PLATE V.
Is a true Projection of the System of the known Comets; in which are represented nine of the chief Trajectories, from their Aphelii to their Perihelii, all in just Proportion and Position to the Orbits of Saturn and Jupiter, which are also represented by the two concentric Circles, supposed to be drawn round the Sun as their Center.
The Ellipsis, or Trajectory, marked A, shews the Position and Path of the Comet which appeared in the Year 1684, whose Period is supposed to be about fifty Years, and has been observed within the Region of the Planets once.
That mark'd B, is the Way of the Comet of 1682;
The Period conjectured to be about seventy-five
Years and a half, and has been observed thrice.
C, Way of the Comet of 1337;
The Period about 100 Years, observed once.
D, That of the Comet of 1661;
The Period about 129 Years, observed twice.
E, Tract of the Comet of 1618;
The Period about 160 Years, observed once.
F, Way of the Comet of 1677;
The Period about 200 Years, observed once.
G, Way of the Comet of 1744;
The Period about 300 Years, observed once.
H, Way of the Comet of 1665;
The Period about 400 Years, observed once.
I, Way of the Comet of 1680;
The Period about 575 Years, observed thrice.
Plate IV.
Plate V.
The Scale of this System is equal to one Third of the former.
Here I must observe to you, as a Thing I judge may prove of great Consequence with regard to the System of Comets, which is as yet very imperfect: That I am strongly of Opinion, that the Comets in general, through all their respective Orbits, describe one common Area, that is to say, all their Orbits with regard to the Magnitude of their proper Planes, are mathematically equal to one another; which, if it once could be proved, and confirmed by Observation, the Theories of all the Comets that have been justly observed, might easily be perfected, and their Periods at once determined, which now we can only guess at, or may wait whole Ages for more Certainty of. What leads me to believe, that this may prove to be really the Case is this.
I find by Calculation, that the Orbits of the two last Comets, whose Elements have been most corrected by Sir Isaac Newton and Dr. Hally, are to one another, according to their Numbers, nearly as [J]13 to [K]17, notwithstanding one of them is one of the most erratick that ever came under our Observation; and the other one of the most neighbouring to the Sun.
[J] 1316539,968282 Comet of 1680.
[K] 1708155,4644 Comet of 1682.
But it is well known to all Mathematicians, that the first of these Comets moved in so eccentric a Trajectory, that the least Error in its almost incredible Proximity to the Sun will produce a very sensible Difference in the Area of the Orbit: And accordingly, if we moderate the Perihelion Distance of this Comet, by making it but 1000 instead of [L]612, which is but increasing it a 1/35000th Part of the great Radius of the Orbit, (which is an Error every Astronomer will readily grant is very easily made) and we shall find the Orbits of the said two Comets to be exactly equal.
[L] The Number in Dr. Hally's Synopsis.
Further, I must inform you, that the Comet of 1682, which the above is compared with, seems to have been so accurately observed, that it does not appear to have altered its Perihelion Distance half a 68th Part in one intire Revolution. Now, if we can with any Show of Reason, and a Probability on our Side, bring the Areas of these two extream Comets, as I may call them, to an Equality, sure we may conclude, it is a Subject highly worthy to be more considered and enquired into.