310 Lord Rayleigh on the Intensity of Light reflected from 



neighbourhood of the polarizing angle is due to greasy con- 

 tamination. The very close verification of the theoretical 

 formula in this critical case seemed to render its applicability 

 to perpendicular incidence in a high degree probable. I was 

 thus induced to attack the somewhat troublesome problem of 

 designing a photometric method capable of dealing with the 

 reflexion from a horizontal surface. The details of the appa- 

 ratus and of the measures will be given presently ; but in the 

 meantime it may be well to consider rather closely what is to 

 be expected upon the supposition that Fresnel's formulae are 

 really applicable. Fresnel's formulae are spoken of, because 

 although at strictly perpendicular incidence we should have 

 to do only with Young's expression (/*— l) 2 /(/*+l) 2 , in 

 practice we are forced to work at finite angles of incidence. 

 It is thus important to examine the march of Fresnel's ex- 

 pressions, when the angle of incidence (0) is small. 

 Writing 



q_ sin(fl-fl 1 ) T _ tan{0-0 1 ) 

 b " sin (0 + 0j ~~ tan (0 + 6J 



where 

 we find 



sin 0i = sin 6 /fj,, 



~(58r{>-?-6<»-»*+»}..« 



Thus S 2 and T 2 differ from the value appropriate to 0=0 in 

 opposite directions and by quantities of the order 2 . But on 

 addition we get 



S2+T2=2 (^i) 2 { 1 -^ (1 - 4 ' 1+ ^}' • < 3 > 



differing from the value appropriate to 0=0 by a quantity of 

 the fourth order only in 0, When therefore the circumstances 

 are such that it is unnecessary to distinguish the two polarized 

 components, the intensity of reflexion at small incidences is 

 in a high degree independent of the precise angle. If fi is 

 nearly equal to unity, we have 



S 2 + T 2 =2(^J{1 + ^}- .... (4) 

 simply. Again, if fi= ^ 



