IN THE INTERIOR OP TRANSPARENT BODIES. 411 



large the masses of the former must be compared with those of the 

 latter*, it is evident that the motion of the former must be small com- 

 pared with that of the latter: hence, a a and a 3 must in general be 

 small compared with «; and therefore m t C(a, — «) and n^Cia-i — a) 

 must be nearly the same as - m t Ca, and therefore, a fortiori, the 

 expression under the sign 2,, which we know always lies between 

 m^i^a* — a) and m t C{a 3 — a), must in general be nearly the same as 



— m t Ca, and this is evidently true, however small or large C may 

 be. Hence we are justified in proceeding upon the following suppo- 

 sition, viz., that the action of the particles of matter on that of ether 

 in the case of common luminous waves passing through transparent 

 bodies, is very little altered by the motion of the material particles ; 

 and that therefore in estimating that action we may suppose the par- 

 ticles of matter absolutely fixed for a first approximation. 



§ 15. Hence it appears, that the equations of motion of the etherial 

 particles, taking into account the action of the material particles upon them, 

 are as follows, at least for a first approximation. 



1 d'a .d'a „ (d'a d*a\ . . „. d i d(Z dy\ m. „ . 



— i,> = A j - + B \j , + -J—) + ( i -- B) v- -f- + -f-\ ' Ca 



m df dx- \dy % d%' I s J dx \dy dx) m 



1 rf/8 .d'$ D ld*fS d 2 (S\ d (da dy z« „_ 



m df< = A dy +B {d^ + -d¥) + ( A -^T y \dx- + ITy) ~ Tn C ^ U>>- 



m df d% ! \dx- dy' ! J d% \dx dy) m ' 



where C = 2 \<p(r') + \(p'(r') Ax*}. 



7ft Vfh Itl 



The terms — i Ca, — - C/3, — Cy, which I have thus introduced into 

 m mm' 



the equations, lead to very remarkable results, as will appear presently. 



§16. To shew that the law of molecular force is not likely to be 

 such as to make C zero in all cases. 



* That this is the case, I think the very small resistance experienced by the heavenly 

 bodies from the ethereal medium seems to prove. 



