\ 
3 iq Mr. Thompson’s Experiments 
upon the bullet at the moment of the exploflon. If now we 
fuppofe,, that while the bullet moves on from P towards B, the- 
line PM or pm, goes along with it, and that the point m is 
always taken in fuch a manner that the line pm, fhall be to 
pl , . or PL, as the force ading upon the bullet in the point p r 
is to its weight, till pm, coincides with QB, then will the 
area PMQB be to the area PLDB in the duplicate proportion of 
the velocities which the bullet would acquire when aded on by 
its own gravity through the fpace PB, and when impelled 
through the fame fpace by the force of the powd,er, as may 
be feen demonftrated by Sir Isaac newton, in hisMatheraa- 
tical Principles of Natural Philofophy, book I. prop. 39. 
Now what I call the collective prelture, or fum total of the 
aCtion of the powder upon the bullet, is the meafure of the 
area PMQB ; and it is plain, from what has been faid above, 
that its meafures are in all cafes to be accurately determined,, 
when the weight and velocity of the bullet are known. 
If all the powder of the charge was inflamed at once, or be- 
fore the bullet fenfbly moved from its place ; and if the pref- 
fure of the generated fluid was always as its denflty, or inverfely 
as the fpace it occupies, then would the line MQbe an hyberbola, 
the area PMQB would always be the fame when the charge 
was the fame, and confequently the velocities of the bullets 
would be as the fquare roots of their weights inverfely. But 
it appears, from the before mentioned experiments, that when 
the weight of the bullet was increafed four times, the action 
of the powder, or area PMQB, was nearly doubled ; for in 
the 9 2d experiment, when four bullets were difcharged at 
Once, the. coliedive preflure was as 1 ; but in the 89th experi- 
ment, when a Angle bullet was made ufe of, the colledive 
