188 Lord Kelvin on the Motion of Ponderable Matter 



have been actually found by aid of a curve drawn from the 

 numbers of col. 3 Table I., showing r in terms of r 1 . The 

 numbers in col. 2 of Table II. showing, for chosen values 

 of r, the corresponding values of /, have been taken from 

 the curve; and we may verify that they are approximately 

 equal to the roots of the equation shown at the head of 

 col. 2 of Table L, regarded as a cubic for r' with any given 

 values of r and K. 



Thus, for example, taking ?-'= , 929 we calculate r='811, 

 „ / = -816 „ r = -498, 



„ r' = -677 „ r=-301, 



„ r' = -091 „ ?'=-0208, 



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 — l)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 (jo — 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 in- 

 finitely 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; and 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 



* 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., Mav, August, 

 ani October, 1899. 



