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.

    169/566 (page 131)
    If a done upon the earths furface would move in a certain time, as in 5 feconds, fromyr, Plat.V. fig. 5. toL, this motion, which the done has in common with the earth, is not dedroyed by throwing it in the direc¬ tion /F perpendicular to the earths furface.- But after the projection the done will be moved by two forces, one in the direction jrL, the other in the direction f F ; and by both of them together will begin to rife in the diagonal of a parallelogram whofe fides are fF and fL,. So that though the projectile force aCts perpendicularly to the earths furface, yet this compounded with the force that carryes the Hone along with the earth produces a motion in it, as it rifes, in the direction f e, which is oblique to the earths center. And thus the cafe of a done, though thrown perpendicularly, is reduced to the cafe of an oblique projection as explaned in the lad propofition, and confequently the Hone muH de~ fcribe a parabola; which it will do by rifing in the half parabola fA and by falling again in the other half of the fame parabola. To be more particular; fuppofe that the earths furface and Hone along with it, if the Hone was not thrown upwards but reded on the furface, would move from/to P in one fecond, from P to O in another fecond, from O to N in a third, from N to M in a fourth, and from M to L in a fifth. But fuppofe, when the Hone was at f it was to be thrown upwards with fuch a force as would carry it in 5 feconds to its greated height /'F; then the fpaces through which it would afcend in each of the five leconds taken feperately, would be to each other as the five fird uneven numbers taken backwards, or as 9, 7, 5, 3, 1. by propofition 115. That is, it wrould af¬ cend through 9 poles in the fird fecond, through 7 in the next, through c in the third, through 3 in the fourth, and through 1 in the fifth. Now to trace out the line which the done will defcribe, we mud compound thefe two motions together. For the motion, which the done had in common with the earth, is not dedroyed by throwing it perpendicularly upwards, but continues the fame, whild the done is in the air, that it was, whild it laid upon the earths furface. By one of thefe motions it is to be carryed in a fecond from f to P and by the other it is to afcend through fp fup- pofing fp equal to 9 poles, and therefore by both together it will de¬ fcribe fe the diagonal of a parallelogram, whofe fides are fF and fp. In the next fecond the motion, which the done has in common with the earth, will carry it through a fpace equal to PO, but the done at the beginning of this fecond is not at P but at e, therefore it will be car¬ ryed through <?x, = PO : and iince it will in the mean time by the pro¬ jectile force afcend through e e equal to 7 poles, by both forces together it will defcribe ed3 by propofition 16. In the third fecond it will be carryed in the lame direction as the earth from d to i or through a fpace equal to ON, and will rile from d to or 5 poles; therefore by both r 2 motions