upon Gunpowder, See, 
Of the comparative goodnefs , or value , of powder of different 
degrees ofjlrength, 
Let V denote the velocity of the bullet with the {Longer 
powder, and put v equal to the velocity with the weaker, 
when the charges are equal, and the weight and dimenfions of 
the bullets are the fame, and when they are difcharged from 
the fame piece. If the charge is augmented when the weaker 
powder is made ufe of, till the velocity of the bullet is in- 
creafed from v to V, or becomes equal to the velocity with the 
given charge of the {Longer powder, the value of the charges 
may then be faid to be equal ; and confequentiy the weaker 
powder is as much worfe than the {Longer, or is of lefs value 
in proportion as the quantity of it required by the pound, to 
produce the given effeff 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, 
muff be as the fquares of the velocities, and confequentiy the 
charge of the weaker powder muff be to that of the {Longer, 
when the velocities are equal, as VV is to vv. The weaker 
powder is therefore as much worfe than the {Longer as VV is 
greater than vv ; or the comparative goodnefs of powder, of 
different degrees of {Length, is as the fquares of the velocities 
of the bullets when the charges are equal. 
The mean velocity of the bullets, as {hewn by the pen- 
dulum in the 104th and 105th experiments, when the piece 
was fired with 145 grains of government powder, was 894 feet 
S f 2 in 
