2*4

PlateLXIII.Fag. I.

ASTRONOMY.

great Deficiency by shewing a direct and gc6iri et1 ^ jMethod of Computation of all the Phænoniena ^Comet moving in any Conic Section, which '# aSinvented by M. Bongtier , in AA-r. Paris. An.

which Method I shall explain, illustrate, and ex ern Pin the following Articles. ’ ' a st

36. Let A KB I be the Trajectory of a Cornet, ^its longest Axis, I K the shortest; S, F, the tWP ^in one of which the Sun is at S ; C the place oComet, C S its Distance from the Sun ; D C E agent to the Curve'in the Point C; C c the Space p.

over by the Comet in a small Particle of Tim e;

FE, Perpendiculars from the Foci to the Taj 1 ?. \gi

refit

Alt” 1 '-

s

th e -

And draw S G parallel to D E, and join F CANO be the elliptic Orbit'of any Planet; !

Foci. Lastly, let A L B be a Circle described'■Q gj.longer Axis., AB; A P T B a Rectangle about thlipsis A IB ; and A Q_R B as the Square abCircle ALB; and put S'C = s , SD^ b,the Time in which it. is described == f. ' The 1 K,Axis of the Cometary Orbit ABzi, of the * ^gtary Orbit AOr?, the Circle described on th^^tAxis A V O

U1C Silicic UtitUUCU U1A

:p; the periodical Time of the ^

— t, arid that of the Planet = n.

37 ; The Space C c described, the Distance S C

the Angle LCD, are all known by Observation^therefore given Quantities. The mean Dist aliceComet is A H x, and of the Planet is A g> ^ fAnd because the Squares of the Periodical "Ti^ eS % ^

the Cubes of the mean Distances, we have \ p

nd : t*; and therefore t ; (Ann.y^f

q ^ q '

11.) *

38. It is necessary now to find another Exp I ' e ” I ^ I)a lJthe periodical Times, thus : Because C c is.a very ^Portion of the Orbit, it may be esteemed aRigb 1 - of®,and the Sector C S c as an evanescent Triangle? « r eifArea f SDxGc = f if is given ; but as the gp\ b e is to the Timeyj so is the whole Area of * t >.AKBI=A to the whole neriodical T J

}ipsis^hat is, t

- \b e

to the whole period

X A.

39 -