154 -

Astronomy.

a.d et l

The Orrery is, therefore, anRepresentation of the True Sofa * 1 gjii

to

I

in the Point A. Wherefore \ fd • ^/~g

^ a ^

n ; whence we have nnad—bb. 0 ( $

28. And when x — d — AC, the Piit anc e ^

£ V/ %ax -f xx ^ ^

Centre of Force, we have

become iad^. dd:±d

a — -—" and b —

■ b b ~ n n a d.± nd

Whence

^co

^ 2 — 1

Having there!

fore

vd 1

Diameters 2 a and 2 b, the Conic Section i s ^Specie. ^ f'

29. Now because Unity, or 1, represents ^jectile Force to describe a Circle, the FofC^^e^be any other Number greater or less toConic Section. And first let — 2; then

rh ± T - . , „ r th e

-=-= Infinite, or the Centre of

2~n % 0

will be at an infinite Distance from A, and conly be the Parabola A N. ot ,

30. If the Value of n z be between x and j

be any Number between 1 and */ 2, then JJnic Section be an Ellipse between the Circle Cand the Parabola A N, having the Centre of ^

the upper Focus next A, as the Ellipse A L j

31. But if n be any Number less than 1, :

will still be an Ellipse, but within the Circ c, ^ qC i 1the Centre of Force C in the lower or rem°as the Ellipsis Al GO.

32. Again; if n z be greater than 2, ° r n » Qv'

2, then will a be negative ; consequently 1will be an Hyperbola , as A O.

33. Lastly ; if n' 1 = 0, then b —

0~\d-, that is, if the projectile Velocity

~h

be dim' 11 ’' --