Edmond Halley Quotes

Wherefore, if, according to what we have already said, it should return again about the year 1758, candid posterity will not refuse to acknowledge that this was first discovered by an Englishman.

Next, Hevelius (a Noble Emulator of Ticho Brahe) following in Kepler's Steps, embraced the same Hypothesis of the Rectilinear Motion of Comets, himself accurately observing many of them. Yet, he complain'd, that his Calculations did not perfectly agree to the Matter of Fact in the Heavens: And was aware, that the Path of a Comet was bent into a Curve Line towards the Sun.

So that 'tis to the Greeks themselves as the Inventors (and especially to the Great Hipparchus) that we owe this Astronomy, which is now improv'd to such a Heigth. But yet, amongst these, the Opinion of Aristotle (who wou'd have Comets to be nothing else, but Sublunary Vapours, or Airy Meteors) prevailed so far, that this most difficult Part of the Astronomical Science lay altogether neglected; for no Body thought it worth while to take Notice of, or write about, the Wandring uncertain Motions of what they esteemed Vapours floating in the Æther; whence it came to pass, that nothing certain, concerning the Motion of Comets, can be found transmitted from them to us.

The principal Use therefore of this Table of the Elements of their Motions, and that which induced me to construct it, is, That whenever a new Comet shall appear, we may be able to know, by comparing together the Elements, whether it be any of those which has appear'd before, and consequently to determine its Period, and the Axis of its Orbit, and to foretell its Return. And, indeed, there are many Things which make me believe that the Comet which Apian observ'd in the Year 1531, was the same with that which Kepler and Longomontanus took Notice of and describ'd in the Year 1607, and which I my self have seen return, and observ'd in the Year 1682.

The Construction and Use of the general Table.As the Planets move in Elliptick Orbs, so do the Comets in Parabolick ones, having the Sun in their common Focus, and describe equal Areas in equal Times. But now because all s are similar to one another, therefore if any determinate Part of the Area of a given Parabola, be divided into any Number of Parts at Liberty, there will be a like Division made in all Parabolas, under the same Angles, and the Distances will be proportional: And consequently this one Table of ours will serve for all Comets.

In the mean time, those that desire to know how to construct Geometrically the Orb of a Comet, by Three accurate Observations given, may find it at the End of the Third Book of Sir Isaac Newton's Principles of Natural Philosophy, entituled De Systemate Mundi, in the Words of its renowned Inventor. Which have since been more fully explained by my very worthy Collegue Dr. Gregory, in his Learned Work of Astronomia Physica & Geometrica.

The Astreonomical Elements of the Motions in a Parabolick Orb of all the Comets that have been hitherto duly obferv'd. ...This Table needs little Explication, since 'tis plain enough from the Titles, what the Numbers mean. Only it maybe observ'd, that the Perihelium Distances, are estimated in such Parts, as the Middle Distance of the Earth from the Sun, contains 100000.

[I]n the Year 1456, in the Summer time, a Comet was seen passing Retrograde between the Earth and the Sun, much after the same Manner: Which, tho' no Body made Observations upon it, yet from its Period, and the Manner of its Transit, I cannot think different from those I have just now mention'd. Hence I dare venture to foretell, That it will return again in the Year 1758. And, if it should then return, we shall have no Reason to doubt but the rest must return too: Therefore Astronomers have a large Field to exercise themselves in for many Ages, before they will be able to know the Number of these many and great Bodies revolving about the common Center of the Sun; and reduce their Motions to certain Rules.

All the Elements agree, and nothing seems to contradict this my Opinion, besides the Inequality of the Periodick Revolutions: Which Inequality is not so great neither, as that it may not be owing to Physical Causes. For the Motion of Saturn is so disturbed by the rest of the Planets, especially Jupiter, that the Periodick Time of that Planet is uncertain for some whole Days together. How much more therefore will a Comet be subject to such like Errors, which rises almost Four times higher than Saturn, and whose Velocity, tho' encreased but a very little, would be sufficient to change its Orbit, from an Elliptical to a Parabolical one.

Next to Ticho, came the Sagacious Kepler. He having the Advantage of Ticho's Labours and Observations, found out the true Physical System of the World, and vastly improv'd the Astronomical Science.
For he demonstrated that all the Planets perform their Revolutions in Elliptick Orbits, whose 'Plains pass thro' the Center of the Sun, observing this Law, That the Area's (of the Elliptick Sectors, taken at the Center of the Sun, which he proved to be in the common Focus of these Ellipses) are always proportional to the Times, in which the correspendent Elliptical Arches are describ'd. He discover'd also, That the Distances of the Planets from the Sun are in the Ratio [3:2] of the Periodical Times, or (which is all one) That the Cubes of the Distances are as the Squares of the Times. This great Astronomer had the Opportunity of observing Two Comets, one of which was a very remarkable one. And from the Observations of these (which afforded sufficient Indications of an Annual Parallax) he concluded, That the Comets mov'd freely thro' the Planetary Orbs, with a Motion not much different from a Rectilinear one; but of what Kind, he cou'd not then precisely determine.

[I]n the Year 1472, which being the swiftest of all, and nearest to the Earth, was observ'd by Regiomantanus. This Comet (fo frightful upon the Account both of the Magnitude of its Body,and the Tail) mov'd Forty Degrees of a great Circle in the Heavens, in the Space of one Day, and was the first, of which any proper Observations are come down to us.

These necessary Things premis'd, let it be propos'd to compute the apparent Place of any one of the mention'd Comets, for any Given Time.

Hitherto I have consider'd the Orbits of Comets as exactly Parabolick; upon which Supposition it wou'd follow, that Comets being impell'd towards the Sun by a Centripetal Force, descend as from Spaces infinitely distant, and by their Falls acquire such a Velocity, as that they may again run off into the remotest Parts of the Universe, moving upwards with such a perpetual Tendency, as never to return again to the Sun. But since they appear frequently enough, and since none of them can be found to move with an Hyperbolick Motion, or a Motion swifter than what the... Comet might acquire by its Gravity to the Sun, 'tis highly probable they rather move in very Excentrick Orbits, and make their Returns after long Periods of Time: For so their Number will be determinate, and, perhaps, not so very great. Besides, the Space between the Sun and the fix'd Stars is so immense, that there is Room enough for a Comet to revolve, tho' the Period of its Revolution be vastly long.

After this manner... the Astronomical Reader may examine these Numbers, which I have calculated, with all imaginable Care, from the Observations I have met with. And I have not thought fit to make them publick before they have been duly examin'd, and made as accurate as 'twas possible, by the Study of many Years. I have publish'd this Specimen of Cometical Astronomy, as a Prodromus of a designed future Work, left, happening to die, these Papers might be lost, which every Man is not capable to retrieve, by reason of the great Difficulty of the Calculation.

A General Table for Calculating the Motions of Comets in a Parabolical Orbit.