280 
NATURE 
[Aug. 7, 1873 
period perform the office of repelling atom from atom, 
and rendering their collision for ever impossible, Other 
waves, somewhat longer, bind the atoms together in mole- 
cular groups. Others contribute to the elasticity of 
bodies of sensible size, while the long waves are the cause 
of universal gravitation, holding the planets in their 
courses, and preserving the most ancient heavens in all 
their freshness and strength. Then besides the waves of 
aether, our author contemplates its streams, spiral and 
otherwise, by which he accounts for electric, magnetic, 
and galvanic phenomena. 
Without pretending to have verified all or any of the 
calculations on which this theory is based, or to have 
compared the electric, magnetic, and galvanic phenomena, 
as described in the Essay, with those actually observed, 
we may venture to make a few remarks upon the theory 
of action at a distance here put forth. 
The explanation of any action between distant bodies 
by means of a clearly conceivable process going on in 
the intervening medium is an achievement of the highest 
scientific value. Of all such actions, that of gravitation 
is the most universal and the most mysterious. What- 
ever theory of the constitution of bodies holds out a 
prospect of the ultimate explanation of the process by 
which gravitation is effected, men of science will be found 
ready to devote the whole remainder of their lives to the 
development of that theory. 
The only theory hitherto put forth as a dynamical 
theory of gravitation is that of Lesage, who adopts the 
Lucretian theory of atoms and void. 
Gravitation on this theory is accounted for by the 
impact of atoms of incalculable minuteness, which are 
flying through the heavens with inconceivable velocity 
and in every possible direction, These “ultramundane 
corpuscules ” falling on a solitary heavenly body would 
strike it on every side with equal impetus, and would 
have no effect upon it in the way of resultant force. If, 
however, another heavenly body were in existence, each 
would screen the other from a portion of the corpuscular 
bombardment, and the two bodies would be attracted to 
each other. The merits and the defects of this theory 
have been recently pointed out by Sir W. Thomson. If 
the corpuscules are perfectly elastic one body cannot 
protect the other from the storm, for it will reflect exactly 
as many corpuscules as it intercepts. If they are in- 
elastic, as Lesage supposes, what becomes of them after 
collision? Why are not bodies always growing by the 
perpetual accumulation of them? How do they get 
swept away ? and what becomes of their energy? Why 
do they not volatilise the earth in a few minutes? I shall 
not enter on Sir W. Thomson’s improvement of this 
theory, as it involves a different kind of hydro-dynamics 
from that cultivated in the Essay, but in whatever way 
we regard Lesage’s theory, the cause of gravitation in the 
universe can be represented only as depending on an 
ever fresh supply of something from without. 
Though Prof. Challis has not, as far as we can see, 
stated in what manner his ethereal waves are originally 
produced, it would seem that on his theory also the 
primary waves, by whose action the waves diverging from 
the atoms are generated, must themselves be propagated 
from somewhere owéséde the world of stars. 
On either theory, therefore, the universe is not even 
temporarily automatic, but must be fed from moment to 
moment by an agency external to itself. 
If the corpuscules of the one theory, or the zthereal 
waves of the other, were from any cause to be supplied at 
a different rate, the value of every force in the universe 
would suffer change. * 
On both theories, too, the preservation of the universe 
is effected only by the unceasing expenditure of enor- 
mous quantities of work, so that the conservation of 
energy in physical operations, which has been the subject 
of so many measurements, and the study of which has 
led to so many discoveries, is apparent only, and is merely 
akind of “moveable equilibrium” between supply and 
destruction. 
It may seem.a sort of anticlimax to descend from these 
highest heavens of invention down to the “equations of 
condition” of fluid motion. But it would not be right to 
pass by the fact that the fluids treated of in this Essay are 
not in all respects similar to those met with elsewhere. 
In all their motions they obey a law, which our author 
was the first to lay down, in addition—or perhaps in some 
cases in opposition—to those prescribed for them by 
Lagrange, Poisson, &c, 
It is true that a perfect fluid, originally at rest, and 
afterwards acted on only by such forces as occur in 
nature, will freely obey this law, and that not only in the 
form laid down by Prof. Challis, in which its rigour 
is partially relaxed by the introduction of an arbitrary 
factor, but in its original severe simplicity, as the con- 
dition of the existence of a velocity-potential. 
But, on the one hand, problems in which the motion is 
assumed to violate this condition have been solved by 
Helmholtz and Sir W. Thomson, who tell us what the 
fluid will then do; and, on the other hand, Professor 
Challis’s fluid is able, in virtue of the new equation, to 
transmit plane waves consisting of transverse displace- 
ments. As this is what takes place in the luminiferous 
zether, other physicists refuse to regard that zether as a 
fluid, because, according to their definition, the action 
between any contiguous portions of a fluid is entirely 
normal to the surface which separates them. 
It is not necessary, however, for us to say any more on 
this subject, as the Essay before us does not contain, in 
an explicit form, the equation referred to, but is devoted 
rather to the exposition of those wider theories of the 
constitution of matter and the phenomena of nature, — 
some of which we have endeavoured to describe. 
HENSLEV’S “SCHOLAR’S ARITHMETIC” 
The Scholar’s Arithmetic. By Lewis Hensley, M.A. 
(Clarendon Press Series, 1873.) 
ae is scarcely any subject more carelessly taught 
= than arithmetic ; and, if one would wish to ascer- 
tain the reason of this, he has merely to glance at the 
text-books which have been hitherto most commonly em- 
ployed. Lately, however, several books of some worth 
have been presented to the public, and for these we are 
indebted in a great measure to the late Prof. De Morgan, 
whose “ Elements of Arithmetic,” published so far back 
as 1830, is still regarded as the very best handbook for 
advanced students. It has, nevertheless, some pecu- — 
liarities—we cannot call them defects—which have pre~ — 
