their vortical motions is considered, and from thence the Cartesian doctrine of the Vortices of the celestial matter, carrying with them the planets about the sun, is proved to be altogether impossible. The third and last book is entitled, De Systemate Mundi, wherein the demonstrations of the two former books are applied to the explication of the principal phænomena of nature. Here the verity of the hypothesis of Kepler is demonstrated, and a full resolution given to all the difficulties that occur in the astronomical science; they being nothing else but the necessary consequences of the Sun, Earth, Moon, and Planets, having all of them a gravitation or tendency towards their centres, proportionate to the quantity of matter in each of them, and whose force abates in duplicate proportion of the distance reciprocally. Here likewise are indisputably solved the appearances of the tides, or flux and reflux of the sea; and the spheroidical figure of the Earth and Jupiter determined, (from which the precession of the equinoxes, or rotation of the Earth's axis, is made out,) together with the retrocession of the Moon's nodes, the quantity and inequalities of whose motion are here exactly stated a priori. Lastly, the theory of the motion of comets is attempted with such success, that in an example of the great comet which appeared in 1680-1, the motion thereof is computed as exactly as we can pretend to give the places of the primary planets; and a general method is here laid down to state and determine the trajectoriæ of comets, by an easy geometrical construction, upon supposition that those curves are parabolic, or so near it that the parabola may serve without sensible error; though it be more probable, saith our author, that these orbs are elliptical, and that after long periods comets may return again. But such ellipses are by reason of the immense distance of the foci, and small ness of the latus rectum, in the parts near the sun where comets appear, not easily distinguished from the curve of the parabola, as is proved by the example produced. The whole book is interspersed with lemmas of general use in geometry, and several new methods applied, which are well worth the considering; and it may be justly said, that so many and so valuable philosophical truths, as are herein discovered and put past dispute, were never yet owing to the capacity and industry of any one man. Advertisement. Whereas the publication of these Transactions has for some months last past been interrupted, the reader is desired to take notice that the care of the edition of this book of Mr. Newton having lain wholly upon the publisher, (wherein he conceives he hath been more serviceable to the commonwealth of learning,) and for some other pressing reasons, they could not be got ready in due time; but now they will again be continued as formerly, and come out regularly, either of three sheets or five, with a cut, according as materials shall occur. No. XXII. PREFACE AND CONCLUSION OF HALLEY'S PAPER ON THE TIDES. May it please THE KING'S MOST EXCELLENT MAJESTY. I would not have presumed to approach your Ma jesty's royal presence with a book of this nature, had I not been assured that, when the weighty affairs of your government permit it, your Majesty has frequently shewn yourself inclined to favour mechanical and philosophical discoveries. And I may be bold to say, that if ever book was worthy the favourable acceptance of a Prince, this, wherein so many and so great discoveries concerning the constitution of the visible world are made out, and put past dispute, must needs be grateful to your Majesty, especially being the labours of a worthy subject of your own, and a member of that Royal Society founded by your late royal brother, for the advancement of natural knowledge, and which now flourishes under your Majesty's most gracious protection. But being sensible of the little leisure, which care of the public leaves to Princes, I believed it necessary to present with the book a short extract of the matters contained, together with a specimen thereof in the genuine solution of the cause of the tides in the ocean, a thing frequently attempted, but till now without success, whereby your Majesty may judge of the rest of the performance of the author. (Then follows the statement as printed in the Philosophical Transactions, vol. xix. p. 445, and at the end there is the following addition.) If by reason of the difficulty of the matter, there be any thing herein not sufficiently explained, or if there be any material thing, observable in the tides, that I have omitted, wherein your Majesty shall desire to be satisfied, I doubt not but, if your Majesty shall please to suffer me to be admitted to the honour of your royal presence, I shall be able to give you such an account thereof as may be to your Majesty's full con tent. No. XXIII. MEMORANDA OF DR. DAVID GREGORYP. Oxon. 21 May 1701. 1. To discourse with Mr. Newton about the change of the inclination of the orbit of a satellite; the draught of my objection is in a paper apart. 2. To get the æquatiuncula in the theory of the Moon, of [which] Mr. Newton spoke to Mr. Halley, as Mr. Halley wrote to me. 3. To know what Mr. Newton and Mr. Halley mean by desiring me to leave out somewhat I have of Mr. Halley, concerning the comet of 1680. 4. To talk with Mr. Newton concerning my doubt about inserting some things in my Astronomy: those things are among the Indexes, &c. torn from the end of my Astronomy. 5. To endeavour to get Mr. Newton's Table of Refractions. 6. To consult Mr. Newton about a Preface, and upon the whole. 7. To talk about Euclid, especially the Data; and if I should write a Preface, and what instances put in it. 8. To endeavour to get his book of Light and Colours, and to have it transcribed if possible. 9. To see to get at least his book De Curvis secundi generis. p From the original in the possession of D. F. Gregory, Esq. |