542 
Proceedings of the Royal Society 
volume and a surface integral, the limits being determined by any 
simply continuous closed space : — 
fff^Tds=ff Uj/ rds. 
If in this equation we assume r (which is arbitrary) to be equal to 
Uv at every point of the surface, we have 
r = Uv = UVP 
where P = C is the (scalar) equation of the surface. The equation 
then becomes 
^7'VU(VP)(fs= -ffds. 
Applied to the ellipsoid — 
x 2 y 2 z 2 _ 
— v— -i — = 1 
a 2 h 2 e 2 ’ 
this gives for the whole surface the expression- 
x 2 ( 1 
7-0 + 
fffdxdydz 
a 4 \6 2 
2/7 1 , 1 
+ fr 4 \ c 2 a 2 
dKa 2 h 2 
(x 2 y 2 z 2 \ f 
U + fs + ?) 
the limits being given by the equation of the surface. 
6. On a White Sunbow. By Sir Bobert Christison, Bart. 
As the phenomenon of a colourless rainbow, which was seen here 
in the forenoon of Thursday the 10th January, seems to be very 
rare, never having been witnessed before either by myself or by 
any of my friends to whom I have mentioned the subject, I beg to 
offer the Society the following description : — 
On my way that forenoon to the Botanic Garden, and arriving 
about a quarter-past eleven at the open view of the north at the 
bottom of Pitt Street, my attention was arrested by the appearance 
of a magnificent white bow, visible in its entire arch from end to 
end in the northern sky. 
The air was frosty, very dry, uncommonly still, and in most quarters 
moderately clear. The smoke of the Old Town, however, rising 
high in the stillness above the ridge of the High Street to the south, 
obscured greatly the sun, which shone through the upper region of 
