316 
MINUTES OF PROCEEDINGS OF 
GRAPHICAL SOLUTION 
OP 
PROBLEMS ON ARTILLERY MACHINES. 
BY 
MAJOR AY. II. AYARDELL, R.A., 
INSTRUCTOR IN MATHEMATICS AND MECHANICS, R.M. ACADEMY. 
It] ias been suggested to me that the graphical solution of the following 
simple problems—extracted from a pamphlet drawn up for the use of the 
Gentlemen Cadets of the Royal Military Academy—might prove of some 
interest to the regiment at large. 
The convenience of this method will be evident if we compare the labour 
required to obtain numerical answers from some of the analytical expressions 
for the various strains, &c., with the simple process of constructing a diagram, 
and measuring off the results upon the scale used. This scale need not be a 
large one; the space afforded by a half-sheet of foolscap, together with 
the aid of a pencil and graduated rule, will enable us to ascertain the con¬ 
ditions of equilibrium, in any given case, with rapidity and great accuracy— 
in fact, the problem may be solved in much less time than is required to 
describe the process. 
The mode of solution here indicated may be extended to particular questions 
which arise in the transport and mounting of heavy ordnance. 
Analytical investigations of some of the following problems were, a few 
years since, published in these papers, which were cumbrous and not quite 
accurate; I have therefore thought it well to insert a short analytical solution 
in each case, dependent only on simple trigonometry and the most elementary 
principles of mechanics—avoiding altogether the use of co-ordinate axes. 
Hydraulic Jack. 
The hollow cylinder LMNR (Eig. 5), is raised by the water pressure 
upon the solid stand or piston IIKFG, the roughened surface IM } or the 
projection at R, being placed beneath the weight to be lifted. A valve at 
R admits the water from the upper cistern to the passage underneath the 
plunger RE, and there is also a valve at V, supported by a spiral spring, 
which allows the water to pass into the lower cistern when the least pressure 
