416 
MINUTES OF PROCEEDINGS OF 
But 
cPcf) _ 7vr d?z' 
dfi Ji ’ dft 5 
and making the necessary substitutions, we obtain for the ratio between the 
forces producing potation and translation, 
-K =- ^ ---... (26) 
G .W 
sin — 
IH - (Z-xpVc - rX) + _ T , t _ (2m>* s i n 1 + rm 
Vi.+ tf /, 3 , /. »v B 
V /c+ ( sm «j 
In precisely the same manner as in the former case, and on the same 
hypotheses, we may show that if G" denote the gaseous pressure in a bore 
rifled on the system we are now considering, and G denote the gaseous 
pressure in a similar smooth-bored gun, we shall have 
G" == G + R 
_ , 
(27) 
Hence if we have three guns of the same diameter of bore, viz. a smooth¬ 
bore gun, a rifled gun, the grooves of which are similar to those shown in 
fig. 1, and a third rifled polygonally, and if we suppose that the shot in each 
case are of the same weight, and further, that in each case the velocity- 
increments at the moment under consideration are equal, then the pressures 
upon the base of the shot will be as follow :—In the case of the 
Smooth-bored gun, pressure = G; 
First rifled gun, pressure = G + 
Polygonally-rifled gun, pressure 
R 
Vl + k* 
0 hh +i) > 
= G + R« 
tht 
n/ 1 -J- / 
aA+HTj 
.(28) 
We shall now give examples of the cases we have been discussing to 
exhibit numerically the above results. 
Let us suppose that two seven-inch guns are rifled—the first according to 
the method shown in fig. 1, with a pitch of one turn in 294 inches, the 
other octagonally, with a pitch of one turn in 130 inches. It is required to 
determine in each case the pressure on the driving-surface in terms of the 
pressure on the base of the shot. Now, in the first case, from (13), 
