102 Professor Airy on the 



E therefore is - — -, and consequently G = Tx ( 1 ^— 0-\ . 



We may remind the reader (as we shall have occasion to use it afterwards) 



e T 



that — j- is the angle through which the analyzing plate must be turned 



A. 



from the crossed position to produce darkness at the center for the particu- 

 lar colour used. We may also remark that, if we still consider 9 as posi- 

 tive (which we shall continue to do), all our expressions (as appears from 

 this comparison of theory and observation) must be understood to apply to 

 a right-handed crystal : if the sign of k be changed, they will apply to a 

 left-handed crystal. But if, more correctly, we put a negative symbol for 

 B, then our expressions would apply to a left-handed crystal, unless the 

 sign of Jc were changed.* 



The value ot — — is therefore — - + ^r 6: Let us suppose 



X X" 2«X Ir 



that \' + S \ may represent the length for rays of any colour, \' being that 

 for one of the mean rays, and therefore constant, and S\ being small for 



7T 6 



all the bright colours. Then for -7 s- we have 



A + OA 



^ + -Hbjr- 6 ' ~ x^(— + \b 6 i nearl y- 



The mixture of colours in the rings will depend only on the difference of 



7r9 . 



the values of — — for different colours, and not on its absolute values, and 



* The reader who will take the trouble of tracing the expressions will find that, if the 

 sign of © and of k be changed at the same time, not only will the right-handed-ness of the 

 crystal remain the same, on comparing the expression with Biot's experiment, but also all 

 the directions of the spirals &c. in the succeeding experiments will remain the same. Thus 

 the connection between the right-handed-ness and the direction of the spirals is independent 

 of the sign assumed for 6. With this consideration, I have thought it best to use the same 

 symbol in the theorems for calc spar and for quartz. 



