F. E. Wright — Measurement of Extinction Angles. 353 

 The resultant displacement at any time t is 



y= l J, + y* = a , sin^f*— fj + a.siny (t—t t ) 



. 2tt' , 2tt 2tt\ 2tt / . 2tt . 2tt , 



= sin — t(a 1 cos — t % + « 2 cos — -£ 2 ) — cos — t(a^ sin ^ + a 2 sm — y 



= Asm — (t-t 3 ) 



if 



2-7T 



A cos t^ — a^ cos-^ ^ + « 2 cos 27r £ 2 

 and 



. 2tt . 2tt 



A sin 0,=^ sin — ^ + « 2 sin — t 2 



By squaring and adding the last two expressions, we obtain 



A t =a* + a m t + 2a l a, cos -^ (*,.-*,) (3) 



2tt 



In this expression — (&,—£,) denotes the difference in phase 



of the two component periodic displacements and A the 

 amplitude of the resultant vibration. 



In considering the effects which different crystals exert on 

 transmitted light waves, it has been found, both in practice 

 and theory, that these influences can be predicted accurately 

 and satisfactorily by reference to a triaxial ellipsoid, the optical 

 ellipsoid, the position and relative axial lengths of which vary 

 in general with different minerals, and with the wave length of 

 light employed. Thus the directions of vibration of light 

 waves emerging normally from a mineral plate are parallel 

 with the major and minor axes of the ellipse which a central 

 diametral plane parallel to the given plate cuts out of the 

 optical ellipsoid for the particular mineral and wave length 

 used. The determination of the actual position of these 

 directions in the plate is accomplished in polarized light by 

 observing the relative intensity of the transmitted light for 

 different positions of the plate parallel to the principal planes 

 of the nicols. 



Light waves emerging from the lower nicol are plane polar- 

 ized and their vibration is given by the equation 



u = a sin -— - 



On entering the crystal plate, this vibration is resolved into 

 two vibrations in planes normal to each other. If 6 (fig. 1) 

 be the angle included between the major optic ellipsoidal exis 



