Interference Methods to Spectroscopic Measurements. 285 



rapidly with i, so that, unless $ = 0, it is impossible to see all 

 parts of the interference-bands in focus with equal distinct- 

 ness. If, however, <f> = 0, that is, if the two surfaces are 

 strictly parallel, then P = 00, and if the observing-telescope 

 is focused for parallel rays, all parts of the bands are equally 

 distinct. Under these circumstances the interference-fringes 

 are concentric circles, whose angular diameter is given by 



cosS=A. 



If for A we put 2t — riX, and for cos 3 its approximate 

 value 1 — ~ , we have 



-^ 



i=jj 



rik 



In order to obtain an idea of the order of accuracy required 

 in this adjustment, suppose the angle 3 to be so small that its 

 influence on the distinctness may be neglected. The intensity 

 at the focus of the observing-telescope will be 



2<7T 



cos 2 ^tcAdxdi/, where k— -^ • 



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

 2a. 



I=2M cos 2 |/eAd<r. 



«/ —a 



But A = 2(£ + </>^), 



whence T n7 f , . sin 2k(J)o~] 



1 = 26 a 4- cos 2tct — k~6 I 



The maximum value of I is 



„ 7 f sin 2K(ba~\ 



and the minimum value is 



~ 7 r sin 2/e<baT\ 



2 T — i^jrJ' 



whence v _ sin 2ic§a 



2ic§a 



In attempting to verify this formula by actual observation, 

 one is met by the difficulty that all parts of the bands are not 

 in 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 



Phil. Mag. S. 5. Vol. 34. No. 208. Sept. 1892. X 



