as applied to Micrometric Observations. 445 



whence the intensity of light 



4A 2 i 2 A* 2™ , . . 9 2*k, N . ,2tA, 



I = ~T7 — , \2? — i — ^2 cos "FT W + w ) Sln T^ - (? + v ) sm ~TT" (P 



This may be written 



64AW 2™ , x Sm Tx ^ v) Bm !x ( ^ + " } 





This gives fringes parallel to x and y : k being very small 

 compared with a, the quick variation term in v is 



2 27ra , . 

 ° TxT ^ + ^- 



Consider the other two factors, namely : 



sin^-7— (g -f r) sm 2 -^— (p + u) 



and 



sin <27 

 If we draw the curve y= — %~ (see fig. 2), we see that 



OS 



these factors are only sensible, and therefore their product is 

 only sensible, for values of p + u and q + v which are numeri- 

 cally less than bX/2h and bX/2k respectively. 



Fig. 2. 



Hence the intensity becomes very small outside a rectangle 

 whose centre is the geometrical image and whose vertical 

 and horizontal sides are bX/k and bX/h respectively. 



This rectangle I shall refer to as the " visible " rectangle of 

 the source. 



Inside this rectangle are a number of fringes, the dark 

 lines being given by 



q -f- v = — -. bX 



* 4« 



and the bright ones by q+ v = nbX/2a. 



