from the surface of Transparent Bodies. 



87 



those used by Mr. Green (24) ; the first two are the same as 

 two of Mr. Green's equations. This supposition is equivalent 

 to supposing the normal wave velocity to be infinite. 



From (10) and (11) it is easy to deduce the following: — 



a cose 



/3cose ( =;j(. 



/*■ + 





asm e= — 



0* 2 -i) 5 



/3sine.= -=- 



2«Vi- i u. 2 6 2 +/A 2 vr^?" 



16 (/* 2 -l) 2 



(12) 



2 a v r i-/A«+>*Vi-*€* ' ¥ 



Dividing the first of these equations by the third, and the 

 second by the fourth, and writing 



Oi 



VI -/j?e 2 + /j? a/1-6 2 

 (/* 2 — I) 2 



(13) 



„ , , . sine a, tan t 

 we find (since «,= -i — , — = - , 



smr a tanr 



and 



tan i) 



cot e = Q (/a 2 cot t + cot r ) 



f+cotrn < ; , 

 cot e y = — Q(/a 2 cot z— cot r) J 

 which agree with equations (2). 



Again, dividing the sum of the squares of the second and 

 fourth by the sum of the squares of the first and third, we find, 

 writing for shortness 



A=/^ 2 cot i+ coir 



Hence we obtain 



B = /a 2 cot i — cot r, 



T2 _^_Q 2 B 2 + 1 



~ «*-Q 2 A 2 +r • 



J 2 



2 



Bin 8 (i + r) Q 2 B 2 + 1 



(15) 



(16) 



iin»(»W) Q 2 A 2 + 1' ' ' ' 

 which is reducible to the form (3). 



As it has been shown that equations (2) and (3) will represent 

 accurately the laws of reflected polarized light, provided the value 

 of Q be suitably determined, it is plain that the equations (14) 

 and (16) will represent the observations, as they contain two 

 constants, one of which only is known independently of the laws 

 of reflexion, and the other is determined by the observations 

 themselves. 



Having thus shown that equations agreeing in form with those 

 found by Mr. Green may be obtained without the restriction 

 which determines the value of Q, and having shown that these 



