JuLy 31, 1902] 
1827, and is still regarded as the most finished and use- 
ful introduction to the study of infinitesimal geometry. 
The translation is based on a copy of the original paper, 
but in the work of preparing it and the present notes all 
the other editions were consulted. This is followed by 
a translation of the abstract presented by Gauss to the 
Royal Society of Géttingen. Under the title of “ Vew 
General Investigations of Curved Surfaces,” the trans- 
lators next give a paper really written by Gauss at an 
earlier date (1825), but which was not published until the 
eighth volume of Gauss’s works appeared in 1900. Both 
papers contain the fundamental properties of what is 
now known as Gauss’s measure of curvature, the theorem 
that the spherical excess of a geodesic polygon is pro- 
portional to the corresponding area on the auxiliary | 
sphere, and the proof that the locus of points the geodesic 
distances of which from a fixed point are equal cuts 
these geodesics orthogonally. The paper of 1825, how- 
ever, contains introductory matter on curvature in a 
plane which was omitted by Gauss from his 1827 paper, 
and while, in 1825, Gauss used geodesic polar coordinates 
only, in 1827 he introduced the notion of generalised co- 
ordinates # and g. It will thus be seen that the order 
in which the papers have been printed is the reverse of 
chronological order. 
A large number of notes have been inserted by the 
translators, those on the 1827 paper occupying twenty- 
eight pages. Many of these notes contain proofs of results 
merely stated by Gauss ; others consist of explanatory 
matter, restatements of Gauss’s conclusions, or simple 
corollaries. The “bibliography” contains a list of 343 
papers dealing chiefly with the following subjects :— 
Curvilinear coordinates, geodesic and isometric lines, 
curvature of surfaces, deformation of surfaces, ortho- 
gonal systems and the general theory of surfaces. A 
large proportion of the papers listed are of comparatively 
recent date, thus affording a guide to the literature 
about curved surfaces which has grown up in the develop- 
ment of methods first laid down by Gauss. 
The Elements of Mind. By H. J. Brooks. 
312. (London: Longmans, Green and Co., 
Price tos. 6d. net. 
THE author claims to have made the correlation of 
chemistry physiology and psychology possible by the 
discovery of the “simple elementary substances of mind” 
which, according to him, “ when compounded with those 
of force and matter, constitute the mysterious substance 
we call life.” It is not easy to gather his exact meaning, 
as his definitions of his fundamental terms are partly 
defective, partly circular. Matter and force he leaves 
undefined ; of life he simply says that he “uses it in its 
ordinary sense.” Mind—when not further defined by a 
restricting adjective—is “‘ everything that is not matter,” 
a definition which would include, ¢.g., space, time and the 
series of natural logarithms. As an instance of a defini- 
tion which is circular as well as obscure, “ By Ego I mean 
that whichis known as the personality of the brain... . 
Personality I employ in the ordinary sense of a person’s 
physical and mental characteristics.” Substance, again, 
should have been defined with special accuracy by a 
writer who attaches so much importance to his professed 
discovery of the “elementary substances” of mind. Yet 
all that Mr. Brooks has to say of it is that “ substance is 
philosophically described as that which exists and re- 
mains.” Now space and time may be said to “exist and 
remain” ; are they substances or are they not? Mr. 
Brooks, of course, knows whether he means to say that 
they are, but a reader is nonplussed. And finally, what 
exactly does Mr. Brooks mean by an “element”? By 
“elements of matter,” as his examples show, he means 
chemically undecomposable constituent parts ; but what 
exactly are meant by the “elements” of force, which 
“scientists with somewhat less success have de- 
NO. 1709, VOL. 66 | 
Pp. xvili+ 
1902.) 
NATURE 
| made. 
4 
317 
scribed”? So far as the absence of precise definition 
perinits us to form a judgment, Mr. Brooks’s doctrine 
seems to agree with the “ mind-stuff” theory of W. K. 
Clifford. He quotes Prof. James’s trenchant refutation 
of this theory of the composition of a unitary conscious- 
ness out of atomic constituents and attempts to turn its 
edge. He does not, however, seem to realise its full 
force. The case of “light” is no exception to Jameys’s 
contention that “all the combinations which we know 
are effects wrought by the units said to be combined” 
upon something other than themselves. Still less is the 
relation between an organism and its members the same 
as that between an aggregate and its parts. I confess 
that I have been unable to discover in Mr. Brooks’s 
book any one consistent theory of the relation between 
his elements and the single whole which he calls the 
“greater Ego.” Sometimes this whole is spoken of as 
controlling, dominating and using the elements, some- 
times as built up by their mechanical interaction. So 
with his general metaphysical theory. He appears 
sometimes to hold that “ mind,” “force” and “ matter” 
are things which can compound quasi-chemically, some- 
times that they are different “aspects” of a single 
reality. Where I do understand him, he appears to 
be expounding in novel language a psychology of the 
extreme associationist type, though not without moments 
of deeper insight in which he seems to uphold the 
ultimate identity of mind and body. IN Db 
A Graduated Collection of Problems in Electricity. By 
Prof. Robert Weber, D.Sc. Translated from the third 
French edition by E. A. O’Keeffe, B.E., M.I.E.E. Pp. 
xv+ 351. (London: E. and F. N. Spon, Ltd.; New 
York: Spon and Chamberlain, 1902.) Price 7s. 6d. 
net. 
THIS book is intended to be a help to the teacher of 
physics, and consists of a collection of problems of vary- 
ing difficulty in almost all the branches of electrical 
work. The third edition differs chiefly from the previous 
ones in the inclusion of some fresh problems and in the 
careful revision and correction of errors which has been 
The author has adopted the plan of giving the 
solution immediately after each problem, and though 
objections may be urged against this method, we think 
on the whole it is the most satisfactory for a book of this 
kind. Those interested in electricity from its practical 
side will regret that most of the problems are of an 
academic character. Thus, to quote one example, the 
section on glow lamps gives the impression that lamps are 
usually made for 40 or 50 volts and that lighting is 
carried out by means of primary batteries. Occasionally 
one comes across a problem in which the data are 
not sufficient in reality. Apart from a few minor 
defects of this sort, the book is a very useful one, as the 
questions are well calculated to show whether or not the 
student has really grasped the meaning of the work he 
is doing, which should be the principal aim of a teacher. 
The addition of a short section on units and a number 
of tables enhances the value of the work. M. S. 
Junior Chemistry and Physics. By W. Jerome Harrison. 
Pp. vi + 224. (London: Blackie and Son, Ltd, 1902.) 
Price 1s. 6d. 
SoME of the fundamental principles of physics and 
chemistry are simply described in this book. Common 
objects are used as subjects of observation and experi- 
ment, and an attempt is made to show the scientific 
aspects of familiar things. The first few pages seem out 
of place in a book of this character. Pupils beginning 
the study of science ought not to be troubled with such 
statements as “The universe is composed of matter, 
“We have given the name of e¢/ey to an extremely rare 
kind of matter,” “ Matter has extension,” “ Matter is in- 
destructible,” &c. These subjects belong to the later 
| stages of natural philosophy. 
