Transmission of Light and Heat in uncrystallized Media, 337 

 By expansion we obtain 



d ^r 

 ^{r + q)=:^{r) + -^?+ 



and {r^qf = (8.r+d^a)^+ (5y + ^/3)^ + (8^ + §yr 



,*. q = — (S a: S a + S^ § /3 + ^' 2; S y) omitting small quantities ; 

 and by substituting this value in the above equation, it gives 



but -5* <^ r . S .r is evidently the accelerating force, resolved pa- 

 rallel to x, on the particle P in its state bf rest, and conse- 

 quently is equal to zero: we have then 



which we will call equation (I.). 



I shall pass over the argument for the^rm of the solution, 

 and assume at once that 



ex, = a cos (nt—kx) 



^ = b cos {n' i—kx) 



y = c cos {n" t—kx) 



the quantity k being the same for all, as it is the ratio ; 



A 



A being the length of a wave. We shall thus obtain, 

 8a = fl cos {nt— k x—k^ x) — a cos nt — k x 



= a cos(n t—kx) Q.osklx-\-a sin nt—kx ^xnklx 



— a cos {nt—kx) 



k ^x 

 = — 2acofi{nt—^x) sin^— ^— + asin(«/— ^j?)sinA:5^ 



= — 2 a sin^ ^ h a sin {nt—k x) sin ^ 8 ^ 



k^ X 

 8|3 = — 2/3 sin® — ^— + b sin {n' t—kx) sin A: 8^ 



8 y = — 2 y sin® — 1- c sin {ril' t—k x) sin kl x. 



Now we have supposed the medium to be one of symmetry: 

 to fix the ideas, conceive the particles arranged in a cubical 

 form, the edges of the cube being parallel to the coordinate 

 axes. Hence for every value of 8 jt there is a set of j)airs 



ThirdSeries, Vol. 10. No. 62. May 1837. 2 X 



