Polarization of Sky Light. 87 



proportion of light, polarized in the plane of incidence, which 

 traverses a pile of n plates is 



1— a 

 l + (2n-l)a' 



A similar formula holds good for the light polarized at right 

 angles to the plane of incidence. In this case let us write 

 h for a. Thus if a broad beam of ordinary light enter a pile 

 of plates, the ratio of the principal intensities in the emergent 

 beam is 



l-g l + {2n-l)h 



l+(2n-l)a 1-h 



So far the formulse are perfectly general and independent of 

 the truth of any particular laws of the reflexion of polarized 

 light. To proceed further we must assume certain values of 

 a and h. Now Fresnel's laws are known to be at least 

 approximately true, and these give 



_sin^(fc — t') ,_ tan^(i,— 4) 



Using these values I have calculated the following figures 

 for the ratio of the intensities in the beam emergent from 

 twenty plates when the incident light is unpolarized : — 



Angle of Incidence . . 30^. 40°. 50°. 



yci = l-52 . . . -580 -360 -182 



/i=l-56 . . . -562 -355 -174 



By Eubenson's Standardizer -532 -293 -120 



I presume that we may safely assume that Eubenson's plates 

 (of which he gives no special description) had an index of 

 refraction nearer 1*52 than 1"56. The most uncertain point 

 seems to be the truth of FresneFs laws. In working out the 

 following results from Rubenson's figures I have assumed 

 their truth as well as the index 1'52. It must be distinctly 

 understood that these results are only rough approximations. 

 There are several diflperent methods of expressing the 

 strength of partial polarization, and it is not easy to choose 

 between them. If A, B be the intensities of light polarized 

 in the two principal planes, of which B is the lesser, the most 

 natural expression seems to be the simple ratio B/A. I shall 

 call this r. In completely polarized light 7' = 0, in unpola- 

 rized light r=l. But in the special subject of this inquiry 

 it will be often convenient, though not very accurate, to 

 regard sky light at the maximum point as composed of some 

 completely polarized light. A— B, consisting of scattered sun- 

 light, and of some unpolarized light 2B, consisting of 



