stronomy.

°W A, where the Planet is farthest dif-from the Sun, (for that Reason calPd

the

*49

tile soU S Y be a Perpendicular let fall from S uponj, § e nt P R produced ; then will the centripetal

^ be as SY^xtSjP b£CaUse thC Rcctan S le SY X

^*44 > for the evanescent Arch Q_P is co-

A>d

w ‘th the Tangent P R, and mav therefore be

‘ore

ft

is

^ the Base of the Triangle S P Q_, whose

there-to be

„ Zither i ,S P X Q_T, or | X S Y ;“°X QJT = QJP X S Y. Which

was

iew n .

* V 7 ‘ ^ rbe Orbit were a Circle, as PQVF, and Pl.LVI.the^jChorf drawn through the Centre of Force S; Fig- 6.he bis r A Wln g the Chord Q_M in such Manner'as it mayV^ted inK ^ rhe Chord P V, we have QjKP =

(hy Euclid, III. 35.) but in the vanishing

n e Of P i?V , ’ -r-Tr J t.t- ' rr r. T, Tr-

of dV^ A1J -

>y Jr P K- it will be V K:

I 3 -) also QJC — Q_P, therefore QP 1 =VP

(k

Mr,

V P, and QJR. = P K

*c

and P y :

QP 1

whence, in this Cafe, the

Mi-al p 0-^ ’

borce will be inversely as S Y* XP V.

-8

SY»

Wh

‘erefore, since the Velocity is as p-so we have

the Cf ^ s 4 e ^si uare of the Velocity inverse y ; thereforetlire^i tr ‘petal force is as the Square of the Velocityl 9-B an< ^ 4 e Chord PV inversely.

Ml an if the curvilinear Figure A P Q_ be given,ti>iu a]] y °»tt S to which the centripetal Force is con-" fc fout^i ‘tedled, the Law of the centripetal Force may* r ight.p .> w i 1 ‘ c h any Body P perpetually drawn from^at p- ln d Course shall be detain’d in the Perimeter ofc “ Ure > and by revo ving shall describe it, viz. by

«»S* ! ,hc Va ‘“ ° f th ' L'p'-R---- si-rAd-.

ao.p *, p V.

<Un fcre n l >X I" Xan ‘P'- e : Let a Body P revolve in the Cir-~ e °J a Circle , ’tis required to find the Law of theL ^ centripetal