NEW EXPERIMENTS

TRACT 34.

we take this expression a maximum, and make its fluxion— 0, i only being variable, we shall obtain pg o = b i i, and

i — for the distance of the centre of percussion, or

the point where the ball must strike, so as to cause thegreatest vibration in the pendulum ; which point, in thiscase, is neither the centre of gravity nor the centre of oscil-lation ; but will be at a great distance below the axis whenp is great in respect of b, as in the case of our experiments,in which p is 600 or 800 times as much as 5.

30. It may not be improper here, by the way, to enquirea little into the time of the penetration, its extent or depth,and the measure of the resisting force of the wood. It wasfound above, Art. 28, that

_ peoun , b , , ,,

‘ l - TkiiJt’ aIKl * + Z = 4*K * {*■ “ V ')’

Now, substituting in these, ———, the greatest value of° ’ pgo + bn’ a

u, for u and v, we have ,

x - LL1 x b * * and 7 - ZA? *

*h it (p g o + b zi) 27 4 hit />go 4 + Oil

The latter of these being the greatest depth penetrated bythe ball into the wood, and the former the distance movedby the point c of the pendulum at the instant when thepenetration is completed. Both of which, it is evident, aredirectly as the square of the original velocity of the ball,and inversely as the resisting force of the wood ; the otherquantities remaining constant.

Hence also it appears that, other tilings remaining, thepenetration will be less, as i is greater, or as the point ofimpact is farther below the axis. It is further evident, thatthe penetration will diminish as the sum of the forces pgodiminishes.

Now, for an example in numbers, a ball fired with avelocity of 1500 feet per second, has been found to pene-trate about 14 inches into a block of sound dry elm, when,the dimensions of the pendulum were as below :