40 Mr. W. Baily on Starch and Unannealed 



of the axes of the ellipse makes with the axis major, and the 

 direction in which the rotation takes place. 



Let the angle SRP = <J»; produce R P to X and draw P Y 

 J.PX; take any point Q on the ellipse, let P Q=^ and the 

 angle QPX = 0. 



The resolved part of the vibration at P along R P has been 

 retarded in passing through the body differently to the resolved 

 part perpendicular to R P. Let the resolved part along R P 

 have been retarded by a quantity a more than the mean amount, 

 and the other part have been retarded by the same quantity 

 less than the mean amount. The quantity a is a function of 

 the distance R P. 



Let sin t represent the vibration in the aether after the light 

 has passed through the Nicol. This is equivalent to 



cos p sin t || SS' 

 and 



sin p sin t || TT'. 



After passing through the quarter-undulation plate the 

 vibrations become 



cos p sin (£ + 45°) || SS' 

 and 



sin^sin^-45 ) || TT'. 



These may be written (the coefficient — —^ being omitted) 



cos p (sin t + cos t) || SS' 

 and 



sin p (sin t— cost) || TT'. 



It is easy to show that these vibrations represent motion in 

 an ellipse whose axes are parallel to SS' and TT', and the ex- 

 tremities of whose axes are joined by a line making an angle 

 p with the axis major. 



These vibrations are equivalent to 



cos (p - <f>) sin t + cos (p + (j>) cos t || PX 

 and 



sin (p — <£) sin t — sin (p + <£) cos t \\ P Y. 



After passing through the body the displacement || PX is 

 r cos 6, and that || P Y is r sin 6. Hence 



r cos Q— cos (p — (f>) sin (t + a) + cos (p + <£) cos {t + cr), 



rsin0= sin(/> — <£)sin(£ — o-)— sin (p + <p) cos (t— a) ; 



which may be written 



r cos 0= a sin t + b cos t, (1) 



r sin^=a / sin^ + ^ / cos^, (2) 



