TRACT 37.

OF GUNNERY.

295

common ones, then the same formula becomes® = vi-- X com. log-. —), or it is also nearly

. _ . > r? hri " 1 , h i . .

v = 47y'(^— x log. —), the same velocity; or it isv — 46'1 x log. —includinnr the allowance for the

K p + w o a n °

counter-pressure of the air.

169. But now, as we have determined by numerous ex-

periments, detailed in the 34th Tract, the actual velocitiesof balls in a great multitude of instances, by substituting thenany of those velocities for v, in the last theorem, it is mani-fest that the equation will give us the value of the unknownquantity n, which has hitherto been assumed to denote thefirst force of fired gunpowder; the values of all the otherletters in the formula being known. Considering all the otherquantities then as given, and-reducing the last equation tofind n, it gives us n = + ..™v 7 ‘ — log. of — for the general

value of the first force of the elastic fluid, or how oftenit is stronger than the pressure of the atmosphere; a quan-tity which has been assumed equal to 1000 by Mr. Ilobins,but imagined by several other persons to be some largernumber. In the theorem, d and h denote inches, v feet, andp and w ounces.

170. Now, to make application of this theorem to someof the cases in Tract 34, to the end of the year 1786, forthe three cases of 4, 8, and 16 ounces of powder, with allthe four different lengths of guns. We have seen that theball there employed, was of T96 inches in diameter, and itsmedium weight 16 oz 13 dr = 16‘81 oz. It lias been foundalso, that the weights of the bags containing the 4, 8, and 16ounces of powder, were 8 dr, 12 dr, and 1 oz 5 dr; thesethen being added to the respective weights of powder, thesums 4\5 oz, 8 75 oz, 17*31 oz, are the correspondent valuesof 2/?; and their halves, 2'25 oz, 4‘38 oz, and 8’66 oz, arethe values of the quantity p for those three charges; thesethen being added to 1681, the constant weight of the ball,there result the three values of p + w for the said three