476 The Astronomer Royal on the Equations 



4tt 2 . 2tt/ .r\ A 4-9r 2 /l\ 2 7 . 2ir/. x\ 



+ ^ b . sin -{ t -^J=+A^^Jb.sm T (t- w J 



„ 2 7T 7 . 2 it ( x\ 

 which agree in giving 



w = 



'-f. c 



Hence t/ x is less than i/ ;r 



In the second experiment, for Ray No. I., 



tn, 2 7T / , X \ 



■ \ V / 



T 



and the equations become 



4w 2 

 + — T a ' 



„2tt 2t/\ x\ 



+ C -a.co S -[t + 7 J, 



„2t . 2*/. , J?\ 

 — C — a . sin — I ^ + -p ) , 

 r t \ t/ 2 / 



which agree in giving 



W k - 



2tt 



Similarly, 



(A) 2 = 



1 + k c 



Hence t/ 2 is greater than i/' 2 . 



Thus if in one experiment the Ray No. II. travels more 

 quickly than the Ray No. I., in the other experiment the Ray 

 No. II. travels more slowly than the Ray No. I. And there- 

 fore if in each experiment there is incident a plane-polarized 

 ray consisting of the combination of a Ray No. I. and a Ray 

 No. II., the plane-polarized ray which is formed by their 



