Volume 1

A system of natural philosophy, being a course of lectures in mechanics, optics, hydrostatics, and astronomy / By T. Rutherforth.

  • Rutherforth, T. (Thomas), 1712-1771.
Date:
1754
Catalogue details

Licence: Public Domain Mark

Credit: A system of natural philosophy, being a course of lectures in mechanics, optics, hydrostatics, and astronomy / By T. Rutherforth. Source: Wellcome Collection.

    141/566 (page 105)
    accelerated, is as the fquare of the laft acquired velocity. And, fince the quantity of motion or moment is, by the fecond law of motion, as the moving force, the moment mull likewife be as the fquare of th<* lad acquired velocity. What has been already faid concerning the acceleration of a body by the force of gravity might ferve to confute this whole argument. For when the firft impulfe of gravity has communicated one degree of ve¬ locity to it, a fecond impulfe, which is only equal to the former, will double the velocity, and a third equal impulfe will triple it. So that in the cafe of this acceleration we find that to double the velocity, which a body has, a double force need not be made ufe of, nor a triple one to triple it: neither is the fum of the accelerating forces as the fquares of the laft velocity, but as the velocity itfelf. But the defenders of the opinion, againft which I am difputing, have an anfwer ready for this objedion. They diftinguifib between an internal force and an external one. Gravity, they fay, is an internal force j it ads upon bodies in motion, juft as it does upon bodies at reft: and therefore as one impulfe would produce one degree of velocity; fo the fecond impulfe, though only equal to the former, will have the fame effed upon the body in motion as the firft had upon it before it began to move, and will produce a fecond degree of velocity; and a third equal impulfe will for the fame reafon produce a third degree. But an external force does not ad upon a body in motion and at reft in the fame manner. A force which prefles on the outfide of a body may produce one de¬ gree of velocity, but if it continues to prefs with the fame force, then inftead of doubling or tripling the bodys velocity, it will move on dole to the body without altering its motion at all. To double the velocity you muft prefs with twice the force, and to triple it the force itfelf muft be tripled. This miftake in the cafe of an external force, fuch as our hand is, has arifen from not diftinguifhing between the force with which our hand moves, and the force with which it ftrikes or impells the body. For though the fum of the moving forces in our hand is as the fquare of the velocity laft acquired by the body in motion, yet the moment of the body will not be in this proportion, unlefs the fum of the forces, with which the hand has impelled it, is likewife as the fquare of this velocity. But it is eafy to {hew, that the fum of thefe impulfes, or forces, ading upon the body and communicating motion to it, are in a iimplc ratio of the velocity, which it acquires. For fuppole with a force or ve¬ locity of your hand as 1, you communicate 1 degree of velocity to the O body