148 
The case of the catenary curve for a heavy rectangular sheet 
suspended by two of its opposite sides from two parallel hori- 
zontal straight lines is easily and concisely discussed from these 
equations, 
The case of the “curva velaria” of James Bernoulli is easily 
investigated by means of them. 
The case of the form which a piece of bladder tied over the 
circular aperture in the receiver of an air-pump, when a portion 
of air is withdrawn from the interior, depends on the difference 
of the pressures on the internal and external surfaces, and the 
nature of the surface to bear them. When the form the bladder 
takes is known then the tensions at given points are found from 
the formule. 
The phenomena of capillary attraction being those of flexible 
surfaces, the results which the author had obtained by longer 
methods of procedure are more concisely investigated by means 
of these equations. 
May 10, 1869. 
The President (Professor SzLwyn, D.D.) in the Chair. 
New Fellows elected: 
RICHARD SHILLETO, M.A., St Peter’s College. 
THomas M‘Krnny Hucues, M.A., Trinity College. 
Communications made to the Society : 
(1) On a Group of Figures with archaic imscriptions 
on one of the Leake Vases in the Fitzwilliam 
Museum. By Mr Patey. 
This vase has been described as “the invasion of Troy by Her- 
cules.” Mr Paley thought it perhaps rather the conflict of Her- 
cules with the Amazons. The interest of it was that it bore 
in some respect on the Homeric question; for it alluded to 
a legend mentioned by Pindar but not by the Homer whose 
works we now possess. Mr Paley first spoke of the purpose 
of vases in tombs, doubtless to contain food for the use of 
