361 
with Professor Downing, and conversed on guns, &c., in April or May, 
1855. 
The third shows the design in accordance with which the mortars 
were completed subsequently to the bankruptcy of the first contractor 
in December, 1855, and in which Mr. Mallet reverted fully to the prin- 
ciple of the original design; and having in the interval had his ideas on 
the subject. of construction with initial tension enlarged and made exact 
by the mathematical investigations communicated to him by Dr. Hart, 
6th July, 1855, was enabled to develop the principle completely in both 
the chase and chamber, by constructing both in several successive plies 
extended and compressed. 
A.§. Hart, LL. D., Professor Jellet, and Rev. 8. Haughton, made 
some remarks on Mr. Mallett’s and Captain Blakely’s communications. 
The Academy then adjourned. 
MONDAY, NOVEMBER 12, 1860. 
James Henroorn Topp, D. D., President, in the Chair. 
Mr Hennessy, F. R.S., read a paper— 
ON A THEOREM RELATING TO CONICAL SURFACES. 
Tue Theorem is announced as follows :—‘‘If a cone of maximum 
volume, under a given conical surface, roll on a plane with its vertex 
constantly touching a point in the plane, the interior envelope of the 
cone will be a second cone which possesses the property of containing a 
maximum volume under its total surface.” : 
If we denote by 0, the angle at the summit of the cone of maximum 
volume under conical surface, and by 9, the corresponding angle for the 
cone of maximum volume under total surface, we shall have 
sin 3 0, = s 
ly 
11, 2, being the respective radii of the bases, and 4,, /,, the respective 
slant heights of the cones. 
By the usual methods we easily find 
n= eh rg=—l 
Whence 
= 24/3 
sin 0, ==? cos $= 
R, I. A. PROC.—YOL. VII. 3r¥ 
