and its Use in Experiments of Polarization. 



321 



Or since this must be true for all values of vt — x, we may expand 

 the sines and cosines and equate the coefficients of 



. 2tt , , 2i 



sin — (vt — x) and cos — 



(vt - X). 



Thus we have 



a = p . cos q + p cos q 

 = p . sin q + p sin q 

 a sin 9 = — p . sin q + p' sin q 

 a cos 9 = p . cos q — p cos q . 



From these, 



^ = a cos - , p = ft sin - , g> = - , q = 270° + - 



and the vibrations are 



9 . 2ir 

 « cos — . sin —— 

 2 A 



9 2tt 



rt cos — . cos — - 

 2 X 



[vt - X -\- 

 (vt — X + 



9 



\ 

 2*- 



2)erp. to princ. plane 

 par. to princ. plane 

 9 



constituting light A, 



a sin — . sin — (vt — x + 270° + — j perp. to princ. plane 



— a sin — . cos 



2 X 



f vt — x + 270° + - ) par. to princ. plane 



constituting 

 light B. 



If the analyzer is of such a kind that it can transmit light A, 



9 



the intensity of the light that reaches the eye is 2<rcos 5 -: if 

 it transmits light B, the intensity of light is 2 a* sin* - . The former 



S3 



of these g-ives light at the place where there is no double re- 

 fraction : the latter gives dark at the same place. But in both 

 cases it is plain that the brightness depends only on 9, the 

 quantify which one ray has gained or lost on the other, and that 

 it does not at all depend on the position of the planes of polari- 



Vol. IV. Part II. S s 



