168 Professor Powell o}i certain points 



From the last two forms (38.) (39.) we have 



7r=-^S [«p2sin"-^]. (40.) 



«-= ^S [/Sy 2sin^6l]. (41.) 



For plane polarized light from the conditions (5.) let 

 jS = 0, and the form (22.) will become 



= S [apsin 2d']. (42.) 



In like manner (23.) will give 



= 2 [« fy 2 sin- ^] (43.) 



and (24.) = 2 [« <? sin 2 ^] ; (44.) 



while from (21.) we find 



n- = ^ 2 [« ;? 2 sin^ 6]. (45.) 



Hence the formula for plane polarized li^ht is only a solution, 

 provided these conditions are fulfilled in the original equa- 

 tions. 



Since A >) and A ? are both of the form 

 M sin 2 ^ + N 2 sin^ 6, 

 the above conditions give 



^{qAr)) = (46.) 



2 (? A = 0. (47.) 



Thus when they are fulfilled in the terms of the original 

 equations, those equations become, for unpolarized light, 



^ = 2[i.A,] (48.) 



^ = %[p'^Q, (49.) 



while for plane polarized light the second of these forms dis- 

 appears. 



(7.) Now recurring to the supposed constitution of the me- 

 dium, to examine the conditions under which these terms can 

 vanish, we may first observe, that since none of the factors 

 can separately become = 0, the terms can only become no- 

 thing by sums with opposite signs being equal and destroying 

 each other. 



That this may happen depends on an hypothesis respect- 

 ing the arrangement of the (Ct/iefial molecules in spaces, viz. 

 that they are distribiited tiniformly. This is the supposition 

 adopted by M. Cauchy and other writers. 



