Bessel- Clifford Function, and its applications. 521 

 with a. — TTrt 2 . j3 = ttA 2 ; and the vibration at P is 



27T 



2ircadaG(x) cos — — (Yt — b), .... (5) 



of amplitude cdaC(x), where da is the area of the slit. 



If the slit grows in breadth to an annnlus between the 

 radii a and a', and circles a and a', the amplitude of the 

 vibration diffracted through it to P becomes 



,fW^7 C ^V P "P n «'I3\ 



c } a c m) d " = 7'l c - i vr c - i 3?p) 



A similar result will hold if the circular hole is filled with 

 a lens, of focal length b ; and then 



T (2iraA\ 



c M-ZOL) m 



Xb 



The first root of J 1= =0 being 3*8 =1'22 ?r, the area /3 



of the first diffracted circle is given by 



r (8) 



subtending a conical angle /3 _ (1*22 x ^ttX) 2 \ 

 in the sky. p — ^~ ~~ '' 



equivalent to an angular radius S, such that 



sin 8 = P22^ (9) 



2a 



In seconds of angle, taking A, = 5 X 10~ 5 on the average, 



a// 206265 x 1-22 x5xl0' 5 12-6 /im 



S = " 2a" = !«' * ' (10) 



say S = l"i for an object-glass 10 cm in diameter. 



For the pupil of the eye, take 2a = 0*3 cm, 8 = 43" 

 (Schuster, 'Optics'). 



These considerations of definition and separation of image 

 are required in the working of the Barr and Stroud range- 

 finder. 



If a range of R yards is to be measured within /\\\ yards. 



