TO SPECTEOSCOPIC MEASUBEMENTS. 9 



From this it will be seen that the focal plane varies very rapidly with /, so 

 that, unless 'f =0, it is impossible to see all parts of the interference bands in 

 focus with equal distinctness. If, however, cp =0, that is, if the two sm-faces 

 are strictly parallel, then P=oo, and if the observing telescope is focused 

 for parallel rays, all parts of the bands are equally distinct. Under these cir- 

 cumstances the interference fringes are concentric circles, whose angular 

 diameter is given by 



cos * = ^. 



If for A we put 24— n\ and for cos %•, its approximate value 1 — -^, 



we have *„=\/'?l\ 



In order to obtain an idea of the order of accuracy required in this ad- 

 justment, suppose the angle %■ to be so small that its influence on the dis- 

 tinctness may be neglected. The intensity at the focus of the observing 

 telescope will be 



1=11 eos^ ^ V. A dx dy, where x = ~. 



If the aperture be a rectangle whose height is 26, and width 2a, 



I=2b f^cos'iyt. Adx. 



But A=2(fo + '^x), 



whence I=2b [a + cos2v. U ^i^l^L^iUL 



L 2% 'f 



The maximum value of / is 



L 2x rp _ 



and the minimum value is 



sin 2% 9 a 



2& 



a- 



2-iC 'f J 



whence y^ sin2-^'?a ^ 



2v.'f (I 



In attempting to verify this formula by actual observation, one is met by 

 the difficulty that all parts of the bands are not m focus at the same time, 

 the right and left bands being more distinct than the central one, to which 

 attention ought to be directed. Notwithstanding the rather rough character 

 of the observations, the results agi-ee fairly well with theory. If 's„ is the 



