258 Proceedings of the Royal Physical Society. 



Now 



d(hv x ) d(bx x ) d(d* z ) 



-~j — u + — f— v + \ iv — 

 ax ay az 



and therefore the expression on the left hand side is of the 

 second order in u v w, and may therefore be neglected. 



Hence the resultant action at x + u, y + v, z + w, parallel 

 to the axis of x, due to the material molecules in motion, 



dfcr x dic x 



= ** + -di u+ ~dy v + S W + ■ ■ • (2) 



and 



(dic x , dit x , d* r . 1 

 m % + w v + m w | ( 3 ) 



Similar expressions may be found for the resultant actions 

 parallel to the axes of y and z. 



The action on the particle of ether at x + u, y + v, z + w, 

 parallel to the axis of x, due to the etherial medium when 

 in motion, may, by analogy from (2.), be expressed in the 

 form 



d<p x d<p x d<p x 

 + -dx U + lTy V + dz W + to % 



and 



_(d<p x d<p x d<p x 1 

 = 2 {^ + df^ + dz\ w * ] < 5) 



Hence, adding (2.) and (4.), and recollecting that <ie x + <p x = 0 

 we have for the motion of the ether the equations 



d 2 u d<p x d<p x d<p x 

 aW=dx u+ dy v+ dz- w + d ^ 



d* x cU x dv x 

 + te u + -dy v + ~dz W + *** ■ ■ ' ^ 



d 2 v . . ■ "i- . ' . 



^2 = similar expression, involving ie y and <p y 



^pr = similar expression, involving ic z and <p. 



