430 WRIGHT— POLARIZED LIGHT IN THE 



The amplitudes Rs, Rp (equation 20, 24) are complex and of the 

 form f-\-ig. In order to compound these two vibrations (vectors) 

 and to ascertain the directions of the resultant elliptical vibration let 

 (equation 21) 



Rs = rie'^'-'''\ 



(sq) 



If i/' be the angle between the Rp axis and the major axis of the 

 resultant ellipse of vibration, then we find by taking the real parts of 

 (39), namely 



Rs = r. cos (t — A,), 



(40) 

 and Rp = r^ cos (t — Ag), 



and compounding them into the form 



Mo = n cos (r — Ao), 



(41) 

 7:^0 = ^0 sm (t — Ao), 



which obtains for the components after the principal axes of the 

 elliptical vibration, that 



2rir2 



tan 2^ = — -cos (Ai — A2). (42) 



^1 — r<t 



To effect this transformation the normal transformation equations 



Uq = u cos ip -^r V sin xp, 



• ,1 , ^43) 



z'o= — « sm i/'-j-z' cos </', 



are used and the coefficients of cos r and sin t of equations (41) 

 and (43) are equated. 

 If we put 



= tan §, (44) 



equation (42) may be written 



tan 2 i/' = tan 2 (9 cos (A^ — Ao). (45) 



The quantities on the right hand of this equation can be computed 

 from equations (27), (29), (40) and (41), (44); but the expres- 

 sion thus obtained is too complicated to be readily interpreted. The 

 fact that the phase difference for most opaque substances is, as 



