271 the Undidatory Theory. 165 



can express the varieties of elliptically or circularly polarized 

 light,) It IS easy to show this formula is the solution of the 

 differential equations in the form just given (10.) (11.), if n 

 have a certain value, which we proceed to determine. 

 Taknig the increments of these expressions, we have 



I -2sm--^^sm(.i^_/:^-) ' 

 '" 1 • z ^ -1 ^ (12.) 



S {/3cosi[-2sin^i|i:sin(n/_;t^,)1 

 —^\nk^xco■i{nt—kx)\\ I 

 + S -j^/3 sin ^> r ?:mkLx%m{nt^lcx) 



-2sin2 __?cos(7«^-/ca:)]\. 

 Also differentiating them, we find 

 j-^= —n^^u sm {71 1 —k x) 



Ar=<i 



>(i3.) 



(H.) 



^-3= -^2^2;{/3cosisin(«^->?:.r)-/3sinicos(?z^-/ta-}}(15.) 

 Now for brevity writing 



P = ^ (?•) + ^ (r) Aj/2 

 i^' = <f> ('•) + ^ (r) A z^ 

 g =: ^ (r) Aj/ A z 

 2d= kAx 



(16.) 



the equations (10.) and (11.) will be expressed by 



^=?«[2;(;5A,,) +S(ryAr)] 

 ^=:»?[S(//A?) + 2(yA>j)]. 



(17.) 



(18.) 



And here substituting the above values of A >; A ^ and ar 

 ranging the terms, these equations become 

 f + sin i V [-^ g gi„ 2 5IJ -| 



- ^ = jnJ — ^lup2 sm^ . 6]] 



■ - S[«;; sin 2^]-] (19.) 



- cos i S [/3 <7 sin 2 ^] I cos (« /!-/ a:) 



- sin Z* S [/3 (7 2 sin- 6]] 



