202 The Rev. M. O'Brien on the Projiagation 



of linear differential equations with constant coefficients, we 

 shall have linear differential equations with variable coeffi- 

 cients, of which we do not even know the law of variation. 

 Thus it appears almost hopeless to attempt making any use 

 of the general equations of motion as applied to determine 

 the circumstances of propagation of luminous waves hi the in- 

 terior of transparent bodies, supposing each material particle 

 surrounded by many particles of aether. 



But if vve adopt a different hypothesis and suppose that 

 there are not so many, or at most as many, particles of aether 

 as there are particles of matter in the transparent body, then 

 it is evident that the particles of fether will be arranged with re- 

 spect to each other in a perfectly symmetrical manner (suppo- 

 sing of course that the same is true with respect to the particles 

 of the transparent body, i. e. supposing it to be perfectly ho- 

 mogeneous and uncrystallized) ; this will appear immediately, 

 without any further explanation, from the following figures. 



Fig. 1. 



• e « « «- • 



• 9 • $ • • 



• » • . . 



9 • • • • • 



•> • • • # • 



Fig. 3. 



• e «i 

 « e • 



• • • 



• • « 



Fig. 2. 

 • o e 



9 



Fiff. 4. 



