190 Proceedings of the Royal Society of Edinburgh. [Sess. 
corresponding element of the surface of the sphere of radius a, centre C, 
as indicated by the two close diverging rays from E in fig. 9. 
Let /3 be the angle CEP and 0 the angle of incidence of the ray at P, 
so that the angle PCE has the value (0 — /3). 
The energy which passes across the annulus of area 
(b — a)df3 . 2tt(& - a) sin f3 
at position Q falls on the annulus of area 
ad(6 — (3 ) . 27 ra sin (0— (3) 
at position P, so that for every unit radiating across the unit area at Q 
there falls on unit area at P the amount 
(b — a) 2 d(3 sin (3 
Now 
a 2 d{0 — f3 ) sin (6- (3)' 
so that 
a sin 0 = b sin (3 . 
■ ■ 0) 
ad6 cos 0 — bd(3 cos (3 
and 
d/3 a cos 0 
d(Q - /3) b cos (3 - a cos 6 
and the energy per unit surface of the nucleus is 
(b - a) 2 a cos 6 sin (3 (b — a) 2 tan f3 
a 2 (b cos j3 - a cos 6) sin {0 — /3) a(b cos j3 - a cos #)(tan 0 - tan /3) 
( 2 ) 
Equation (1) gives for each chosen value of /3 the corresponding value 
of 0 and its trigonometrical ratios, and by means of equation (2) the 
energy incident on the nucleus may be calculated. In Table VIII 
the first column contains values of fi increasing by steps of 3° up to 21°, 
the last being 23° 35', the position of the tangent line ; the second column 
contains the corresponding values of 0 , the angle of incidence on the nucleus ; 
