92 The Hon. J. W. Strutt on the Reflection of 



The corresponding quantity when the light is polarized in the 

 plane of incidence is 



R/' 2 _ sin 2 (0-0,) 

 ft 2 "" sin* (0 + 0/)' 



and therefore 



R' 2 _ cos 2 (0 + 0,) + M 2 sin 2 (0 + 0,) 

 R" 2 ~ cos 2 (0 - 0-) + M 2 sin 2 (0-0,) 



(18) 



Equations (14), (15), (16), (17), (18) constitute the solution of 

 the problem on the hypothesis that n = n' } and are equivalent to 

 results given by Green. 



Case 2. Let D = D' ; n r :n=l: ft*. (9') and (10) assume the 

 form 



^V + ^^Y-^^^^-^l^t-X)-^--^}, 



^(b^-atX) -5 2 X + ff/ty,= - (ji*-l)ib{aY-a^, 



the value of <f> — <£ y being substituted from (8), or, on expressing 

 a, bj &c. in terms of the angles of incidence and refraction, 



cot 0Y-cot0^= ^ji sin 2 0|^p^ - cot 0Y- cot Oft\, 



^{f — cot 2 0X) -X+ cot 2 0,f ,= -f(/* 2 -l)(cot 0Y- cot0^) . 



From these two equations the values of X and Y as functions 

 of the angle of incidence might be tabulated with any given value 

 of p. One particular case is very remarkable. At the polari- 

 zing angle (tan -1 ft) the amplitude of the reflected wave is the 

 same as it would be given by FresnePs sine-formula — a coinci- 

 dence for which I have not been able to see any reason. 



My object in bringing forward the present hypothesis is to 

 disprove it, and is sufficiently attained by the disproof of a 

 particular case. Let us therefore suppose that the difference of 

 refrangibility between the two media is so small that the square 

 and higher powers of (/a 2 — 1) may be neglected. In the small 

 terms we are to put 



X=Y = -f y , cot0=cot0 r 



The second equation gives 



Y _ ft* 2 + cot 2 0, 

 A ~ l+^cot*0™ 

 while from the first 



v COt0, o^ 2 — 1 • o/, . 



Y= &rf*i~*-jSr sm °fr 



