FIRED GUN-POWDER^ 77

To find the velocity u with which the ball impinged onthe pendulum, another valui of 64. 36 G I must hesought: As the chord — c of the arch F G H described bythe stylette, and radius C F = b are known, the versed sine

of this arch will be — : Then radius C F is to its versed2 b

fine as radius C G is to its versed sine G I or, f 1 .. P ad + qf* c* P ad + qf % __

‘ ib " Pa + qf lb x Pa + qf ’

and thus the uniform velocity of the point G will be ex*

presied by 7 ^64 . 36 c 1 Pad + qf* . an d on com-v/ 2 b* Pa + qf

paring the two expressions of these velocities

Pa + qf

35

32 18 X

P gd+gf*Pa + qf

and u = c

■x /^32 18 X ■ x F a —. if — the velocity sought,

bqf

163. The weight and length of the pendulum should besuch that its vibration may not describe an arch of more thanfive degrees; apd as the bails fired into it increase its weightand alter the centres of gravity and oscillation, the, values of P,a, d. should be corrected after each discharge.

164. Sig. Mattei, mathematical instrument-maker tothe King, has invented a machine for finding with facilitythe initial velocity of balls measured near the mouth of thegun.

Fig. XIX. A B is a horizontal wheel with a verticalaxis C D turned by the weight Q_, appending to therope G G and raised by the winch N. It may be turnedin any other manner, provided that its motion be perfectlyuniform and rapid. A E, B F is a circular band ofwriting paper about 6 inches high, fixed round the cir-cumference of the wheel. The gun for the experimentis immoveably fixed at 20 feet distance, and pointed sothat the axis of the gpn produced would pals throughthe points B, K, the exact diameter of the wheel. R