440 Lord Kelvin on Electro-ethereal Theory of the 



that is to say devoid of intrinsic inertia, and to possess virtual 

 inertia only on account of the kinetic energy which accom- 

 panies its steady motion through still ether. This is in 

 reality an energy of relative motion ; and does not exist when 

 electrion and ether are moving at the same speed. See 

 App. A passinij and equation (202) below. 



§ 240. Come now to the wave-velocity problem and begin 

 with the simplest possible case, — only one electrion in each 

 atom. Consider waves of <r-vibration travelling y-wards 

 according to the formula (203) below. Take a sample atom 

 in the wave-plane at distance y from XOZ. The atom is 

 practically unmoved by the ether-waves ; while the electrion 

 is set a vibrating to and fro through its centre. 



At time t, let x be the displacement of the electrion, from 

 the centre of the atom (or its absolute displacement because 

 at present we assume the atom to be absolutely fixed) : 



f the displacement of the ether around the atom) : 



p the mean density of the ether within and around the 

 atom, being, according to our assumjDtions, exactly the same 

 as the normal density of undisturbed ether : 



n the rigidity of the ether within and around the atoms, 

 being, according to our assumption, very approximately the 

 same at every point as the rigidity of undisturbed ether : 



N the number of atoms per unit of volume : 



ex the electric attraction towards the centre of its atom, 

 experienced by the electrion in virtue of its displacement, x : 



m the virtual mass of an electrion : 



E a volume ^, of ether, having the centre of one, and only 



one, atom within it. 



The equation of motion of E, multiplied by X, is 



^^=^V~ ^^' ^^^' 



and the equation of motion of the electrion within it, is 



m'^^^^^^ =-cx (202). 



§ 241. The solution of these two equations for the regular 

 regime of wave-motion is of the form 



^=C sin CO (t-^); a^ = d^in co ft -^ . . (203), 



where <^ is given. Our present object is to find the 



