TRACT 3f.
IN GUNNERY.
331
M’hole ; and therefore this effect scarcely ever amounts toso much as half a foot: being indeed about
i of a foot when the velocity of the ball is 2000 feet,
- when - - it is 1000 r
-f - when - - it is 1500
and so on in proportion to the whole velocity of the ball.
And even this small effect may be supposed to be balancedby the method of determining the centre of oscillation, orthe number of vibrations made in a second. So that thenumber of oscillations, and the chord of the arc described,being both diminished by the resistance of the air; and theone of these quantities being a multiplier, and the othera divisor, in the formula for the velocity ; the one of thosesmall effects will nearly balance the other ; much in thesame way as the effects of the first cause, or the friction onthe axis. So that these effects may both of them be safelyneglected, as in no case amounting to any sensible quantity.
In the beginning of this investigation, it is supposed thatthe resistance of the medium is equal to the weight of acolumn of it, whose base is the moving surface, and itsaltitude equal to that from which a heavy body must fallto acquire the velocity of that surface. But some philoso-phers think the altitude should be only one half of that, andconsequently the pressure only one half: which would ren-der the resistance still less considerable. But if the altitudeand resistance were even double of that above found, itmight still be safely neglected.
28. The third seeming cause of error in our rule, is thetime in which the ball communicates its motion to the pen-dulum, or the time' employed in the penetration. Theprinciple on which the rule is founded, supposes the momen-tum of the ball to be communicated in an instant: but thisis not accurately the case, because this force is commu-nicated during the time in which the ball makes the pene-tration. And though that time be evidently very small,scarcely amounting to the 500th part of a second, it willbe proper to enquire what effect that circumstance may