Edmond Halley Quotes

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.

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.

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

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.

Yet almost all the Astronomers differ'd from this Opinion of Seneca; neither did Seneca himself think fit to set down those Phænomena of the Motion, by which he was enabled to maintain his Opinion: Nor the Times of those Appearances, which might be of use to Posterity, in order to the Determining these Things. And indeed, upon the Turning over very many Histories of Comets, I find nothing at all that can be of Service in this Affair, before, A.D. 1337, at which time , a Constantinopolitan Historian and Astronomer, did pretty accurately describe the Path of a Comet amongst the Fix'd Stars, but was too laxe as to the Account of the Time; so that this most doubtful and uncertain Comet, only deserves to be inserted in our Catalogue, for the sake of its appearing near 400 Years ago.

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, 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.

[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.

But Seneca the Philosopher, having consider'd the Phænomena of Two remarkable Comets of his Time, made no Scruple to place them amongst the Cœlestial Bodies; believing them to be Stars of equal Duration with the World, tho' he owns their Motions to be govern'd by Laws not as then known or found out. And at last (which was no untrue or vain Prediction) he foretells, that there should be Ages sometime hereafter, to whom Time and Diligence shou'd unfold all these Mysteries, and who shou'd wonder that the Ancients cou'd be ignorant of them, after some lucky Interpreter of Nature had shewn, in what Parts of the Heavens the Comets wander'd, and how great they were.

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.