TUACT ;37.

OP GUNNERY.

295

common ones, then the same formula becomes

.. _ ..WlOnhd* . b s • • , i

t _ */( -.— x com. og. —or it is also nearly

K f) + w » a n *

. _ .. it fid 2 i A i i * .

v = 47 v(~—, X log.—), the same velocity; or it is

v — 46' I a/ x ] 0ff A) including the allowance for thecounter-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 theiirst 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 it gives us n = —~ log. of — for the generalvalue 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. Robins,but imagined by several other persons to be some largernumber. In the theorem, d and h denote inches, v feet, andp and W ounces.

1 TO. Now, to make application of this theorem to someof the cases in Tract 34, to the end of the year 1786, torthe 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 1'9() inches in diameter, and itsmedium weight 16 oz IS dr = 16'81 oz. It has been foundalso, that the weights ol 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 weigiits of powder, thesums 4'5 oz, 8 75 oz, l7'31 oz, are the correspondent valuesol Up-, 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 16 81, the constant weight of the ball,there result the three values of p + w for the said three