812 REPORT— 1898. 



which ia identical to the condition that 



<^ + 0,,. = |; 



or, in more familiar form, that the reflected and the refracted rays form a right 

 angle with each other. It is evident from tlie above simple relation that, if v and 

 <f> can he determined by experiment, A will be given. 



Even a general examination of the above special equation (3) would be too 

 long here ; I shall, therefore, confine myself to the particular case where A, JS, and 

 C are assigned given numerical values ; ibr sulphur Boltzmann ' has found the 

 following values for the constants of electric induction : 



4-773 3-970 3-811. 



For these values the above equation (3) reduces approximately to 



sin ''<!> + 51-7 sin *(i> + 494-8 sin ^4> - 440 = 0, 

 one root of which is 



(^ = 64° 44' ; 



the other roots are imaginary. 



Similarly, we find another angle of polarisation cj} on interchanging the above 

 X {A) and i/ (B) co-ordinate axes with each other. The general equation in cf) 

 must then evidently be written 



»* [v"" + (A^ - B-) sin 20] cos ^ = A.^/^^ = B^ sin '0 [v' - (A- - B*) sin -'</)], 

 This equation reduces for the given particular case to 



sin "0 - 53.35 sin ^cft + 617.53 sin 2(/) - 465 = ; 

 one root of which is 



<^ = 6i°7'.30"; 



the other roots are imaginary. 



If now we are able to determine by experiment two such critical values of 0, 

 characterised by linearly polarised light or other phenomena, we should then have 

 two equations for the determination of the quantities A and B. Although the 

 actual solution of these equations with regard to A and B offers difficulty, very 

 approximate ones can always be found. 



Similarly, to determine the third medium-constant C, we have only to choose 

 those principal planes of the given crystals as reflecting and incident planes, for 

 which the above formula (2) reduces to a. function of C and A oi B only. 



' Cf. Poflff. Ann. 153, 1874. ' Experimentaluntersuchung iiber das Verhalten 

 uicht leitender Korper nnter dem Einflusse elektrischer Kriifte.' Also Poincar6"s 

 Electricitc et antique, vol. i. p. 129. 



