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It is needlcfs to obferve, that the like Rules would 
obtain in Hyperbolic Orbits, mutatis mutandis . But 
that which perhaps may not appear unworthy of being 
remarked, concerning this fort of Solution from the 
Cubic Root, is, that although the Rule be altogether 
inipoffible, upon a total Change of the Figure of the 
Orbit either into a Circle, or into a Parabola 5 yet it 
will operate fo much better, and hand in need of lefs 
Correction, according as the Figure advances nearer 
in its Change towards either of thofe two Forms. 
That the Ufe of the Method may better appear, it 
may not be amifs to add a few Examples. 
I have given two for the Orbits of Planets, one the 
mod, and the other the leaft Eccentrick; but which 
.are more to fhew the Extent of the Rule, than to re- 
commend the Ufe of it in fuch Cafes; for there are 
many other much better and more expeditious Me- 
thods in Orbits of fmall Eccentricity. The other two 
Examples are adapted to the Orbits of two Comets, 
whofe Periods have been already difcovered by Dr. 
Halley i the one is to fhew the Ufe of one of the 
Rules in the firft Corollary , and the other is to ex- 
plain the Ufe of the other Rule. 
Example I. 
For the Orbit of Mercury. 
If an Unit being put for the Semi-tranfverfe Axis (t) y 
the Eccentricity 0,20589 will become (/), and the 
Ferihelian Diftance (/>) will be 0,79411 s wherefore 
by means of the Number R given as before, the con- 
ftant Numbers for this Orbit will appear to be, 
**?= 3,56755, ^=0,5 85727 1 , >=^=0,4651319, andhence 
0,0085965 
Example. 
