528 
NATURE 
and is presented with considerable force and 
literary skill, and this circumstance makes its 
faults all the more regrettabie. Besides that to 
which allusion has already been made there are 
two others, first the obtrusive egotism of the 
writer, and secondly his habit of misrepresenting 
people from whom he differs in opinion. To say 
that “for years the chief object of the biometrical 
laboratory at University College has seemed to be, 
and now clearly is, to prove the inheritance of 
this or that human character is ‘not Mendelian’ ” 
is little short of libellous. Nor is it just to assert 
“Newton was a weakly baby, prematurely born, 
and would promptly have been condemned as not 
worth keeping had the statistical school been in 
power in his day.” 
Finally we should like to know what eugenists 
maintain that “a high birth-rate and a high infant 
mortality rate are to be commended because of 
their ‘selection value,’” or that “slums are de- 
fensible on the ground that in the course of time 
there is bred in them a slum race which withstands 
and even thrives in such conditions.” 
‘ 
A PRINCETON COLLOQUIUM ON 
MATHEMATICS. 
The Princeton Colloquium: Lectures on Mathe- 
matics, delivered September 15 to 17, 1909, 
before Members of the American Mathematical 
Society in connection with the Summer Meeting 
held at Princeton University, Princeton, N.]. 
By G. A. Bliss and E. Kasner. Pp. iii+ii+ 
107+i1+117. (New York: American Mathe- 
matical Society, 1913.) 
HE first of the courses contained in this 
volume deals mainly with the theory of a 
set of implicit functions y;, defined by a set of 
equations, fj =o (i=1, 2,...mn), each involving the 
implicit functions and also the independent vari- 
ABIES, “44, Xo, In its general character the 
treatment is similar to that invented by Cauchy; 
but it is noticeable how the analysis has been 
simplified, and the results generalised, by im- 
provements made quite recently. In particular, 
attention may be directed to the elementary char- 
acter of the proot (by MacMillan) of what Prof. 
Bliss calls the preparation theorem of Weierstrass 
(p. 50): other illustrations might be given of a 
similar kind. 
In carrying out the methods and ideas of Weier- 
strass, the principal result is that we obtain ex- 
pansions for the y; valid “in the neighbourhood 
of a point (a, b).” Prof. Bliss himself points out 
that one main object of his course is to deduce 
from the initial solution (a, b) something more 
than solutions of which we can merely say that 
they are valid very close to (a, b). 
NO, (22 245 eviome@e0 
5 Ghote 
By means of 
‘ 
what he calls ‘‘a sheet of points” he is able to 
deduce from any initial solution (at an ordinary 
point) a sheet of solutions which only fail at “ex- 
ceptional points,” so we have something more or 
less analogous to Weierstrass’s “analytical con- 
tinuation”’ of a branch of a curve. 
There are various interesting paragraphs on 
transformations from one plane region to another ; 
a partial discussion of the singularities of the yj, 
and a final lecture on existence-theorems connected 
with a set of differential equations. 
Prof. Kasner’s course on dynamics presents 
many features of novelty and interest. Broadly 
speaking, it is a quasi-geometrical study of trajec- 
tories with the aid of analytical (mainly contact) 
transformations. Many of the results obtained 
are of a remarkably elegant character: for in- 
stance, in the constrained motion of a particle on 
a surface under the action of positional forces, we 
have the theorem that the «! trajectories starting 
from a given lineal element have osculating 
spheres, at the common point, the centres of 
which lie on a conic in the plane normal to the 
element. A problem of more interest to physi- 
cists is this: given a system of curves in space, 
to find the condition that they may be trajectories, 
and to deduce the field of force from the set of 
curves when the proper condition is satisfied. This 
problem is fully discussed in chap. i., and the 
conditions for a conservative field are put into a 
remarkable geometric form. 
We have also a section on least action, one on 
the space-time transformation used by Lorentz in 
the relativity theory, and various special illustra- 
tions of the general results. 
Both these courses are so advanced that it is 
not easy to do them justice in a review: but from 
what has been said some idea may be gained of 
their general scope. Lectures of this kind are 
very valuable because they focus, so to speak, 
various lines of research upon a limited subject, 
and give an account of the really important results 
obtained. G.AB we 
NATIONAL MUSEUMS AND SYSTEMATIC 
BIOLOGY. 
(1) Manual of the New Zealand Mollusca. With 
an Atlas.of Quarto Plates. By H. Sutersaee: 
xxli+1120. (Wellington, N.Z.; J. Mackay, 
1913.) 
(2) Catalogue of the Ungulate Mammals in the 
British Museum (Natural History). Vol. i1., 
Artiodactyla, Family Bovide, Subfamilies 
Bubalinee to Reduncine (Hartebeests, Gnus, 
Duikers, Dik-Diks, Klipspringers, Reedbucks, 
Waterbucks, etc.). By R. Lydekker, assisted by 
G. Blaine. Pp. xvi+295. (London: British 
[Jury 23, 1914 
ted 
