PROCEEDINGS 
OF THE 
ROYAL SOCIETY OF EDINBURGH 
yol. ix. 1877-78. No. 101. 
Ninety-Fifth Session. 
Monday, 1th January 1878. 
The Eight Eev. Bishop COTTERILL, Vice-President, 
in the Chair. 
The following Communications were read :• — 
1. On Gladstone’s Theory of Colour-Sense in Homer. By 
Professor Blackie. 
2. Note on a Geometrical Theorem. By Prof. Tait. 
In “Trans. R.S.E.” (1864-5) Fox Talbot proved very simply, by 
means of a species of co-ordinates depending on confocal conics, the 
following theorem, at the same time asking for a simple geometrical 
proof. 
If two sets of three concentric circles , with the same common differ- 
ence of radii , intersect one another — the chords of the arcs intercepted 
on the mean circle of each series by the extremes of the other are 
equal. 
A properly geometrical proof may possibly be obtained by show- 
ing that the middle points of these arcs are equidistant from the 
line joining the centres. It is, of course, quite easy to build up a 
quasi-geometrical proof, but Talbot’s would be much better. 
The following investigation shows the nature of the theorem, and 
gives some elegant constructions. 
Let d be the common difference, b and c the mean radii, and a 
the distance between the centres. Then the square of one of the 
chords is easily seen to be 
y> 2 = 2c 2 (l - cos (O' ± $)), 
4 B 
VOL. IX. 
