510

THEORY AND PRACTICE

TRACT 37,

stead of p, as above, and repeating the process, the finalequation comes out nearly a 1 + (96 + b) a — 32 b, where thenumeral coefficients are to those in the former case, as 3 to 2,the same as the two values 'p to -Jp here assumed: and so itwill always be in the cases of other assumptions for that of p.Or the equation will be a 1 + (48 -\-b) a — Ibb ; when a andbare, estimated in calibers of the gun. Then, by computingthe values of a in this equation, for all the four differentlengths of our guns, they come out very near the same asthose before found in the experiments. Also, from the same.equation the following table has been computed, for thelengths of the charges proper to give the greatest velocityby several different guns, the lengths being estimated in ca-libers or diameters of their bores, by the common differenceof 5.

ILength of the piece incalibers.

b

5

10

15

20

25

30

35

40

45

50

Length of the charge iqcalibers.a

1- 47

2- 64

3- 60

4- 42

5- 12

5- 73

6- 27

6- 75

7- 19

7-58

187. All these calculations, from theory, agree very nearlywith the result of the experiments; a coincidence which isat once a proof and confirmation mutually of the one and theother. Mr. Euler has given a similar table from theory, in'which the lengths of the charges are all very erroneous, be-ing too great by quantities in a regular increasing series,from the ratio of 1 to 1*64 the least, to that of 1 to l - 90 the•greatest, being almost double. And in many other cases the