-80 Mr. J. Walker. Relative Retardation between Component* 



points T, P, and P' respectively, and through P and P' draw PE, 

 P'E' perpendicular to OT, meeting it in the points E and E' ; through 

 E' draw E'T' parallel to the surface of the plate, meeting PE in T'. 



Draw OD normal to the plate, meeting the second surface in D, 

 and let the wave fronts CN and CN' meet this normal in the points 

 Q and Q'. 



Then the triangles OPD, CON, CQO are similar, as are also the 

 triangles OP'D, CON', CQ'O, and the triangles T'E'E, COM. 



The relative. retardation, measured in time, of the two waves after 

 both have traversed the plate, is represented by 



OP_OEI _ roF_ojn _ OP _or EE' 



ON OMJ [ON' OMj ~ ON ON~ / 



ON 2 ON' 2 OC~~OC.ON 2 OC.ON' 2 



DP'J " OQ OQ'' 



Hence if the axis of Z be normal to the plate, and 



Z = 1 ZX + wY-HiZ = i 



are the equations of the refracted waves in unit time after passing 

 through O, their relative retardation, measured in length in air, after 

 both have traversed the plate is 



A = i;T(Wi ?z 2 ), 



where v is the propagational speed in air, and T is the thickness of 

 the plate. 



Also i being the angle of incidence, and w the azimuth of the 

 plane of incidence with respect to that of XZ, 



Z = sin i cos w/v, m = sin i sin wfv. 



2. In applying this result to the case of a plate cut in any manner 

 from a, biaxal crystal, let the surface of the plate on which the light 

 is incident be taken as the plane of XT, the plate lying on the side of 

 Z positive, and let the plane of XZ be taken so as to contain the 

 least axis of elasticity of the crystal. 



Let O#, O?/, Oz be the axes of elasticity, and the angle yoY = 0, 

 the angle zoZ = x, then the transformation from the axes of elasti- 

 city to the new axes may be effected by the following successive 

 transformations, each in one plane : 



(1) Through an angle 0, in the plane of xy, from Ox, Oy to 



0*,, Oy. 



(2) Through an angle x, in the plane zx^ from Oz, Ox t to OZ, OX. 



