1901-2.] Mr J. Fraser on Constitution of Matter and Ether. 29 
assumed to be perfectly elastic. ‘ We are forbidden,’ says Sir 
William Thomson, 1 by the modern theory of the conservation of 
energy to assume inelasticity or anything short of perfect elasticity 
of the ultimate molecules, whether of ultra-mundane or mundane 
matter. . . Secchi clearly apprehends the inadmissibility of 
attributing elasticity to simple elementary atoms. c It is evident,’ 
he says, ‘that while it is possible to admit its existence in 
a compound molecule, the same thing cannot be done in the 
case of elementary atoms. Indeed, elasticity in the received sense 
presupposes void spaces in the interior of the molecule, whose form 
is changed by compression so as to return afterward to its original 
figure. Now, we regard the atoms as impenetrable, and not as 
groups of solid particles; hence they cannot include void spaces 
which permit their dilatation and contraction.’ ... The difficulty, 
then, appears to be inherent and insoluble. There is no method 
known to physical science which enables it to renounce the assump- 
tion of the perfect elasticity of the particles whereof ponderable 
bodies and their hypothetical imponderable envelopes are said to 
be composed, however clearly this assumption conflicts with one 
of the essential requirements of the mechanical theory.” 
[It is easy, however, to see that the assumption of perfect 
hardness and perfect rigidity in the ultimate particles of the ether 
may be regarded as identical with perfect elasticity, if that be 
understood in the sense that what Thomson and Tait* call the 
‘ coefficient of restitution ’ is unity for the ether-atoms. To simplify 
matters, consider two perfectly hard, perfectly rigid spherical atoms 
of equal mass ; and let their velocities before and after a direct 
impact be a b and u v respectively. Since no part of the kinetic 
energy due to their motions of translation can be converted into 
internal motion, or otherwise lost, we must have 
u 2 + v 2 — a 2 + b 2 (1). 
Also the third law of motion requires that the sum of their 
momenta shall be the same before and after impact. Hence we 
must have 
u + v = a + b (2). 
* See Treatise on Natural Philosophy by Thomson and Tait (new ed.), vol. i. 
part i. §§ 300-306. 
