474 The Astronomer Royal on the Equations 



which agree in giving 



Hence «/ x is less than v" 1# 



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



it; 27T / #\ 



Y' = — a.cos — it + -J-), 



T \ U' 2 /' 



ry; • 2 7T / , # \ 



Z/ = a . sin — u + -T- J. 



T V t/ 2 / 



The equations become 



, 4?r 2 2w/ .r\ . 4tt 2 / 1 \ 2 2w/ *\ 



+ ^-cos v ^ + ^ = +A^-.^j«.cos T ^ + ^j 



n 87T 3 /1\3 2*/ tf\ 



4w* . 2tt/ a;\ 47r 2 /l\ 2 . 2*/ , f\ 



8^ /l\s . 2*/ *\ 

 which agree in giving 



w 



l + B 2 



2*/iy* 



And similarly, for Ray No. II., 



B 2 





Hence t/ 2 is less than r/' 2 . 



Thus in both experiments (that is, whether the light passes 

 from one side or from the other side) the Ray No. II. travels 

 more quickly than the Ray No. I. And therefore, 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 union after emer- 

 gence will have its plane of polarization turned from the ori- 

 ginal plane of polarization, in both experiments in the same 

 direction as the hands of a watch, or in both experiments in 

 the direction opposite to that of the hands of a watch, as re- 

 ferred to the eye of a person looking in the direction of the 

 path of the light. 



This result agrees with the phasnomena of quartz, turpen- 

 tine, &c. ; and therefore Prof. MacCullagh's equations apply 



