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Mechanics. 131

be fixed to the Cannon perpendicular to itsAxis; and holding a Plumb-Line over theGlass directly under the Eye, the Cannonis to be elevated till the Object appears exact-ly under the Plummet, and there fixed ; ifthen it be discharged, it will strike the Objectas required.

From what has been said, We may easilyunderstand how a Body projected uprightfrom the Earth’s Surface does really de-scribe a Parabola, though to Appearance itascends and descends in a Right Line. Forit is urged by two Forces, viz. the Projec-tile upwards, and the Force arising fromthe Motion of the Earth about its Axis from.

Weft to Eaft\ in which Cafe it must neces-sarily describe a Parabola (XXXIII).

I SHALL

(XXXIII) 1. In the Parabola, it is demonstrated pi . irthat the several Abscissa A G, A H, Al, We. are as W “ /the Squares of the Ordinates G M, HN, I O, &c. '

and since this is the Property of the Curve which theProjectile describes, it is evident the Projectile describesa Parabola.

2. Let A M represent the Force with which a Ball is Fig. 7*projected from the Cannon in the Direction AM;this may be resolved into two others A L and L M, ofwhich the first is perpendicular, and the latter parallelto the Horizon. The perpendicular Force or VelocityAL is that by which the Ball rises, and the Heights towhich it will rife with the Velocities A L and A M

_ 2 .

are as the Squares of the Velocities, vix. as A L*tb

AM; but (because AL : AM :: A M : AG) AL:

A M A L : A G; therefore since A G represents the

K 2 Height