86 The Rev. S. Haughton on the Reflexion of Polarized Light 



Substituting these expressions in the general equations of 

 motion, which are 



IF ~ 9 W + dij* ) 

 dt* -7 \<& 2 ^df J 



(8) 



with corresponding equations for the other body ; he finds 



from these equations, since g and g y are infinite, we find 



6 = «'=«/. 



Mr. Green then substitutes (7) in equations (6), and thus finds 

 results from which may be deduced the formula? (2) and (3). 



If, instead of supposing g and g t to be infinite, we merely 

 suppose them to be very great compared with 7 and y p we shall 

 obtain expressions containing an additional constant, and which 

 therefore can be reconciled in the most satisfactory manner with 

 observation. 



Let us suppose, in fact, 



r 



c 2 



<j; 



= -«/ 2 +6 2 =^ 2 » 2 



(9) 



where s is not zero, but small ; and substituting equations (7) 

 in the equations of condition (6), we find from the last two 

 equations (6), 



B= M *B, 



a. cos e 



a sine 



+ ft cos e t = y?a i 

 -fy3sin^=0 J 



(10) 



which are the same as Mr. Green's equations (23) ; and from 

 the first two equations, remembering the relations (10), and 



writing — = e, we obtain 



A— A,+ T-X+^OScos^— acose) = 



B— B^-OSsine,— asin<?) = 

 A */!-€* + A, i/l-j* a e 8 =0 



01) 



B^l- € 2 + B ; \/l-^ 2 6 2 +(M 2 -l)a / = 0_ 

 The supposition e=0 would reduce the last two equations to 



