t 414 3 
tricity, according to the greater or leffer Diftance of 
the Sun from the Earth; and therefore I fet myfelf 
to compute what Change this Difference of the Suns 
A&ion upon the lunar Orbit would introduce in the 
Moon's Place in every Situation of the Sun and lu- 
nar Orbit 5 and found, after many tedious Compu- 
tations, that the Sun being in Apogee, this Change* 
where greateft, would amount to about 4', and to 
4 ; 1 6 U y when the Sun is in Perigee. In other Di- 
fiances of the Sun from the Earth, this greateft Change 
is proportional to the Difference of the Cubes of the 
mean and prefent Diftances; and in every Situation 
of the Moon, and of her Orbit, the prefent is to 
the greateft Equation nearly as the Sine of the Ex- 
cefs of the Moon's mean Anomaly above twice the 
annual Argument to Radius . It increafes the 
Moon's Longitude, when the Sun is in his 
{imgelt [ Scmicircle > and that Excefs j greater \ 
than 1 8o°; and diminifhes it when otherwise * 
In fine, I compared the Theory of the Moon, as 
to her Longitude, with feveral Obfervations, as well in 
the OCtants and Semi-OCtants, as in the Syzygies and 
Quadratures, and found fuch an Agreement when 
the above Corrections were made, as feemed rather 
to be wifhed than hoped for, confidering the many 
Inequalities wherewith the Sun's ACtion difturbs the 
Motion 
* If this Equation be increafed and diminiflied in a direCt Ratio 
of the Moon’s horizontal Parallax, it will become more exaCt. And 
I think, if it were always diminilhed by a fourth or perhaps a third 
Part, it would agree better with Obfervations. 
