( 4S9 ) 
©bfervations Antiquity has left us, are not fufficient to^ 
determine whether the fameGcmet ever return again, . 
But this Author has fihewn how Geometrically to deter- 
mine the Orb of a Comet from ObfervationSj and to 
find his diftance from the Earth and Sun^ which was ne- 
ver before done. 
The third thing here done is the Theory of the 
Moon, all the Inequalities of whofe Motion are proved 
to arife from the fame Principles, only here the efFefl: of 
twaCenters operating on, or attrading a projefted Bo- 
dy comes to be confidered ; for the Moon, tho' princi- 
pally attradedby the Earth, and moving round it, does, 
together with the Earth, move round the Sun once a 
Year, and is according as liie Is, nearer or farther from 
the Sun, drawn by him more or kfs than the Center of 
the Earth, about which (he moves whence arife feve- 
ral Irregularities in her Motion, of all which, the Author 
in this Book, with no lefs Subtility thanfnduftry, has 
given a full Account. And the' by reafbn of thegreat 
^JSomplication of the Problem, he has not yet been able 
to make it purely Geometrical, 'tis to be hoped, that in 
(bme farther E(Iay he may (brmount the difficulty : and 
having perfeded the Theory of the Moon, the long , 
defired difcovery of the Longitude (which at Sea is on- 
ly pradicable this way) may at length be brought to 
light, to the great Honour of your Majefty and Advan- 
tage of yourSubjeds. 
All the furprizingPhenomena of the Flux and Reflusr^-^ 
of the Sea, are in like manner fliewn to proceed from 
the fame Principle ; which I defign more largely to infifi 
on, fince the Matter of Fad is in this cafe much better 
known to your Majefty than in the foregoing. 
If the Earth were alone, that is to fay, not affeded " 
by the Adions of the Sun and Moon, it is not to be 
doubted, but the Ocean, being equally prefled by the - 
