336 Mr KELLAND, ON THE TRANSMISSION OF LIGHT 



(I = // — 3 {m cos- G + p sin- 6), 

 b = // — 3 {m cos" <p + p sin^ ^), 

 c = /< — 3 (?« cos" \/' + ;j sin^ \^) ; 

 JC = 3 (iu — J)) cos (p cos \//, 

 I'' = 3 {m — |j) cos cos v|/, 

 Z = 3 {m — 2^) cos cos ^. 



8. To find the coefficient of A in equation (2). 

 ah + (ic + he = 3h- - Qh {m{co%-6 + cos=0 + cos^//) + ;>i(siir f? + ...)^ 

 + 9 \ m'^ (cos"- Q cos" ^ + cos' d cos= x// + cos" (f> cos" v|/) + jy (sin' sin- f/) +...)} 

 + 9»«/j(cos°0sin'^ + ...) + 9»»J9(cos*^sin'a +...). 

 let COS" 6 cos' (j> + cos^ Q cos- x/r + cos' ^ cos^ >// =,/' 

 cos^ cos^ <p cos" >// = g, 

 and «5 + «c + be = 3lr - 6/r + 9 \nff+ P'{1 + f)\ 



+ 18»«p(l -/) 



= - 3 (»» + 2^)° + 9 {2mp + jr) + 9/(nr - 2mp + jf) 



= - 3{m + 2pY + 9{2mp + p") + 9/(m - p)\ 



Again X' + Y' + Z' = 9 {m - pff; 



.-. coefficient oi A = ah + ae + be - {X^ + Y' + Z ) 



= - 3 {m + 2pf + 9 {^mp + jr), 



- — 3 m" + &mp — 3p^, 



= - 3 {m - pf, 



which is independent of J", or of the direction in which the particle 

 vibrates. 



