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.

    182/566 (page 144)
    the circle, as is obvious from a bare infpection of Plat. VI. fig. 2. where BG the tangent or direction of the projectile force when the body is at Bis perpendicular to BA, or to the direction in which it is impelled towards the center A. So likewife CF is perpendicular to CA, DH to DA, and LK to LA : and univerfaily the tangent is always perpendicular to a line drawn from the point of contaCt to the center. Euc. b. III. prop. 18. Therefore, fince this is the direction of the two forces in refpeCt of each other, when the revolving body defcribes a circle; it may be asked, why the body fetting out from A, Plat. VI. fig. 1. in the line A t per¬ pendicular to AS does not move in a circle having S in its center, and AS for its femidiameter, rather than in an ellipfis having S in its focus. Or why, when it is come to P, where the two forces are perpendicular a- gajn, does not it go on to move in a circle having PS for its femidiame¬ ter. The reader is, I imagine, by this time able to tell any one who fhould make fuch an enquiry, that the revolving bodys velocity at A is too fmall to make it defcribe a circle having AS for its femidiameter, and at P is too great to make it defcribe a circle having PS for its femidiameter. The force, with which the body, when it is at A, moves in the tangent At% is fo fmall, that the other force, which impells it towards S, will make it approach nearer to S than it is at A, or the diftance of it from S will keep decreafing as the body moves on. Till at laid it arrives at P where the two forces are perpendicular again. But then, as in cafe the third, the velocity is fo great in the tangent P />, that the force, which impells the body towards S, will not be fufficient to prevent its running out to a greater diftance from S than PS, fo that its diftance from S, will, as it goes on from P, keep conlhantly encreafing in the fame manner that it decreafed before, and the body will return from P to A in a curve PGA equal and fimilar to the curve ADP, in which it defcended from A toP. But fince the velocity of the revolving body is too fmall, when at A, aad too great, when at P, to make it defcribe a circle round S; it may¬ be farther afked, whether, in fome intermediate part of the orbit between A and P, the velocity is not fuch as would make it defcribe a circle; and if there is fuch a velocity, why does not the body, when it has that velocity go on to defcribe a circle for the future ? There may, and in¬ deed will be, fuch a velocity of the revolving body, in fome point of its orbit, whilft it is moving from A to P. And fuppofe the body to be at the point D, when it has this velocity. Then the queftion is, why it does not go on from the point D to defcribe a circle round S at the di- dance DS ? Now it mud be oblerved, in anfwer to this, that when the revolving body is at D, the projectile force aCts in the line D d3 which is a tangent