On Material Molecules and the Etlterial Medium. 257 



ether when in equilibrium; u v to, u x v l w v their displace- 

 ments parallel to the co-ordinate axes at time t when in 

 motion. 



Let x' y' z be the co-ordinates of a particle of matter 

 when in equilibrium ; v! v w its displacements parallel to 

 the axes at time t when in motion. 



Let ic x %j ie z represent the resolved parts parallel to the 

 axes of the resultant action of the material molecules on the 

 particle of ether at x y z. 



Let <p x <p y <p z be the resolved parts parallel to the axes of 

 the action of the etherial medium on the particle of ether 

 at x y z . 



Then, when the ether is in equilibrium, 



*x + 9x = 0 *y + 9<j = 0 «i + 9z = 0 



Suppose now the ether and the material molecules to be set 

 in motion, so that the motion of both is indefinitely small ; 

 then the particle of ether which was originally at x y z is at 

 time t at the point x -f u, y + % z + iv. 



We have now, therefore, to express the resultant actions 

 on this particle in the position which it occupies at time t. 

 In consequence of the motion of the material molecules let 

 <r x at xyz become r x + 8vr x . Let a-/ denote the resultant 

 action parallel to the axis of x, which the material molecules 

 in their position of equilibrium exert at x + u, y + v, 

 z + w. 



Then, since ic x depends only on xyz, 



dv x dvx die x 



= + + dy v + 3T W (1) 



neglecting terms of the second order in u v w. Hence (he 

 resultant action on the particle of ether at x + u, y + i\ 

 z + to, when the material molecules are in motion 



d(nr r + &*r x ) d(<ie x + d-r,) d(x x + d*,-) 

 = *» + «»' + J^- % + ' du v + dz • 



substituting <*x + &ir r for'<r x ^ (1.) 



