125 
by our previous reasoning; thus we shall find 
(n = 2m +1), {2r (r — 1)?” — 2r (r — 1)"} proper solutions. 
(n = 2m), {2r (r — 1)""* — 2r (r — 1)"} proper solutions. 
For example, the problem to inscribe on a conic a triangle 
whose side shall touch a given curve of the third class admits 
of twelve proper and twelve improper solutions. If the number 
of proper solutions exceeds this number, the problem becomes 
porismatic: that is to say, there is an infinite number of 
solutions. 
We Kae. 
Professor Cayley spoke of the importance of Mr Clifford’s 
remarks. 
The President exhibited some photographs of the transit of 
Mercury, taken at Ely, and described the manner in which they 
were taken. 
The Astronomer Royal said that when a small planet ap- 
proaches the edge of the sun’s disk, a black line is observed to 
shoot out from it, and rapidly thicken out. The cause of this is 
irradiation, by which the sun appears larger and the planet 
smaller than they ought, and the true contact with the sun’s rim 
takes place when the black line is first seen; he thought the 
appearance simply ocular, but wanted further evidence. 
Professor Cayley exhibited a model of a certain developable 
surface. 
November 23, 1868. 
The PRESIDENT (PROFESSOR SELWYN, D.D.) in the Chair. 
New Fellow elected : 
A. MarsHaLy, M.A., St John’s. 
Communications to the Society : 
(1) On the comparatively recent date of the period when 
the works of Greek authors were first committed to 
writing. By C. A. M. Fennewn, M.A. 
