le 
‘Aug. 7,1873| 
NATURE 
279 
tails regarding his works. Heis gone; but his work lives 
after him. 
The two Roses were men of a distinguished presence. 
Heinrich was the taller, but each was a man of spare and 
somewhat stately figure, with an eye of peculiar force and 
truthfulness of glance; an eye that spoke out the 
character of the man, that beamed with kindliness and 
was ever staunch to truth, N. S. M. 
CHALLIS’S “MATHEMATICAL PRINCIPLES 
OF PHYSICS” 
An Essay on the Mathematical Principles of Physics, &c. 
By the Rev. James Challis, M.A., F.R.S., F.R.A.S., 
Plumian Professor of Astronomy and Experimental 
Philosophy in the University of Cambridge, and Fellow 
of Trinity College. (Cambridge: Deighton, Bell, and 
Co., 1873.) 
HIS essay is a sort of abstract or general account 
of the mathematical and physical researches on 
_ which the author has been so long engaged, portions of 
which have appeared from time to time in the Phzlo- 
sophical Magazine, and also in his larger work on the 
“Principles of Mathematics and Physics.” It is always 
desirable that mathematical results should be expressed in 
intelligible language, as well as in the symbolic form in 
which they were at first obtained, and we have to thank 
Professor Challis for this essay, which though, or rather 
because, it hardly contains a single equation, sets forth 
his system more clearly than has been done in some of his 
previous mathematical papers. 
The aim of this essay, and of the author’s long-con- 
tinued labours, is to advance the theoretical study of 
Physics. He regards the material universe as “a vast 
and wonderful mechanism, of which not the least 
wonderful quality is, its being so constructed that 
we can understand it.” The Book of Nature, in 
fact, contains elementary chapters, and, to those who 
know where to look for them, the mastery of one 
chapter is a preparation for the study of the next. 
The discovery of the calculation necessary to deter- 
mine the acceleration of a particle whose position is 
given in terms of the time led to the Newtonian epoch of 
Natural Philosophy. The study from the cultivation of 
which our author looks for the ‘inauguration of a new 
Scientific epoch,” is that of the motion of fluids, commonly 
called Hydrodynamics. The scientific method which he 
recommends is that described by Newton as the “ foun- 
dation of all philosophy,” namely, that the properties which 
we attribute to the least parts of matter must be con- 
sistent with those of which experiments on sensible bodies 
have made us cognizant. 
The world, according to Professor Challis, is made up 
of atoms and wether. The atoms are spheres, unalterable 
in magnitude, and endowed with inertia, but with no other 
property whatever. The ether is a perfect fluid, endowed 
with inertia, and exerting a pressure proportional to its 
density. It is truly continuous (and therefore does not 
consist of atoms), and it fills up all the interstices of the 
atoms.] 
Here, then, we have set before us with perfect clearness 
the two constituents of the universe : the atoms, which 
“we can picture in our minds as'so many marbles ; and the 
ether, which behaves exactly as air would do if Boyle’s 
law were strictly accurate, if its temperature were invari- 
able, if it were destitute of viscosity, and if gravity did not 
act on it. 
We have no difficulty, therefore, in forming an adequate 
conception of the properties of the elements from which 
we have to construct a world. The hypothesis is at least 
an honest one. It attributes to the elements of things no 
properties except those which we can clearly define, It 
stands, therefore, on a different scientific level from those 
waxen hypotheses in which the atoms are endowed with a 
new system of attractive or repulsive forces whenever a 
new phenomenon has to be explained. 
But the task still before us is a herculean one, It ig 
no less than to explain all actions between bodies or parts 
of bodies, whether in apparent contact or at stellar dis- 
tances, by the motions of this all-embracing ether, and 
the pressure thence resulting, 
One kind of motion of the zther is evidently a wave- 
motion, like that of sound-waves in air. How will such 
waves affect an atom? Will they propel it forward like. 
the driftwood which is flung upon the shore, or will they 
draw it back like the shingle which is carried out by the 
returning wave? Or will they make it oscillate about a 
fixed position without any advance or recession on the 
whole ? 
We have no intention of going through the calculations 
necessary to solve this problem. They are not contained 
in this essay, and Professor Challis admits that he has 
been unable to determine the absolute amount of the 
constant term which indicates the permanent effect of the 
Waves on an atom. This is unfortunate, as it gives us no 
immediate prospect of making those numerical com- 
parisons with observed facts which are necessary for the 
verification of the theory. Let us, however, suppose this 
purely mathematical difficulty surmounted, and let us 
admit with Professor Challis that if the wave-length of 
the undulations is very small compared with the diameter 
of the atom, the atom will be urged in the direction of 
Wwave-propagation, or in other words repelled from the 
origin of the waves. If on the other hand the wave- 
length is very great compared with the diameter of the 
atom, the atom will be urged in the direction opposite to 
that in which the waves travel, that is, it will be aétracted 
towards the source of the waves. 
The amount of this attraction or repulsion will depend 
on the mean of the square of the velocity of the periodic 
motion of the particles of the zther, and since the ampli- 
tude of a diverging wave is inversely as the distance from 
the centre of divergence, the force will be inversely as the 
square of this distance, according to Newton’s law, 
We must remember, however, that the problem is only 
imperfectly solved, as we do not know the absolute value 
of this force, and we have not yet arrived at an explana- 
tion of the fact that the attraction of gravitation: is in 
exact proportion to the mass of the attracted body, what- 
ever be its chemical nature. (See p. 36.) 
Admitting these results, and supposing the great ocean 
of zther to be traversed by waves, these waves impinge 
on the atoms, and are reflected in the form of diverging 
waves, These, in their turn, beat other atoms, and 
cause attraction or repulsion, according as their wave- 
length is great or small, Thus the waves of shortest 
