288 Charges of greatest Efficacy for Artillery at Sea , 
al time be greater, yet in any considerable time the whole 
effect would be less than that from a smaller charge of- 
tener fired, on account of the extreme heat it would give 
to the engine after a few discharges ; and in consequence 
of which, greater time would be required for cooling the 
gun and preparing it for further service. 
Example II. 
j Required the charge for a 2^-pounder shot to burst open 
the gates of a city with the greatest ease possible , they be- 
ing of e lm one foot thick. 
Here the object to be penetrated being elm, the small let-, 
S dv 2 w ( (S+-JI ))dv 2 w\ 
ters in the general formula s p,x 16 oy (=-^o<l600 8 J : 
must be made to denote the several numbers of some ex- 
periment made in the penetration of this substance. Ta- 
king, therefore, the experiment of Dr. Hutton contained 
in the 5th problem of his elegant Exercises on Forces, 
1 13 
we have d ~ -g-ft. v zzl500, and Sz —ft. ; also by the 
question S n: 1 ft. Dm *46, and w m 24 lbs. therefore 
(S+fD) dv 2 w 1 *23 x-Jx 1 500 2 X S4__830*25 _ ^ • 
SDsxl600 3 — 3x-46xifxi600 2 ~ '191-36 — 4 ' 338681bs - 
or 4lbs. 5|ozs. nearly the weight of the charge required 
in this ease. 
Retaining the experiment of Dr. Hutton as a standard 
for all cases where the substance to be penetrated is of 
elm, we shall have by reduction 
(S-fJD) dv 2 w 
21)7x1600*“ 
n-0670 
x 
(S+ID)w 
the charge for any piece the diameter of 
/ 
whose shot is D, and weight w : S being the thickness 
of the object as before. 
