*59

Astronomy.

ant ^ t ^ ie * r Magnitudes comparativelyeac h other, and with that of the Sun,

express’d

'viz. P S Q , by the Radius Vector S P de-g in a g ; ven -p ime the Arch P Q_, is as QT di-‘' ' S P inversely ; that is, the Angle P S Q_-

; 1£ . fhis is easy to understand when

ly ?> descvu an y Angle is greater as the Arch P QW°^ Qrt '°n t £ ? ‘ n a gi ven Time, is so; astd less in

' * t|e s Wu.° ^pittance S P and sp, because the Ve-

j„r„^;r, Pr ) are ; n

Vf' e s VstK° ^ distance S P and sp, became , -tyl y as *J* w hich those Arches are described are inj^fvss pj ; he Perpendiculars S Y, Sy, to the Tangentsp e iini(; e j n ^ s 5 asl d when the Arches QJPand qp areA* Q p, Pmal]^ we may esteem them equal to thet, x and q t. Whence the Proposition is evi-46. Hfii

s) ilCe the angular Velocity at P and p is as

Aliv,rA

b Qts r ’’ ^ or t ^ r>e sectors P S Q_ and p S q, be-

’n the fame Time, are equal; whenceSj ^ $ t X Sp. Therefore QJT : qt :: Sp :

' - ^ • C- * QP

:: 3^ : 8?-::

'^henceM>' ^

LP - Sp SP ' S p

^ip^>ndio h f FocI S ’ os the Ellipse A B D let fall p Iate

:f i letth arS S Y ’ ro the Tan § ent Y y m V he LVII.r ne centripetal Force tend to the Focus S ; p- r ,' etlini „rr„„ c — ; 4v - ic Then will the Ve- . "

'V'

Vl 0

- verier aemw**»- Then will the Ve-le to the Velocity (V) m P, m the Ratio

— ft XV f d..*. T T \

S^)soBi eLefferSemi ' Axis ’

ySP. ForV :

:: CB : S Y {Art. ii.)3ut (by Conks) B CPSY X rv : SY 1 -

Qo, Ce VT * v. ForV ; v .. ^ ■ ~ - v.

*v.V V V T :: c B* : SY 1 . But (by Conies) BC

therefore V 1 : v* : '' . o v. .

j>y it ; s ut because of the similar 1 riangies or i am.

: Sp S:f ' S Y ;; s p ■_ S P ; wherefore V 1 ; v % ::

E- Pr 0 !. 0nse si l »ehtly V:,::V7F:/SK

l °ti of a p Y hat has been said it appears, that. thelanet in hs Orbit is very unequal and-i anomalous