204 
NATURE 
[APRIL 11, 1907 
also been quite misunderstood. As usual, the author 
is ready with his blame, and wonders that Lionardo 
da Vinci did not stand up for Copernicus. But as 
he died twenty-four years before the book of 
Copernicus came out, he may be held excused. The 
same is the case with Kepler, who could not very 
well make use of Galileo’s little book on mechanics 
written in 1594, since it was not printed until four 
years after Kepler’s death. Of Galileo we learn 
that he showed that the speed of a falling body in- 
creases with the square of the time (p. 256). Had he 
really done so he would have deserved to be enrolled 
among the delinquents castigated by the author. So 
would Newton, if he really had proved that the mass 
of a body may be calculated if we know the period 
and distance from the central body, or that gravity 
is less at the poles than at the equator (p. 261). 
The author has succeeded better in the last hundred 
pages, which deal with stellar astronomy, the last 
chapter discussing the question of the probable * end 
of the machine.’? His own opinion is that all bodies 
will finally be congregated into a single mass, but 
he also sets forth the view of Arrhenius, that the 
matter of the universe follows a continual round of 
alternating aggression and dispersion. 
Je LED: 
THE MATHEMATICAL ASPECT OF 
SPECTROSCOPY. 
Vorlesungen iiber teoretische Spektroskopie. By 
Prof. A. Garbasso. Pp. viii+256; illustrated. 
(Leipzig: Johann Ambrosius Barth, 1906.) Price 
7 marks. 
N the printed report of the lecture delivered before 
the Royal Institution on March 30, 1906, on 
“ Recent Progress in Magneto-optics,’’ Prof. Zeeman 
concludes with the following remarks :— 
“Maxwell has said, ‘an intelligent student armed 
with the calculus and the spectroscope can hardly 
fail to discover some important fact about the interior 
structure of a molecule.’ I think this statement re- 
mains as true now as it was thirty-two years ago. 
“There can be no doubt, I think, that spectrum 
analysis, and especially the magnetisation of the 
spectral lines, will give us a clue to the inner struc- 
ture of the atom. Fae : 
‘“T hope that I have succeeded in imparting to 
you this my conviction.” 
Now Prof. Garbasso’s book seems to us exactly 
to cover the ground contemplated by Prof. Zeeman 
when he wrote these concluding remarks. It is, in 
fact, a well-planned attempt to build up an electro- 
dynamical theory of the phenomena of spectroscopy, 
using no more difficult mathematics than the ordinary 
calculus of mathematical physics. 
In spite of the fact that the word “ electro- 
dynamical ’’ has gone out of fashion, and that it is 
more proper nowadays to say “‘ electromagnetic,”’ the 
old word is here retained as representing more 
correctly the spirit of the present book. If the equa- 
tions of the electromagnetic field are written down 
NO. 1954, VOL. 75| 
and the quantities in them are defined in the phrase- 
ology of the physicist, the study of these equations 
is rightly described as electromagnetism. By repre- 
senting the quantities in question as generalised 
position coordinates and the corresponding generalised 
momenta in Lagrange’s equations, the study is 
brought under the heading of dynamics. Inasmuch, 
however, as there is no hard and fast line of de- 
marcation between the two methods, and it is a matter 
of convenience which interpretation is used, the name 
“* electrodynamical ”? well describes the methods of a 
book in which both aspects are considered. 
The book is divided into twenty lectures, and is 
based on a course delivered at the University of 
Genoa. Of these, the first four form the first sec- 
tion of the book, and consist chiefly of introductory 
matter, namely, a summary of the principal pheno- 
mena of spectroscopy, a description of certain electro- 
magnetic and electro-optical models and their appli- 
cation to the explanation of optical resonance, and 
a mathematical lecture dealing with the well-known 
theory of small oscillations, transformations of line, 
volume and surface integrals, and similar ‘‘ auxiliary 
propositions. ”’ 
The second section deals with Cauchy’s theory of 
dispersion, Helmholtz’s theory of anomalous dis- 
persion, and a lecture on mechanical models of com- 
pound molecules, based on work by Dr. Filippini, of 
Genoa, who uses various forms of compound pendu- 
lums for the purpose of representing the various 
degrees of freedom of the assumed molecules. 
The subject proper of the book, namely, the build- 
ing up of mathematico-physical theories, commences 
with the eighth lecture, and occupies the two re- 
maining sections of the book. These two sections 
afford typical instances of what has been, and is likely 
to be, the most interesting and prolific field of re- 
search in dealing with complex physical phenomena. 
To ‘‘explain’’ such a phenomenon we formulate 
some system, dynamical or otherwise, the equations — 
of motion of which are capable of being integrated, 
and the integrals of which when interpreted represent 
effects similar to those observed. The assumed 
system then constitutes a model of the given pheno- 
menon. Dr. Garbasso has endeavoured to confine 
his treatise to the discussion of phenomena that are 
capable of being studied by means of models, adding 
that 
““A theoretical exposition which does not take 
account of the properties or of the possibility of its 
model is for physicists no theory but only a chaos 
(ein Unding ’).” 
The models made use of in the third section are all 
electrical oscillators, each represented diagrammatically 
by two or more conducting spheres connected by 
wires. For one-dimensional oscillations, simple 
oscillators each represented by two spheres are 
chosen; for three dimensions the author mainly 
employs compound oscillators having their conductors 
parallel to the three coordinate axes. These are, of 
course, simplifying hypotheses; but, as the author 
points out, for example on pp. 124, 149, the character- 
