On Material Molecules and the Etherial Medimn. 257 
ether when in equilibrium ; u v iv, iv^, 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 ; u v iv its displacements parallel to 
the axes at time t when in motion. 
Let iTy represent the resolved parts parallel to the 
axes of the resultant action of the material molecules on the 
particle of ether at ^ s. 
Let be the resolved parts parallel to the axes of 
the action of the etherial medium on the particle of ether 
dii X y z. 
Then, when the ether is in equilibrium, 
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 ^ s is at 
time t at the point x '\- y + v, 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 
'Tjc 2ii xy z become ir^ + ^^r^. Let 'ffj denote the resultant 
action parallel to the axis of x, which the material molecules 
in their position of equilibrium exert x + u, y -\- v, 
z + w. 
Then, since depends only on. x y z, 
d'X^c dftx dnj: 
|. + + + (1) 
neglecting terms of the second order in u v w. Hence the 
resultant action on the particle of ether at + y -f v, 
z + w, when the material molecules are in motion 
= dx ^ + Wy ^+ dz ^ 
substituting itx + forVa: in (1.) 
