upon Gun-powder^ &c. 
3°3 
Pf the comparative goodnefs, or value , of powder of differ mX 
degreesof Jlrength, 
.[h 
Ify 
Let V denote the velocity of the bullet with the ftrbriger 
powder, and put v equal to the velocity with the weaker, 
when the charges are equal, and the weight and dimeniiohs of 
the bullets are the fame, and when they are difcharged ' from 
the fame piece. If the charge is augmented when the Maker 
powder Is made ufe of, till the velocity of the bullet is ih- 
creafed from v to V, or becomes equal to the velocity with tlte 
given charge of the ftronger powder, the value of the charges 
may then be fa id to be equal ; and coufl quen tly the Weaker 
. powder is as much worfethan the ftron^ej-* or is of lefs Value 
in proportion as the quantity of it required by the pound, to 
'produce the given effect is greater. _ . 
But it is well known, that the velocities, with different 
■ quantities of the fame kind of powder, are in the fub-duplicate 
ratio of the weights of the charges. The charges, therefore, 
muft be as the fquares of the velocities, and confequently the 
' charge of the weaker powder muft be to that of the ftronger, 
when the velocities are equal, as VV is to m. The weaker 
powder is therefore as much worfe than the ftronger aS VV is 
greater than vv ; or the comparative goodnefs of powder, of 
different degrees of ftrength, is as the fquares of the velocities 
of the bullets when the charges are equal. 
The mean velocity of the bullets, as fhewn by the pen- 
dulum in the 104th and , 105* experiment?, when the piece 
.was fired with 145 grains of government powder, was 894 w 
S f 2 m 
