C 73 ] 
orbit ; this increafe is very near cotnpenfated by the 
comparative fmallnefs of the angular velocity. 
Let AD a reprefent the moon’s elliptic orbit, 
whofe centre is C, its axes Aa, Dd, the mean excen- 
tricity CT, and the circle of her mean motion MDmd, 
cutting Aa in M and m. Then, becaufe it is a mean 
motion we feek, generated while the axis A a paftes 
thro’ all its different afpeds of the fun ; we may con- 
ceive the dired motion already found, of 3 0 2' 21"-, 
to be produced by a conftant disturbing force — K, ad- 
ing on the moon as She revolves in her circular orbit 
MDmd ; and we have only to enquire, how much this 
force, and its effeds, are to be increafed, the moon 
really moving about the fame centre T, in the ellip- 
tic arc AD ; and how much diminished in the arc 
1 6. For which purpofe, the conftant force k is to be 
increafed in the ratio of the mean of the cubes of 
the moon’s diftances, in the arc AD , to the cube of 
TD or CA, and diminished as the mean of the cubes 
of the diftances in Ida. Let the forces refulting be 
K x G and k x H; and thefe being fubftituted in 
the formula, with the arcs 2 DM, 2 Dm, refpedively, 
the fum of the motions found will be the whole 
mean motion of the apogee, including the corredion 
for the excentricity. 
Now K will be found to be *00557337, and the ex- 
centricity TCbeing *055o5,and jTthe quadrantal arcto 
radius 1 j the ratio G , or, which is the fame, the fefqui- 
plicate of the time, in which the elliptic arc AD is de- 
scribed, to the time in the circular arc DM, that is, 
2 ) a. 
8 --TC 
' DM 
K 
