196 Lord Kelvin on the Motion of Ponderable Matter 



the same bulk as the atom, and the same density as the un- 

 disturbed density of the ether. Thus if the ntom, which we 

 are supposing to be a constituent of real ponderable matter, 

 has an inertia of its own equal to I per unit of its volume, 

 the effective inertia of its motion through space occupied by 



ether will be ^- s 3 (I-f "634) ; the diameter of the atom being 



now denoted by s (instead of 2 as hitherto), and the inertia 

 of unit bulk of the ether being still (as hitherto) taken as 

 unit of inertia. In all that follows we shall suppose I to be 

 very great, much greater than 10 6 ; perhaps greater than 10 12 . 

 § 15. Consider now, as in § 11 above, our atom at rest ; 

 and the ether moving uniformly in the space around the 

 atom, and through the space occupied b} r the atom, according 

 to the curved stream-lines and the varying velocities shown 

 in fig. 5. The effective inertia of any portion of the ether 

 containing the atom will be greater than the simple inertia of 



IT 



an equal volume of the ether by the amount ^- s a '634. This 



follows from the well-known dynamical theorem that the 

 total kinetic energy of any moving body or system of bodies 

 is equal to the kinetic energy due to the motion of its centre 

 of inertia, plus the sum of the kinetic energies of the motions 

 of all its parts relative to the centre of inertia. 



§ 16. Suppose now a transparent body — solid, liquid, or 

 gaseous — to consist of an assemblage of atoms all of the same 

 magnitude and quality as our ideal atom defined in § 2, and 

 with I enormously great as described in § 14. The atoms 

 may be all motionless as in an absolutely cold solid , or 

 they may have the thermal motions of the molecules of a 

 solid, liquid, or gas at any temperature not so high but that 

 the thermal velocities are everywhere small in comparison 

 with the velocity of light. The effective inertia of the ether 

 per unit volume of the assemblage will be exceedingly nearly 

 the same as if the atoms were all absolutely fixed, and will 

 therefore, by § 15, be equal to 



l + N^ 3 -634 (15), 



where N denotes the number of atoms per cubic centimetre 

 of the assemblage, one centimetre being now our unit of 

 length. Hence, if we denote by V the velocity of light in 

 undisturbed ether, its velocity through the space occupied by 

 the supposed assemblage of atoms will be 



1+N|j>-634Y (16). 



v/( 



