142 Proceedings of Royal Society of Edinburgh. [sess. 
contact will be equally inclined to the axes ; and from these facts 
the conditions are easily found to be a = b = 3/4. 
In the cubic x 3 + q'x + r' = 0, put x = \y, then 
y 3 + (q'/X 2 )y + (r'/X 3 ) = 0 . 
Put q/X 2 = ±1, that is X = (±q) 112 , and the equation reduces to 
y 3 ± y + r = 0 . This may be solved graphically by means of the 
fixed curves y 3 = x and the straight line x ± y - r = 0 . 
Notes on the Zodiacal Light. By Prof. O. Michie Smith. 
(Read April 7, 1890.) 
So much has been written on the zodiacal light that it may 
appear rather rash to say that a really accurate examination of this 
phenomenon has yet to be made. Still I have no hesitation in 
saying that neither its position, its shape, nor its spectrum has yet 
been determined with sufficient accuracy. In the hope of being 
able to add something to our knowledge of the last of these, I 
obtained, in 1882, a grant from the Government Grant Fund for the 
construction of a spectroscope specially designed for observing and, 
if possible, photographing the spectrum of the zodiacal light. 
The apparatus, which was made by Mr A. Hilger, consists of two 
interchangeable collimators of 36 inches and 8 inches focal length 
and 1 \ inch aperture ; an Iceland spar prism inch high, 
2J inches side, a camera with a lens of 8 inches focal length, and an 
observing telescope and a heavy glass prism which can be used for 
eye observations. The camera and telescope are fixed to a common 
base movable about a pivot concentric with the pillar carrying the 
prism, so that they are readily interchanged. The lenses are all of 
quartz, and the dark slide carrying the sensitive plate can be placed 
at such an angle that the whole or at least a considerable part of 
the spectrum is in focus at the same time. The slit is provided 
with shutters for exposing any required portion alone, and the 
jaws of the slit both move equally, so that the centre remains fixed 
in position. A photographed scale can be thrown in in the ordinary 
way, but I have found this useless when dealing with faint spectra, 
since any illumination which will render the divisions visible quite 
obliterates the spectrum. After trying various plans I finally 
