'TRACT 34.

IN GUNNERY.

341

Then, writing these values in the theorem, instead of theletters, it becomes v ~ 12‘15c. So that the number 12 - 15multiplied by the difference between two chords describedwith any charge, the one with and the other without a ball,will give the velocity of the ball when the dimensions are asstated above. And when the values of any of the lettersvary from these, it is but increasing or diminishing that pro-duct in the same proportion, according as the letter belongsto the numerator or denominator in the general formulaX £77^* When such variations happen, they will bementioned in each day’s experiments. And further, whenonly the values of G, g, i, n are as before specified, thesame formula will become 12718 x .

b r

But note that these rules are adapted to the gun n° 2only; therefore for n° 1 we must subtract the 400th part,and add the 400th part for n° 3, and add the 200th partfor n° 4.

of The experiments.

37. We shall now proceed to state the circumstances ofthe experiments, for each day separately, as they happened ;by this means showing all the processes for each set of expe-riments, with the failure or success of every trial and mode ofoperation; and from which also any person may recomputeall the results, and otherwise combine and draw conclusionsfrom them as occasion may require. Making but a veryfew cursory remarks on each day’s experiments, to explainthem when necessary; and reserving the chief philosophicaldeductions, to be drawn and stated together, after the closeof the experiments, in a more connected and methodical,way.

The machinery having been made as perfect as the cir-cumstances would permit, 20 barrels of government powderwere procured, all by the best maker, and numbered from1 to 20. A great number of iron balls were also cast ohpurpose, very round, and their accidental asperities groundoff: they were a little varied in their size and weight, but