Charges of greatest Efficacy for Artillery at Sea . 
Lemma II. 
The whole spaces or deaths to which spheres impinging 
on different resisting substances penetrate ; are as the 
squares of the initial velocities, the diameters and specific 
gravities of the spheres directly, and the absolute strengths* 
n 7 S V 2 D 
of the resisting substances inversely ; or, — zz-^s* x 
N r 
x — x 
n R 
S V 2 f 
For by mechanics we have — z: x and by the 
f r D N 
preceding lemma jr= jr x x which substituted in 
, , . , S V* D N r 
the above it becomes — x g» 
These being premised, I now proceed to resolve the 
following most important 
Problem : 
To find a general formula which shall express the 
quantity of charge for any given piece of ordnance to pro- 
duce the greatest destruction possible to an enemy’s ship 
at sea ; it being supposed of oak substance of given thick- 
ness, and at a distance not affecting the initial velocity of 
the shot , 
V* S d n 
By Lemma 2, we have, generally, zz — x jy x 
R 
— . Also the charges of powder vary as the squares of the 
velocity and weight of ball jointly. * Hence, since it has 
* This law of variation of the charges does not exactly obtain in practice after 
a certain charge, on account of the definite lengths of the guns ; but it is presu- 
med the deviation from it, if known, would not materially affect our results. 
