Retardations, and on the Theory of FoucauWs Test. 177 

 Table IV. 

 tf0fi = 7r, *0f 2 = 5OO. 







0- 



Formula for Vibration. 



I. 



I. 



sin p. 



sin p. 



4--1. 



-•1. 



4-1/ V2. 



- 1/ V2. 

 58-9 

 58-0 



23-4 



9-0 



5-5 



2-3 



1-2 





 •001 



•010 



•050 



•100 



•250 



•500 



sin T{ — -56 cos p + 1029 sinp} 



sin T{ - -56 cos p + 10-16 sin p } 

 4- cos Tx "99 sinp 



sin TJ — '56 cos p + 5 - 53 sinp} 

 4- cos Tx 3-10 sinp 



sin T { — '55 cos p + 2*71 sin p } 

 + cosT{— -10 cos p 4-2-83 sinp} 



sin T{ - '53 cos p + 1-37 sin p } 

 + cos T{ - -20 cos p 4-2-52 sin p } 



sin T{ - -37 cos p — -17 sin p } 

 4- cos T{ - -46 cos 4-1-66 sin p} 



sin T{ 4- '16 cos p — '67 sin p } 

 4- cos T { - -67 cos p 4- -64 sin p ( 



•22 



•22 



-10 

 •11 

 •16 

 •23 



•38 



253 

 2-50 



1-34 



•83 

 •66 

 •52 

 •59 



47-3 

 46-6 



172 



6-0 

 30 



•86 

 •13 



It will be seen that the direction of the discontinuity 

 (<£ = 0) is strongly marked by excess of brightness, and that 

 especially when p is small there is a large variation with 

 the sign of p. 



Perhaps the next case in order of simplicity of a variable 

 R is to suppose R = from 6——Q to = 0, and R = o-# 

 from = to 0= +6, corresponding to the introduction of a 

 prism of small angle, whose edge divides equally the field of 

 view. For the vibration in the focal plane we get 



rl— cos(f— a)0 1— cosftf 



+ cosT 



]■ 



(36) 



S—r i 



In order to find what would be seen in direction <£, we 

 should have next to write (T 4- </>£ ) for T and integrate again 

 with respect to f between the appropriate limits. As to this 

 there is no difficulty, but the expressions are rather long. 

 It may suffice to notice that whatever the limits may be, no 

 infinity enters at <f> = 0, in which case we have merely to 

 integrate (36) as it stands. For although the denominators 



Phil. Mag. S. 6. Vol. 33. No. 194. Feb. 1917. N 



