Top 15 Edmond Halley Quotes

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.

I design to treat of all these Things in a larger Volume, and contribute my utmost for the Promotion of this Part of Astronomy, if it shall please God to continue my Life and Health.

[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.

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.

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.

By comparing together the Accounts of the Motions of these Comets, 'tis apparent, their Orbits are dispos'd in no manner of Order; nor can they, as the Planets are, be comprehended within a Zodiack, but move indifferently every Way, as well Retrograde as Direct; from whence it is clear, they are not carry'd about or mov'd in Vortices. Moreover, the Distances in their Perihelium's are sometimes greater, sometimes less; which makes me suspect, there may be a far greater Number of them, which moving in Regions more remote from the Sun, become very obscure; and wanting Tails, pass by us unseen.

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.

5. From these Things given (by the very same Rules that we find the Planets Places, from the Suns Place and Distance given) we may obtain the Apparent or Geocentrick Place of the Comet, together with the Apparent Latitude. And this it may be worth while to illustrate by an Example or two.

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.

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.

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

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.

Wherefore (following the Steps of so Great a Man) I have attempted to bring the same Method to Arithmetical Calculation; and that with desired Success. For, having collected all the Observations of Comets I could, I fram'd this Table, the Result of a prodigious deal of Calculation, which, tho' but small in Bulk, will be no unacceptable Present to Astronomers. For these Numbers are capable of Representing all that has been yet observ'd about the Motion of Comets, by the Help only of the following General Table; in the making of which I spar'd no Labour, that it might come forth perfect, as a Thing consecrated to Posterity, and to last as long as Astronomy it self.

Not long after, that Great Geometrician, the Illustrious Newton, writing his Mathematical Principles of Natural Philosophy, demonstrated not only that what Kepler had found, did necessarily obtain in the Planetary System; but also, that all the Phænomena of Comets wou'd naturally follow from the same Principles; which he abundantly illustrated by the Example of the aforesaid Comet of the Year 1680, shewing, at the same time, a Method of Delineating the Orbits of Comets Geometrically; wherein he (not without the highest Admiration of all Men) solv'd a Problem, whose Intricacy render'd it worthy of himself. This Comet he prov'd to move round the Sun in a Parabolical Orb, and to describe Area's (taken at the Center of the Sun) proportional to the Times.