﻿812 On the Propagation of Periodic JEtlier Disturbance. 



so that the whole system is equivalent to the three forced 

 oscillations 



I2al' 2 + mtal'm' + ntan'V, llaVm' -f mlam' 2 + nt 



am n. 



IZan'l' + mXam'n' + nXan 2 . 



The effect of the resonators is therefore equivalent to changes 

 in the density of the aether along the axes for which 



%aVm\ Sam'n', and Xan'V 

 are zero. 



The irrotational wave has the same velocity along the 

 three axes. The equations of motion are therefore 



-^ + (v-^)|(24;+f>- 



Hence for the train 



ft V-> %—Pi 9) r cos fc{lx-\-my + nz—ct), 

 I 2 m 2 n 2 __ n 



(vi.) 

 (vii.) 



(viii.) 



and the displacement is in the direction 



'Y2_ v 2 y2_ v 2 Y 2 — - 2 



/V J — v/ vz — V V V \ 



\c 2 -^ ' ^^7 m ' c*-vj* n )' 



and therefore lies in the plane 



# 



y 



z 



/ 



m 



n 



I 



m 



n 



• 2 — .< 



,2_„ 2 



,2__„ 2 



= 0. 



It is noteworthy that the plane of polarization and the 

 velocity are independent of the velocity of the irrotational 

 wave, although the motion involves change of volume. 



4. It is now possible to determine the circumstances of 



