272 DR. L. N. G. FILON ON THE 



(7) The knife-edges are never quite accurately adjusted. (8) The weight of the 

 beams themselves will affect the stresses. (9) The beams are not always perfectly 

 annealed and the permanent stresses in the glass modify the appearances. 



In the following sections the corrections due to these errors will be investigated. 



4. Effect of Introducing the Polarizing Nicol. 



We shall now consider the effect of introducing the polarizing Nicol upon the 

 inclination of the rays of light. In order to estimate the magnitude of this effect, it 

 will be sufficient to treat the Nicol as a singly-refracting substance. If the larger 

 index of refraction be adopted this should, in general, give us an upper limit to the 

 error introduced. If no sensible disturbance is found to be thus introduced, we may 

 assume that this will be the case in the actual experiment. 



Let S (fig. 4) be the source of light, P the image of a point of the mid-plane of the 



Fig. 4. 



nearer slab, viewed by refraction through the face nearest S. If the Nicol were not 

 present the light would travel along the line SP. In consequence of the introduction 

 of the Nicol it travels along the broken path SCDP. 



Let <j>, i/f be the angles of incidence and refraction, x the angle which SP makes 

 with the normal to the faces of the Nicol. 



Let the perpendicular distances of S and P from the nearer faces of the Nicol be m 

 and n, and the thickness of the Nicol be t. 



Then 



(m + u) tan <j> + t tan ^ = (m + n + t) tan x , 



or, writing t((m+n + t) = y, 



tan x tan (f> = y (tan / tan <) (9). 



Using p. sin /i = sin <f>, 



tan t/ = tan <f> [y + (/x 2 - 1) tan 2 c^]' 1 a . 

 Hence (9) becomes, retaining only first powers of y, 



tan x - tan < = y tan x ([/**+ (ft 2 - l)tan a x ]~ 1/a -l) .... (10). 



