OF projectiles! 173

of the shot may severally be on planes one below the other*I,et these different planes be 4, 16, 36, 64, 100, and 144.feet below the gun’s axis ; then the time of the shot’sBight through the several spaces will be £, 1, if, 2, 2f, and Zseconds; thus, the equation of the scale will be more easilyfound.

Then, with a charge that gives a known initial velocity,fire some rounds towards the place, 4 feet below the planeof the gun, in order to obtain the mean of the horizontalranges (144, No. 3) which may be called dg (PI. 5, Fig.17): turn the gun to the place 16 feet below its plane;fire some rounds, and call the mean r p; let n b be theMean to the place 36 feet, and K y to the place 64 feetbelow the gun. On the directrix a K set off the times t —

V

y 2 s

32. t8

— a d, ar, an, a K, corresponding to the lines of

descent 4, 16, 36, and 64 feet; and erect from the points d,r, n, K, perpendiculars to the line a K, respectively equalto the means of the ranges already found; the line agpbypassing through the extremities of these perpendiculars, willbe the scale of spaces passed through during the times of theretarded movements of impulsion.

157. If no convenient place can be found for this purposethe experiments may be made in another manner: on thefide of a hill or mountain as (PI. 5. Fig. r6) H LA, at thebottom of which is a horizontal plain M Z, chuse the sta-tions A, L, H, of different heights ; and from them fire thegun in the horizontal directions A K, L F, H X : then theperpendicular lines GK,PF, ZX will be spaces that theshot soli through by the power of gravity. The longest ofthese lines should he less than 260 feet, that the resistance ofshe air may not sensibly affect the gravitating power, and thatthe difference of the heights may not occasion any alterationin the inflammation of the charge. From each of the pointsA, L, H, fire some rounds with charges of which the initialvelocities are known, in order to obtain the mean of thpranges (144, No. 3 ), then supposing that from the pointA the mean of ranges isD G, from the point L — R j?,from the point H = N Z ; mark upon the directrix a K (Ps.c, Fig. 17.) the times corresponding to the vertical linesGK,PT,ZX ; erect from the points d,r, n , the normallines dg, rp, n b equal to the means of ranges already found,

and