PNEUMATICS. 269 



things being " the same, is nearly as the square root 

 of the weight of the gunpowder, or more generally, 

 if v be the initial velocity of the shot, P the weight 

 of powder, and B the weight of the ball, that 



/ P 



v=:my ~-; m being a constant co-efficient, to be 



determined by experiment. 



Philosophical Transactions, 1778. Also BUTTON'S 

 Course of Mathematics, vol. m. p. 270. 



/ T* 



Now that v = mL/ , is exactly the conclusion that 



would be deduced, from supposing the acceleration 

 of the ball to depend simply on the expansion of the 

 elastic fluid, without taking into account the dimi- 

 nution of the impulse, arising from the velocity 

 which the ball has already acquired. This may be 

 shewn from the Principles of Dynamics ', 100. 

 That diminution, therefore, is inconsiderable, which 

 arises no doubt from this, that the velocity acquired 

 by the ball is very small, compared with the im- 

 mense velocity with which the elastic fluid in the 

 gun expands itself. 



The value of v given above, is only exact on the sup- 

 position, that the piece is long enough to allow the 

 elastic fluid generated by the gunpowder to pro- 

 duce its full effect. The augmentation of the 

 charge may so much lessen the space over which 

 the fluid is to act, that the velocity of the ball 



shall 



