i66
OF PROJECTILES.
third method is applicable to fusils and pieces of vferysmall calibre ; but not to guns of large calibre, firedwith the common charges of powder: because in thelatter, the initial velocities are compounded of the im-pulsion and pressure, as has been explained in the fit stpart.
T46. The initial velocities are found very nearly by thefirst method (145, No. 1.) if the butt be perfectly homo-geneous and consistent. To determine its consistence, firea piece of small calibre, with an iron (hot 1 inch in diameter= D: and measure the initial velocity = «= 1200 feet, ( Trea-tise on Powder 164, 165). Then the piece being loadedand fired as before, the penetration of this shot into the buttwill be 15 inches—-S; and substituting these data in theformula fS -DU’i we shall have / x |- = T V x 1200 1 ;then f = 96000 for the consistence of the butt: let it bewritten in the formula, which then becomes 96000 S ~D U LPlace the gun, the velocity of whose shot is sought, verynear the butt, and sire tome rounds in a horizontal direc-tion, in order to obtain the mean — 8 of the penetrations ofthe shot; suppose it — 8 feet, and the diameter D of theshot = 4 inches; then by substituting these data in the for-
mula, 96000 x 8 =t 4 U* ; hence U —
4
1517 feet, the initial velocity sought. In these experiments,the penetrations should be at such a distance from each other,that the loosening of the earth by the first shot, may notfacilitate the entrance of the others ; the least difference willbe then perceptible, since the penetrations of the lame shotare as the squares of the initial velocities.
147. To determine the initial velocities, by analysing thecurve (145, No. 2); let us take the nrst part of the curve,where the effect of gravity has not been sensibly alteredby the resistance of the air. it is a matter of indifference,whether the space that the shot pass through by the gravi-tating or impelling power, be first considered ; since the lattermay be deduced with equal facility from the former, as theformer from the latter. Let us in the first place examinethe space passed through by the power of gravity.
(PI. 5, Fig 14.) Let the gun A B, mounted on its car-riage, be placed on an even and solid platform, and laid in ahorizontal direction A C j so that the shot at the first graze
Way