of a Stream of Light passing through a Crystalline Plate. 89 

 whence 



2 = #! = -73 = ^ 



and 73 = a 3 , 3 = 



Again, from the terms involving sin 4 i'/y 4 



= 0, 



whence a3 = -fa = - 73 = 3, = _ ?L = __ . J,, 



and a 4 = 74, /3 4 = 6 4 . 



Similarly the terms involving sin 5 i/v 5 give 



) +^1(^4+ ^) = 0, 

 + 2 J3i_p 2 +p*pa) 2 + 2po02a3 = 0, 



* 3 p z ) + 2 2 = 0, or a 4 /3 4 = 0. 



Hence 



Pbpi pi 4P ' 4P S 



and a- -75, /? 5 = r> 5 , 



and so on. 



Hence, as far as terms of the fourth order, 



_o - sin 2 ** sin 3 i . sinS' 



__._ smn 55Ui sin*t 



where 



2 = cos w , a 3 = cos* ?y , 



(& 4 a 2 c 3 ) 2 sin 2 w } cos z^^ 



