1872.] 



Crystals in Circularly Polarized Light. 



335 



Q is inclined at 45° to the principal section of P, we have the condi- 

 tions 



a + 6 = 90°, i=45°; 



whence 



sin(a + 6) = l, cos(a + 6) = 0, 

 . sin2a=sin2§, cos 2a = — cos 2b, 



sin 2(i+f) =cos 2j, sin 2i= 1, cos 2i=0. 



Introducing these into the general expression for the intensity, we obtain 



P == i { 1 + sin 2j cos + sin 2b cos 2j sin 0} . 



This shows that if the analyzer be placed parallel to the polarizer (j=4 5°) 

 and then turned round in a positive direction until j= 90°, sin 2j will retain 

 its sign + , while cos 2j will take a negative sign. Also if we exchange the 

 crystal supposed positive for a negative one, cos will retain its sign while 

 sin0 will change it. It follows, therefore, that if in examining uniaxal crystals 

 with this arrangement the analyzer be turned in one direction, the distor- 

 tion of the rings from a circular to an oval form will take place in a vertical 

 line for positive crystals and in an horizontal for negative ; while if the 

 analyzer be turned in the opposite sense, the distortion of the rings will 

 likewise be reversed. This process, therefore, will give a method of distin- 

 guishing positive from negative crystals. 



That the same law holds good for biaxal crystals is clear from the 

 formulae which apply equally to both classes ; but it may be experimen- 

 tally verified by applying the method to the series of mica plates crossed in 

 different groups so as to show the transition from the biaxal to the uni- 

 axal condition. In the case of biaxal crystals, however, the readiest method 

 of making the experiment is to observe the rings near the centre of the 

 field where the lemniscate loops meet, and to notice whether, on turning 

 the analyzer in a given direction, the rings appear to stream in towards one 

 another from the axes, or to be drawn out towards the axes. If for a given 

 arrangement of the plates the rings of a negative uniaxal crystal are drawn 

 out horizontally when the analyzer is turned to the right, for the same 

 arrangement and motion the rings of a negative biaxal crystal will appear 

 to flow together. 



The Society adjourned over Ascension Day to Thursday, May 16. 



2 b 2 



