TRACT 37.

GF GUNNERY.

305

form n — v 1 -r- log. — for the value of the initial

force 7i. For, though these two thus depend the one uponthe other ; and the one of these, as v, be very well deter-mined by the experiments ; yet the formula includes a quan-tity p, the exact value of which it is impossible to assign, butmust remain very uncertain, being only guessed at byjudgingfrom circumstances as near as may be. In these formulae, phas been assumed equal to half the weight of the powder andbag; a portion which, from the uncertain circumstances be-fore mentioned, must evidently be too large a quantity, be-cause it presupposes a uniform diffusion and density through-out the mass of inflamed powder, both of the gross and theelastic parts. Such as it is however, we shall proceed to em-ploy the first of these formulae to determine the velocity ofthe flame, and afterwards make such corrections in the resultsas other reasons may happen to suggest.

181. Now, in the formula v = 4G*7 V(-

nhd 2p + to

X 1(J g--) =

46'7 c W(~rZi x l°g. ■“) giving the ultimate velocity of theball, whose weight is to, it is manifest that the less the weightto, in the denominator, is, the greater will be the value ofthe velocity v, of the ball, and the fore part of the elasticfluid, which pursues and urges it on; therefore, by supposingthe value of to diminished till it quite vanishes, or becomesequal to nothing, the formula must then give the velocity ofthe expanding elastic fluid itself, subject only to the uncer-tainty of the assumed part p. Now, by omitting the weightw in that theorem, it becomes ® = &6 ,r ldV(y x log. —); or,substituting 1*96, the value of cl, instead of it, the formula

becomes 91 - 532y'(^ x log. ; by which we shall nowproceed to compute the values of ®, according to the differentvalues of all the quantities a, b, 71 , h, p, as before assigned,which several values, for the four guns, are as in the'sub-joined table.

VOL. in.

X