10 



ART. ?.. ATCHT AND TANAKADATE : THEORY OF 



deviation, so tliat Airy 's theory applies. It is most convenient, 

 in this case, to neglect the visual angle of the drop. Take the 

 Fiçr. 1. elementary area of the projection s of 



the source on the unit sphere, s be- 

 ing that of the centre of tlie circular 

 source, and denote the angle between 

 s s and so by (/', the angular distance 

 between s' and s by (p, the angle sco 

 by Tf — d and the angle s'fo by D — x. 



Then, in the spherical triangle ss'o, 

 we have the relation 



cos (D — x) — coRcr cos(D — 0) + sxxKp sin(D — ^)co?ç^ , 

 which reduces to the form 



x = 6 + <p cos</', 

 since x, 6, (p are small. 



The intensity of light at o due to the elementary area s 

 which is equal to (f d(p d4', is expressed by 

 i (Ö)= const. Af\y.x) 



from whicli it follows at once as the expression for the total 

 intensity in the direction co, that 



1(6, 0)=const. AF(/, (D, xd) (4) 



where F(;^,0,/^) =-^ J J^^ ^r/^#/2|^(ö + ^coss^)j. , (4J 



/2{z(/? + ç'Cos^'')} = I cos J^ <u"--y.{d + (fC0S</')îii(l2c . 



Thus the function /- in Airy's theory is replaced by a 

 more general function F. From tlie form of the function /^ 



