86 Mr. J. Walker. Relative Retardation between Components 



Leaving then for the present the case in which a 3 = A 2 ) the roots 

 have the form given above, and 



jwi4"vl -. JJ(\ "U i 4 f 1 ! -1-2/W+l 



1 'W pjMt 



~~ "2 3 tf~2 ' 







a,r /V a<r /V 



whence 



A 



2ft 1 4- (ao 2 -*- A 2 ) ^i 8 ^ u * i^- + S 2 sin'- 



__lRi+S4 sin 4 1 



2 ^ /J y.,4 ' 





the terms of which may be readily calculated in succession. 



5. It is now necessary to consider the case reserved above, in 

 which oo 3 = /3 2 - When this occurs, the two refracted waves, corre- 

 sponding to normal incidence of the light, traverse the plate with the 

 same velocity, and hence the plate is perpendicular to an optic axis. 

 The case, then, of a plate cut perpendicularly to an optic axis 

 requires a special investigation. 



Now for a plate so cut 



= 0, cos X = v/(^-c^/v/K-c^, sin X = 

 and the biquadratic (ii) has the form 



_ , sin i . / ' , , sin 2 i\ /, r sin 



^here 



= -cos w 



, sin- i , sin 4 



p V(tf 1>~) (b~ c 2 ), 



. 



