518 Mr. R. H. M. Bosanquet on the 



variation of thickness from zenith to the horizon, and it is quite" 

 insufficient to admit of this explanation. 



If we admit that A 2 and A 2 cos 2 + B 2 represent the vertical 

 and horizontal components in the case in which is not the neu- 

 tral angle, we have for the polarization 



A 2 sin 2 0-B 2 sin 2 6- sin 2 a 



or . 



A 2 (l + cos 2 d) + B 2 ' 1 + cos 2 6 + sin 2 * 



Now it is true that this assumption is unsupported by evi- 

 dence, except that the expressions are true in the case 6 = ot. 

 But they derive from this a certain probability, and may be use- 

 ful as giving a simpler empirical formula than the one derived 

 from Brewster's expression. In one point the result is curious. 

 That is, that this expression agrees with TyndalPs observations 

 and with Brewster's original and modified formulae (if the cor- 

 rection ^sin introduced by me be omitted) in making the 

 negative polarization increase continually up to the smallest in- 

 clinations to the beam in cases where there is a neutral angle. 

 (Of course, if there is no neutral angle, either we are in 

 Stage I., and B = 0, or we are in Stage III., and B>A.) The 

 Brewster formulas, as well as the one last stated, must neces- 

 sarily be wrong in attributing the greatest value of negative 

 polarization to a point of view ultimately coinciding with the 

 beam. But the coincidence of the indications of both with Tyn- 

 dalFs observations, as far as they go, is curious. For the present 

 I am inclined to keep both formulae as probable empirical repre- 

 sentations, affecting them with the factor £/sin 0, the purpose 

 of which has been already explained. 



The methods employed in reducing the indications of the 

 polarimeter to absolute values have been based on two different 

 principles. I shall discuss these briefly, and then indicate a 

 third method, which seems to me preferable to either. The first 

 method is that of Brewster; it is similar in principle to that de- 

 veloped in a paper by Professor Adams (Phil. Mag. vol. xli. 

 p. 205) . The methods differ only in that Brewster's formula 

 appears to be based on experiment, Adams's on theory. 



The form of the polarimeter is always the same. It consists 

 of: — an analyzing eyepiece, a Nicol or tourmaline; a test-object, 

 which, with the eyepiece, indicates the existence of polarized 

 light and the direction of polarization ; and a bundle of glass 

 plates placed in front of the test-object, by which the polariza- 

 tion of partially polarized light incident on the instrument can 

 be compensated. The eyepiece and test-object together consti- 

 tute a polariscope. The problem is, from the observed incli- 

 nation of the bundle of glass plates, to deduce the value of the 



