2q6 philosophical transactions. [anno 1778. 



Let us now take the means among those of the same quantity of powder, 

 thus: 



And these mean velocities, with 2, 4, and 8 ounces of jrawder, are as the numbers 

 1, ].-ll6, and l.yg'i; but the sub- duplicate ratio of tlie weights (2, 4, and 8) 

 of powder, gives the numbers 1, 1.414, and 2, to which the former are suf- 

 ficiently near. It is obvious however, that the greatest difference lies in the last 

 number, which answers to the greatest velocity, and which is again in defect. 

 It will be still a little more in defect if we make the allowance for the weights of 

 the balls; for the mean weight of the balls with the 2 and 4 ounces is 1 8|- ounces, 

 but of the 8 ounces it is 18i; diminishing therefore the number I.993 in the 

 reciprocal sub-duplicate ratio of 18a to 18|-, it becomes I.9S5, which falls 

 short of the number 2 by .015 or the 133d part of itself; which defect is to be 

 attributed to the same causes as it was in the last course of experiments before 

 explained. 



Let us now compare the corresponding velocities in this course and the last. 

 In this course they are 701, QQS, 1397; 

 In the last they were 6l3, 873, ]l62. ' 



Now the ratio of the first 2 numbers, or the velocities with 2 oz. of powder, is 

 that of 1 to 1.1436 ; the ratio of the next 2, is that of 1 to 1.1373 ; and the 

 ratio of the last is that of 1 to 1.2022. But the mean weight of the shot was, 

 for 2 and 4 ounces of powder, 28J- ounces in the last course, and 1 8f ounces in 

 this; and for 8 ounces of powder, it was 28^ in the last, and 18i in this: 

 taking now the reciprocal sub-duplicate ratios of these weights of shot, we ob- 

 tain the ratio of 1 to 1.224 for that of the balls which were fired with 2 oz. and 

 4 oz. of powder, and the ratio of 1 to 1.241 for the balls which were fired with 

 8 ounces. But the real ratios above found are not greatly different from these. 

 And the variation of the actual velocities from this law of the weights of shot, 

 incline the same way in this course, as they appeared to do in the 2d course of 

 these experiments. 



We may now collect into one view the principal inferences that have resulted 

 from these experiments. ^ 



I. And first, it is made evident by them, that powder fires almost instanta- 



