174 REPORT— 1892. 



rrom this ifc will be seen tliat the focal plane varies very rapidly with i, 

 so that, unless 0=0, it is impossible to see all parts of the interference 

 bands in focus with equal distinctness. If, however, 0^0, that is, if 

 the two surfaces are strictly parallel, then P=co, and if the observing 

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

 distinct. Under these circumstances the interference fringes are concen- 

 tric circles, whose angnlar diameter is given by 



cos 5'=^--. 

 If for A we put It^—vX, and for cos S' its approximate value 1 — , we have 



Wt- 



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

 adjustment, suppose the angle •& to be so small that its influence on the 

 distinctness may be neglected. The intensity at the focus of the observ- 

 ing telescope will be 



1= cos^ \K^dxdii, where Z; = — - . 



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



I=2&['^"cos2 \K\dx. 



But 



A=2 (^0 + <^ ■^), 

 whence 



The maximum value of I is 



and the minimum value is 



whence 



T oi, ■" I o < sin 2kd)a~| 



1=20 I a -H cos IkIq --- — ^_ . 

 L 2c<^ J 



'I is 



f), r , sin 2(>-<ia~l 



in 2/v-^a"] 



2h\a 



sin 2K<^a 



2K:(^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 observations, the results agree fairly well with 

 theory. If <^o is the ratio of the wave-length to the width of the rectan- 

 gular aperture, the above formula becomes 



V = si n 27r(^ /^o 



