600 Messrs. Aichi and Tanakadate : Theory of 
i ne Th 1 
f (KO) =2?3-4(K6) *M cos (u- a ae sl 
KA@\3 
Behe Ni 
M=1—0:03474-?, tand=0-0694y-): 
where 
or, approximately, 
| pe ones ‘K@\: 1 
S KO) = 273—-4(K0)—* cos nf *) sain 
It must be remarked that both expansions only represent 
J(K@) for @>0. But for 0<0, f(K@) being a function having 
no characteristic property, itis at once seen that no important 
difference between a point and a circular source makes its 
appearance. In the following discussion the places where 
@<0 are therefore excluded from consideration. 
3. Passing now to the case of a circular source, the apparent 
diameter of the source 2® will be supposed so small that we 
can neglect *, and confine our attention to the neighbourhood 
of the minimum deviation, so that 62=0,cos@=1. Take the 
elementary area of the projection S’ of the source on the 
sphere, 8 being that of the centre of the circular disk, and 
denote the angle between S/S and SO by y, the angular 
distance between S/and §S by ¢, and the angle S’CO by D— «. 
Then we have the relation 
cos (D)—.w) =cos ¢ cos (D— 6) +sin ¢ sin (D—@) cos, 
which reduces to the form 
v=O+¢ cos , 
since a, 0, @ are very small. 
The intensity of light at O due to the elementary area S/ 
which is equal to @d¢dyp, is expressed by 
x! 
igdgdy (9) = const.( fax) f2(Ke) = const.( jax) f2{K (6 +¢ cos }; 
from which it follows at once as the expression for the total 
intensity at O, 
iz 
I(0, ®) =const. ( Pr 
