[ 72 ] 
14- The rule is founded in this, that if, from the 
centre F, a circular arc Ff be defcribed, including in 
the angle CFN the fedtor FT"), equal to the elliptic 
lector CFP, the cube of TF, the radius of this cir- 
cle, may be taken for the mean of the cubes of the 
moon’s diftances in the arc CP. And becaufe the 
area CPT is to the fedtor CMF, as PK to KM, or 
as FA to FC j and T o or TE is a geometrical mean 
between FA and FC, it will eatily appear, that 
TF 3 : Fo 1 :: CM- : CN And that P, found from 
the tables, being (nearly at lealt) the ftationary point 
in the oval, if the force k is increafed in the feiquipli- 
cate ratio of CM to CN, and the arc CN fubftituted 
for A in the formula, we (hall, by § i, find the retro- 
grade motion of the apfis. 
Now, when the conftant force is given, the 
regrefs R is as the arc A ; and when A is given, and 
k is but a little augmented, R is proportional to k : 
in general therefore, if k is but a little augmented, R 
is as k x A. Write i^for the regrefs in the oval, R 
Handing for that in the circle, already found ; and it 
kxA \ hcN'. 
will be R 
CM 
CN\ 
k x CM, or 
:RX 
according to the rule. The like reafoning for 
CN 
the diredt motion. 
Second corredtion for the Excentricity. Fig. 5. 
1 5. This equation is inconftderablcj becaufe, altho’ 
the ratio of the difturbing force, when the moon is 
at a greater than her mean diftance, is more increafed 
than it is diminifhed in the oppofite points of her 
orbit ; 
