[ 210 2 
The Truth of which will appear from the Refo- 
lution of the Cubic Equation in the laft Corollary to 
the preceding Proportion. 
Corollary I. If the Quadruple of the Quantity 
be many times greater or many times lefs than 
Unity 5 or, which amounts to the fame, if the mean 
Anomaly M y be many times lefs, or many times 
greater, than the Angle denoted by the given Quantity 
Ry'P (one or the other of which two Cafes mod 
frequently happens in Orbits of very large Eccentri- 
city) then the Theorem will be reduced to a fimpler 
Form near enough for Ufe. 
Cafe I. If M be many times lefs than , 
then the Angle A may be taken for that whofe Sine is 
/ x M 
v pXR 
Cafe 11 . If A/ be many times greater than ^yyPy'p, 
P 
then let A be the Angle whofe Sine is N— - . 
and the Multiple Angle n x A , according to its Cafe, 
will be nearly equal to the Angle required. 
Corollary II. In Orbits of very large Eccentricity, 
the 'Perihelion Diftance p is many times lefs than 
the Se mi-diftance o f the Foci f> and the Number 
» = 5 + ^25 + ^; is always nearly equal to ■/ 1 0 
or to the Integer 3, either of which may be ufed for 
it without any material Error in the Orbits of Comets. 
II. The 
