TRACT 37.

OP GUNNERY.

257

taining a correct and scientific solution of the general pro-blem in that way, or indeed in any way without the aid ofsome further experiments of another kind, viz, to obtain byaccurate experiments, the horizontal ranges and times offlight, of at least one size of ball or shell, discharged at allconvenient degrees of elevation, and with all practicable de-grees of velocity. If the same could be accomplished withseveral sizes of shot, it would render the conclusions themore accurate and satisfactory ; but those data for one sizeat least is absolutely necessary ; and may be made to answerthe purpose of all, by means of calculations founded on cer-tain known scientific principles ; for, the ranges and timesfor other sizes of shot, of equal density, may be ascertainedfrom the experimented one, since all balls discharged withsuch velocities as shall make their resistance proportional totheir momentum, must describe similar curves, at the sameelevation of the piece, and the several lines of the trajectorieswill all be proportional to each other, and to the diametersof the balls.

95. All that can be here done then, in the solution of thepresent problem, is to collect together some of the best prac-tical rules, founded partly on theory, and partly on practice.In the first place then, it may be remarked, that the initialor first velocity of a ball may be computed from the tableof experimented ranges and velocities as in the followingproblem.

PROBLEM XIII.

To assign the Charge of Powder necessary to project a givenBall with a given Velocity .

96. By the foregoing experiments it has been found thatthe velocities to different balls, and different charges of pow-der, with similar guns, are as the square-roots of the weightsof the powder directly, and as the square-roots of the weightsof the balls inversely. Thus, if it be enquired, with whatvelocity a 24lb ball will be discharged by 8lb of powder:VOL. in. s