1899-1900.] Lord Kelvin on the Motion in an Elastic Solid. 225 
Thus, for example, taking r — ‘929 we calculate r=*811, 
where we should have r—' 8 , '5, ’3, and *02 respectively. These 
approximations are good enough for our present purpose. 
§ 8. The diagram of fig. 2 is interesting, as showing how, 
with densities of ether varying through the wide range of from 
•35 to 101, the whole mass within the atom is distributed among 
the concentric spherical surfaces of equal density. We see by it, 
interpreted in conjunction with col. 4 of the tables, that from the 
centre to *56 of the radius the density falls from 101 to 1. For 
radii from ‘56 to 1, the values of (p — 1 )r 2 decrease to a negative 
minimum of - 525 at r=' 93, and rise to zero at r=l. The place 
of minimum density is of course inside the radius at which 
(p - l)r 2 is a minimum; by cols. 4 and 3 of Table I., and cols. 4 
and 1 of Table II., we see that the minimum density is about '35, 
and at distance approximately ’87 from the centre. 
§ 9. Let us suppose now our atom to be set in motion through 
space occupied by ether, and kept in motion with a uniform 
velocity v, which we shall first suppose to be infinitely small in 
comparison with the propagational velocity of equivoluminal* 
waves through pure ether undisturbed by any other substance 
than that of the atom. The velocity of the earth in its orbit 
round the sun being about 1/10,000 of the velocity of light, is 
small enough to give results, kinematic and dynamic, in respect 
to the relative motion of ether and the atoms constituting the 
earth closely in agreement with this supposition. According to it, 
the position of every particle of the ether at any instant is the 
same as if the atom were at rest ; aud to find the motion 
produced in the ether by the motion of the atom, we have a 
purely kinematic problem of which an easy graphic solution is 
found by marking on a diagram the successive positions thus 
determined for any particle of the ether, according to the positions 
* That is to say, waves of transverse vibration, being the only kind of 
wave in an isotropic solid in which every part of the solid keeps its volume 
unchanged during the motion. See Phil. Mag., May, August, and October 
1899. 
YOL. XXIII. 7/3/01. P 
jj 
$|= •498, 
t — *30 1, 
r = *0208, 
