Si (a?) = g- — cos x < - — 



— sm # 



1 



a? a? 



1.2.3 



1.2 1.2.3.4 1.2 



6 



Retardations , a>ze? on ^A^ Theory of Foucaulfs Test. 169 



available when <# is moderate. When # is great, we may 

 use the semi-convergent series 



(16) 



X 



+ 



1.2.3.4.5 



fl 12 

 Ci(#) = sin # J -V- + 



\_x x s 



[1 1.2. . 

 U' 2 ^ 4 



1.2.3.4 ^ 



"*'J 



cos<r 



+ 



1.2.3.4 



■•}■ 



Tables of the functions have been calculated by Glaisher*. 

 For our present purpose it would have been more convenient 

 had the argument been irx i rather than x. Between x=5 

 and #=15, the values of Si(a?) are given for integers only, 

 and interpolation is not effective. For this reason some 

 values of (/>/# are chosen which make (J + <£/0)7r integral. 

 The calculations recorded in Table I. refer in the first instance 

 to the values of 



Si(l + <£/0)7r+8i(l-<£/0>r. . . . (18) 

 Table 1. 



■ <p/0. 



(18). 



(i*) 2 . 



00000 



3704 



13-72 



0-2732 



3-475 



12-08 



0-5000 



2-979 



8-87 



0-5915 



2-721 



7-40 



0-9099 



1-707 



2-91 



1-0000 



1-418 



2-01 



1-2282 



0758 



0-57 



1-5465 



0-115 



001 



2-0000 



-0177 



003 



It will be seen that, in spite of the fact that nine-tenths of 

 the whole light passes, the definition of what should be the 

 -edge of the field at cj> = 6 is very bad. Also that the illumi- 

 nation at </> = is greater than what it would be (V 2 ) if the 

 second screening were abolished altogether f + f=oo). 



So far we have dealt only with cases where the second 



* Phil. Trans, vol. clx. p. 367 (1870). 



