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9- To determine which, we may conceive the earth 
as revolving in an orbit that is already in motion from 
the fun s difturbing force upon the moon : the retro- 
grade motion of the orbit, while the earth moves 
from C to />, being ?i x Cp\ and the diredt motion, 
for the reft of the quadrant, being N*pA- y whence 
it will follow, that the difturbing force = k affects 
the earth’s motion thro’ an arc of her orbit equal to 
i~\-n\ and the force — K adts thro’ the arc 
pA*T-fN. And the motions of the apjis being in 
the fame ratio' r, if r is the regrefs of the ap/is of the 
moon’s orbit (determined as in § 6) and p its pro- 
grefs ; the regrefs of the apjis of 'the earth’s orbit will 
be r x i and its diredt motion, p x T — N. That 
is, the whole motions of the apjis , refulting from the 
fun’s action upon the earth and moon together, will 
be (£=) r x 2 -ff n, and ( P= ) p x 2 — N ; and the 
motions to be afcribed to either arc, r x Tftqpv, and 
p x 1 — iiV. 
Now />, found as above, being 2082''. 9. and N— 
.0105707, P is 4143". 8. And the fame way, R= 
1 375". 7 : whofe difference P — R multiplied by 4, 
thatis, 4 x 2768 '=! io72 ,/ =3° 4' 32'^ is the direct 
motion of the apjis in a revolution. 
Firft corredtion for the moon’s variation. Fig. 4. 
10. In the foregoing calculation, it is fuppofed, that 
the moon’s orbit is nearly circular, more nearly in- 
deed than it poflibly can be, even abftradfing from 
its excentricity. For altho’ the moon had been pro- 
iedlcd with a diredtion and force to make her de- 
fcribe 
