[ 2I 3 ] 
NOTES ON" THE FOREGOING PAPER, 
By the Rev. SAMUEL HORSLEY. 
{*) 
1 R r (a — b) 
d 
This formula is deduced from the following principles, 
iff. That the motion of the fatellite, in its orbit, is uniform, 
or, at leaf!:, may be confidered as fuch, without fenfible error, 
in the prefent inveftigation. 
2. That the time, which the femidiameter takes to enter the 
fhadow, in any eclipfe, is inverfely as the whole time of the du- 
ration of the eclipfe. 
3. That the time, which any given part of the femidiameter 
takes to enter the fhadow, is to the time which the whole femi- 
diameter takes to enter, as that part to the whole. 
Now, let a and b denote the verfed fines of the arcs Ad, AD 
(in the figure p. 189-) refpe£tively, the radius being unity. Let 
R denote the half-time of the duration of an eclipfe, when Ju- 
piter is in the node of the fatellite’s orbit, r, the time which 
the femidiameter takes to enter the fhadow in fuch eclipfes ; 
d, the whole duration of an eclipfe, happening when Jupiter is 
2 R r 
at any given diftance from the node. Then will exprefs 
d 
the time, which the femidiameter of the fatellite will take to 
is 
d (by 
enter the fhadow , in the eclipfe whofe duration 
becaufe d : 2 R — r : 2 ' -V And; - — - being the time that 
d J d 
the femidiameter takes to enter the fhadow. 
will 
be the time that the part B b takes to enter, by 3 d . 
It is to be obferved, that, to compare two eclipfes by this 
formula, it is necefiary, that the planet fhould have been at the 
• F f 2 fame 
