TRACT 31.

IN GUNNERY.

327

a little retard its motion, and cause its vibrations to beslower, and fewer ; so that c the length of a vibration, andn the number of vibrations, being both diminished by thiscause, nearly in an equal degree, and c being a multiplier,and n a divisor, in our formula, it is evident that the effectof the friction in the one case, operates against that in theother, and that the difference of the two is the real disturb-ing cause, and which therefore is either equal to nothing,or very nearly so.

27. The second cause of error, is the resistance of theair against the back of the pendulum, by which its motion issomewhat impeded. This resistance hinders the pendulumfrom vibrating so far, and describing so large an arch,as it would do, if there was no such resistance ; thereforethe chord of the arc, which is actually described and mea-sured, is less than it really ought to be ; and consequentlythe velocity of the ball, which is proportional to that chord,■will be less than the real velocity of the ball at the momentit strikes the pendulum. And though the pendulum be veryheavy, and its motion but slow, and consequently the resist-ance of the air against it very small, it will yet be proper toinvestigate the real effect of it, that we may ascertain whe-ther it may safely be neglected or not.

In order to this, let the annexed figure re-present the back of the pendulum, moving onits axis ; and putf — weight of the pendulum,a — d e its breadth,r = a b the distance to the bottom,e — a c the distance to the top,x — af any variable distance,g = distance of the centre of gravity,o = distance of the centre of oscillation,

' » = velocity of the centre of oscillation, in anypart of the vibration,h = 16-09 feet, the descent of gravity in 1 second,c = the chord of the arc actually described by the centre ofoscillation,

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