M. Lorenz on the Theory of Light. 217 



The velocity s thus receives two notably different values in the 

 case of the perpendicular to the plane of the wave coinciding 

 with the optic axis of the crystal; for the assumed values of 

 u, v, w are precisely those of the cosines of the angles which the 

 optic axis makes with the axes of coordinates. 



In passing on now to the calculation of the amplitude of the 

 excursion, we must bear in mind that, so long as we only consider 

 the cases in which the value of the exponent p is either or 2, 

 it makes no essential difference which of these values be taken 

 in applying the generalized form of FresnePs formula, since the 

 plane of polarization is the same in both cases. Still, inasmuch 

 as in one case (p = 2) the vibrations take place in the plane of 

 the wave, this gives the simplest results, and we will accordingly 

 confine ourselves to the consideration of this case. 



Taking the values that have been assumed for u, v, iv, and 

 applying the symbols f , t] , t that have been previously used, 

 we get from the equations (C) 



1 __ _ _ W ~ — "] 



£o= ^l : o+/Vo-^o= s 2(^?o- M ?o)^ J 



Vo= ^V -fi' + df = ^77 , \ . . (21) 



1 _ _ - u - _ 



in addition to which we have analogous equations formed from 

 these by changing the accented factors for unaccented factors, 

 and the unaccented for accented factors with opposite signs. 



Since d, e, and /are small quantities, we may substitute for 

 |' , 7)' , J' in (21) their approximate values, namely !' o =0 2 !' O j 

 t/ =6 2 ?/ , f' =c 2 f / , whereby the following equations are ob- 

 tained, 



IV 



-uc^ -ea^ + dby )(^ - ^) % 



"~ ""* w- ■ ° "^ 6 2 



0> 



together with three other analogous equations formed in the way 

 already indicated. 



All these equations are solved by the following values : 



&=o, Vo =a, r =o, -i . 



