279 
1912-13.] The Scattering of Light. 
In equation (4) let i the light-intensity equal \o 2 h, where a is any 
constant. Combining this with (3), we have 
J 
1 CM | 1 
2) 
2 ^ 
fx\ 
w 
‘] 
J\ 
U 2 -2I 
© 
| 2 + 1 
(x\ 
w 
•] 
l-‘ 
Disregarding powers of x/a greater than the sixth, and putting /a = 3/2, 
we have 
^ = 2 - 82 s (- N ) + 3m(-Y + 2-w(-) 5 . 
ax \a J \a / \aj 
1 = l-4Hp) 2 + -765(5Y + -493(?) 6 . 
The radius of curvature at the origin p 0 is given by 
Po = 
1 
d?y\ 
da?\ 
= *353a. 
o 
It is evident that the constant a merely determines the scale and not 
the shape of the cavity. Therefore, putting it equal to unity for convenience, 
we obtain p 0 = ‘ 353, and 
X 
0 
T 
•2 
•25 
•3 
•37 
y 
'0000 
•01421 
•05708 
•09150 
•1338 
•2094 
This is plotted as C, fig. 6, the side of a large square being taken as equal 
to T. The comparison of this curve with the others is instructive, represent- 
ing as it does a sort of upper limit for all such cavity curves. The difference 
of scale must, of course, be kept in mind ; for example, if C were drawn in the 
same way as A and B, with the side of a large square as the unit of length, 
then its radius of curvature at the origin would only be a 43rd of that of B, 
and a 65th of that of A. 
In the case of experimental curves such as A and B, it is not easy to 
find the curvatures at points other than the origin with accuracy ; but that 
the curvature changes rapidly, or in other words that there is a marked 
departure from the circular form, can be seen by considering the light- 
intensity distribution that would be given by a hemispherical cavity. In 
such a case we have, putting ^ = 3/2, 
