VELOCITY of bodies moving. in carves. According to Galileo's system of the fall of heavy bodies, which is now universally admitted among philosophers, the veloci ties of a _body falling vertically are, at each moment of its fall, as the roots of the heights from whence it has Callen; reckoning from the beginning of the descent. And hence he inferred, that if a body descend along an inclined plane, the velocities it has, at the different times, will be in the same ratio : for since its Ve locity is all owing to its fAl, and it only falls as much as there is perpendicular height in the inclined plane, the velocity shouid be still measured by that height, the same ai if the fall were vertical, 'the Same principle led him also to conclude, that if a body fall through several conti guous inclined planes, making any angles with each other, much like a stick when broken, the velocity would still be regu lated after the same manlier, 'by the ver tical heights of the different planes taken together, considering the last velocity as the same that the body would acquire by a fall through The same 'perpendicular height.
This conclusion continued to be acqui esced in till the year 1672, when it was demonstrated to be false, by James Gre gory, who shows what the real velocity is, which a body acquires by descending down two contiguous inclined planes, forming an obtuse angle, and that it IS different from the velocity which a body acquires by descending perpendicularlf through the same height ; also that the velocity in quitting the first plane, is to that with which it enters the second, and in this latter direction, as radius to the Yo.
sine of the angle of inclioation between the two planes.
This conclusion, however, it is observ ed, does not apply to the motions of de scent down any curve lines, because the contiguous parts of curve lines do not form any angle between them, and conse quently no part of the velocity is lost by passing from one part of the curve to the other ; and hence he infers, that the velocities acquired in descending down a continued curve line, are the same as by falling perpendicularly through the same height. This principle is then applied, by the author, to the motion of pendulums and projectiles.
Varignon too, in the year 1693, follow ed in the same track, showing that the velocity lust in passing from one right i lined direction to another, becomes n definitely small in the course of a curve line ; and that therefiwe the doctrine of Galileo holds good for the descent of bo diesdown a curve line, riz. that the veto citracquired at any point of the curve, is equal to that which would be acquired by aTall through the same al titude.