of Edinburgh, Session 1863-64. 
181 
4. On Fermat's Theorem. By Professor Tait. 
The author stated that in consequence of Legendre’s work, the 
proof of Fermat’s Theorem is reducible to showing the impossi- 
bility of 
when m is an odd 'prime, x, y, 2 being integers. 
Talbot has shown that in this case x, y, z are necessarily com- 
posite numbers. 
The author shows, among other results of very elementary pro- 
cesses, that if numbers cati be found to satisfy the above equation, 
X and y leave the remainder 1 when divided by m ; and that ^ 
has m as a factor. Many farther limitations are given on possi- 
ble values of x, y, z — the process being based on the consideration 
of their prime factors, and on Fermat’s Elementary Theorem 
- N = Nw. 
5. Professor Archer called attention to a curious binocular tele- 
scope, bearing the following inscription : — 
PETRVS PETRONVS 
SAC : ET CATi= 
MAIES^? OPTICUS 
MEDLANI 1726 
The eye-pieces and object-glasses, each in a separate tube, worked 
in a case 15J inches in length by 5 inches in breadth, and 2 in 
depth, forming, with the bevelled corners, a flat octagon, covered 
with a species of shagreen, and mounted in silver. An exceedingly 
simple and ingenious arrangement, consisting of a double screw 
working four small arms of brass, was placed at each end for the 
purpose of regulating the distances between each pair of glasses, 
and silver dial plates enabled the operator to set the instrument 
according to his ascertained requirements. The instrument belongs 
to the Eoyal Institution of Liverpool, and is supposed tc have been 
part of a collection of rarities, made by Win. Eoscoe, in Italy. 
As a telescope, it is of great power ; the focus is adjusted by one 
portion of the case acting as a draw-tube within the other part. 
The following Gentleman was elected a Fellow of the 
Society : — 
William Wallace, Ph.D., F.O.S. 
2 A 
VOL. V. 
