108 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 



latter at is. Ofd. Mr. T. infers that Battle powder is therefore sold at the rate 

 of lOd. a pound, or4l-i percent dearer than in proportion it ought to be. 



Of the relation of the velocities of bullets to their weights. — According to Mr. 

 Robins's theory, when bullets of the same diameter, but different weights, are 

 discharged from the same piece by the same quantity of powder, their velocities 

 should be in the reciprocal sub-duplicate ratio of their weights. But as this 

 theory is founded on a supposition that the action of the elastic fluid, generated 

 from the powder, is always the same in any and every given part of the bore 

 when the charge is the same, whatever may be the weight of the bullet ; and as 

 no allowance is made for the expenditure of force required to put the fluid itself 

 in motion, or for the loss of it by the vent ; it is plain that the theory is defec- 

 tive. It is true that Dr. Hutton, in his experiments, found this law to obtain 

 without any great error, and possibly it may hold good with sufficient accuracy in 

 many cases ; for it sometimes happens that a number of errors or actions, whose 

 operations have a contrary tendency, so compensate each other, that their 

 effects when united are not sensible. But when this is the case, if any one of 

 the causes of error is removed, those which remain will be detected. 



When any given charge is loaded with a heavy bullet, more of the powder is 

 inflamed in a very short space of time than when the bullet is lighter, and the 

 action of the powder ought of course to be greater on that account ; but then a 

 heavy bullet takes up more time in passing through the bore than a light one, 

 and consequently more of the elastic fluid, generated from the powder, escapes 

 by the vent and by windage. It may happen then, that the augmentation of the 

 force, on account of one of these circumstances, may exactly counterbalance 

 the diminution of it arising from the other ; and if it should be found on trial 

 that this is the case in general, in pieces as they are now constructed, and with 

 all the variety of shot that are used in practice, it would be of great use to know 

 the fact : and possibly it might answer as well, as far as it relates to the art of 

 gunnery, as if we were perfectly acquainted with, and were able to appreciate, 

 the effect of each varying circumstance under which an experiment can be made. 

 But when, concluding too hastily from the result of a partial experiment, we 

 suppose with Mr. Robins, that because the sum total of the action or pressure 

 of the elastic fluid on the bullet, during the time of its passage through the 

 bore, happens to be the same when bullets of different weights are used (which 

 collective pressure is in all cases proportional to, and is accurately measured by, 

 the velocity, or rather motion, communicated to the bullet) that therefore the 

 pressure in any given part is always exactly the same, when the quantity of 

 powder is the same with which the piece is fired ; and thence endeavour to prove, 

 that the inflammation of gunpowder is instantaneous, or that the whole charge 

 is in all cases inflamed, and " converted into an elastic fluid before the bullet is 



