290 PHILOSOPHICAL TRANSACTIONS. [anNO 1778. 



By computing the velocities from our theorem investigated in the corollary, 

 they come out as they are here registered in the last column of the table, and 

 they are all pretty regular, excepting the first, which is about i- part less than 

 the rest, with the same weight of powder, and which irregularity must have 

 been caused by some unperceived accident. The values of /j and g were each 

 corrected by their respective theorems; but the value of h was kept the same 

 (7^ feet) throughout, because its correction was so small as not to make a dif- 

 ference of above a foot or two at most in the velocity : and for the same reason 

 this correction is neglected, as quite unnecessary, in the rest of the experiments 

 of the other days following. 



The mean velocity of the 'id, 3d, 4th, 5th, and 6th numbers is 626, and of 

 the 7th and 8th it is 9J5; that is, the velocity with 2 oz. of powder was 626 

 feet per second, and that with 4 oz. was 915 feet; and these 2 velocities are in 

 the ratio of 1 to I.46. But the mean weight of the balls in the former case 

 was 17t-oz., and in the latter it was l7ioz.; and the ratio of the quantities of 

 powder was that of 1 to 2. But the direct subduplicate ratio of the powder, 

 compounded with the inverse subduplicate ratio of the weights of the shot, 

 forms the ratio of 1 to 1.42, which is nearly equal to the ratio (l to I.46) of 

 the velocities; that is, in this instance the velocities are very nearly as the square 

 roots of the quantities of powder directly, and the square roots of the weights 

 of the balls inversely. The powder was forced up with only one stroke of the 

 rammer. 



The 2d course was performed on the 3d of June, 1775, which was a clear, 

 dry day, but windy. Some of the experiments of this day are doubtful, as 

 indeed is evident from their irregularity, on account of the wind blowing the tape, 

 which was not very properly secured by the little brazen machine through which 

 it was made to slide. The powder was taken from the bottom of a barrel, and 

 the charges rammed a little closer than those of the former day; and so tight 

 did the shots fit towards the breech, that many strokes of the rammer were 

 necessary to drive them home. 



The 4th and 5th shots were of a long form, which may be called spherico- 

 cylindrical, as they were cylinders terminated by hemispherical ends, so that 

 their section through the axis was of this form a, and the length of the axis 

 was nearly double the diameter of the shot. 



The 4th shot or 1st of the long sort, struck sideways, making a hole of the 

 shape of the above section, only its length or axis was not horizontal but ver- 

 tical, thus Q. The last shot lay obliquely in the wood; it appeared to have 

 struck with its end foremost, or nearly so, as the oblique position in which it lay 

 seemed to be caused by its striking against a former shot lodged in the wood, 

 with the hance of its end, so as to flatten it in that part. Of the pendulum. 



