Polarization of the Light of the Sky. 519 



polarization of the incident light which is neutralized by the 

 bundle. 



The formula of Brewster appears to be founded on experiment. 

 It was first given in Phil. Trans, vol. cxx. (1830) pp. 136, 141. 

 The formula is cot $ = cos 2n (z — i'), where (/> = 11 + 45°, so that 

 cot <b= tan (45°— R); i is the angle of incidence, i ! the angle of 

 refraction, and n the number of plates. It would appear that in 

 Brewster's paper (Edinb. Trans, vol. xxiii. p. 233) the formula is 

 erroneously quoted, the 2 in the index being omitted. Brewster 

 calculated by this formula the polarization corresponding to 

 various inclinations for the glasses he employed. 



In the paper of Professor Adams above referred to, Tables are 

 given for a few inclinations for four plates and for two values of 

 /jb y and general expressions are given for any case. The mode 

 of statement is more direct than that of Brewster. It is, how- 

 ever, obvious that this method must always be subject to consi- 

 derable uncertainty. It is impossible, by any means with which 

 I am acquainted, to verify the refractive index of the glass of 

 which the plates are composed; and looking to the mode in which 

 the plates are formed, the assumption even that the glass of all the 

 plates has the same refractive index must be of doubtful admis- 

 sibility ; while the assumption that it is the same as that of the 

 sample of which the refractive index has been determined, seems 

 to introduce a still more considerable element of uncertainty. 

 At the same time there is no doubt that a first approximation 

 to the truth may be got in this way. The variation in the colour 

 of the light observed would also seem to be a source of error. 



The second method is that employed by llubenson, which has 

 been already alluded to. The polarization corresponding to the 

 different inclinations of the glass bundle is determined by a 

 process of graduation, which is somewhat as follows. Polarized 

 light issues from a NicoPs prism, and falls upon a quarter-wave 

 plate, the direction of the axis of which is parallel or perpendi- 

 cular to the axis on which the glass bundle turns, the bundle 

 being arranged so as to compensate the resulting polarization. 

 If, then, the angle between the plane of polarization of the Nicol 

 and the axis of the plate be <£, the intensities of the components 

 of the resulting elliptically polarized light along and at right 

 angles to the axis are A 2 sin 2 (j> and A 2 cos 2 <£ respectively, and, 

 as before observed, the polarization is cos 20. 



The objections to this proceeding are : — first, that we depend 

 on the accuracy of the quarter-wave plate, where we may have 

 error of workmanship, and must have error arising from varia- 

 tion of colour ; secondly, that we introduce Malus's law into 

 our determinations ; and strictly speaking we cannot trust the 

 accuracy of this law beyond the point to which it has been car- 



