especially such 
as are essential in hydrokinetics, in elasticity, 
and in the kinetics of non-rigid bodies. There is 
in this part also an occasional departure from 
the modern demands for mechanical precision, 
as on pp. 10, 11, where, by the unnecessary 
suppression of a length symbol, the ancient fal- 
lacies of the equality of linear and angular 
velocities and of linear and angular accelera- 
tions are revived. Again, to cite another illus- 
tration of a lack of clearness, in Chapter V, 
which is entitled ‘Mouvement relatif d’un 
point,’ and which considers the motion of a 
point referred to two sets of rectangular axes, 
one of which moves in any manner with re- 
spect to the other, the author says, p. 121: 
‘On peut avoir a considérer trois mouvements : 
1° le mouvement du point M par rapport aux 
axes fixes ou mouvement absolu ; 2° le mouve- 
ment des axes mobiles ou mouvement d’en- 
trainement; 3° le mouvement de M tel qu’il 
apparaitrait & un observateur invariablement 
lié aux axes mobiles ou mouvement relatif.’’ 
This shows also, among other things, that it is 
still easy to speak of the absolute even in me- 
chanics. 
The second part of the book presents, in the 
first two chapters, a rather elementary intro- 
duction to the theory of the force function, 
potential function and the flux of force, and 
to Green’s theorem and Dirichlet’s problem. 
There is added, also, in the third chapter, an 
elementary investigation of the attraction of 
ellipsoidal shells and of a homogeneous ellipsoid. 
The most interesting and important chapters 
of the book are the last two, which are devoted 
to hydromechanies. The treatment is confined 
to the ideal case of perfect fluids and is, on the 
whole, elementary. About 60 pages are given 
to the theory and applications of the principles 
of hydrostatics. Most prominent and impor- 
tant among the applications is the somewhat 
extended discussion of the conditions of equi- 
SCIENCE, 
[N. S. Von. X. No. 242. 
librium of floating bodies. Among many in- 
structive results it is shown that a right homo- 
geneous cylinder may float in stable equilibrium 
in four different positions, in one of which its 
axis is vertical, in one horizontal, while in the 
other two the axis is oblique to the vertical. 
The final chapter, of 61 pages, is devoted en- 
tirely to hydrokinetics. Proceeding from the 
Lagrangian to the Eulerian equations of motion, 
the author develops the elements of the subject 
with unusual clearness and mathematical ele- 
gance. After the introduction and definition of 
the velocity potential the theorem of Lagrange 
—once a potential always one—is demonstrated 
by an apparently new proof, which seems pecu- 
liarly well adapted to show the meaning and 
limitations of the theorem. The beautiful and 
very important theorem of Bernoulli is also 
demonstrated in a new and rigorous fashion. 
The part of the chapter dealing with irrota- 
tional motion closes with an exposition of the 
motion of liquids under gravity in the case 
wherein the products of the component veloc- 
ities and their space derivatives can be neglected. 
The rest of the chapter is concerned chiefly 
with vortex motion (vortices, tourbillons). Here 
also there is much fine mathematical work, 
though the notation is in some respects repul- 
sive and though the printer would appear in 
some places to have sown his d’s and 9’s broad- 
east. On pp. 348-353 there is some especially 
interesting work preliminary to the proof of 
Helmholtz’s theorem that the molecules once 
observed to be on a vortex line remain on it. 
This work consists in the proof of three special 
theorems drawn from the general equations of 
rotational motion for the particular case of 
steady motion. Let at any point x, y, z of the 
fluid 
ia Pp Vi | dp 
Pp 
where T and V are the kinetic and poten- 
tial energies respectively per unit mass, p is the 
pressure, and p is the density assumed to be 
dependent on p only. Then: Ist, for steady 
irrotational motion, for which the component 
spins and accelerations of the molecules vanish, 
it appears at once that H is constant through- 
out the mass, which is Bernoulli’s theorem gen- 
eralized ; 2d, when the motion is steady but ro- 
