'294 



I'HILOSOPHICAL TRANSACTIONS. 



[anno 177B. 



1 



2 



3 

 4 

 5 

 6 

 7 

 8 

 9 



Let us now collect together the several velocities belonging to the same quan- 

 tity of powder, in order to take their means, thus : 



Vtloc. with 



'J ounces. 



6J2 



622 



605 



3 ) 1839 



3 ) 2620 



3 ) 3487 

 1162 



The means 6)3 873 



The uniformity of these velocities is very striking, and the means with 2, 4, 

 and 8 ounces of powder are 6l3, 873, and II62, which are in the ratio of 1, 

 1.424, and l.Q; which numbers are nearly in the ratio of the square roots of 

 the quantities (2, 4, and 8) of powder, the numbers in this latter ratio being 



1, 1.414, and 2, where the small difference lies chiefly in the last number. A 

 small part of this defect in the greatest velocity is to be attributed to the mean 

 weight of the balls used with it being greater than in the others ; for the mean 

 weight of the balls used with 8 oz. of powder, is 28f ounces, while that with 

 the 2 and 4 ounces is only 284 ; the reciprocal sub-duplicate ratio of these is 

 that of 1 to 1.006, in which proportion, increasing l.Q the number for the 

 greater velocity, it becomes l.Ql, which still falls short of 2 by .OQ, which is 

 about the -^ part too small for the sub-duplicate ratio of the powder. This 

 defect of a 22d part is owing to 3 evident causes, viz. 1 . The less length of cy- 

 linder through which the ball was impelled ; for by inspecting the 4th column, 

 denoting the height of the charge, it appears, that the balls lay 3 or 4 inches 

 nearer the muzzle of the piece with the 8 ounce charge than with tlie others. 



2. The greater quantity of elastic fluid which escaped in this case than in the 

 others by the windage; this happens from its moving with a greater velocity, in 

 consequence of which a greater quantity escapes by the vent and windage than 

 with the smaller velocities. 3. The 3(1 cause is tiie greater quantity of powder 

 blown out unfired in tliis case than in that of the less velocities; for tiie ba!!, 

 being impelled with tlie greater velocity, would be sooner out of the piece 



