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been seen by Leibnitz. There can now be no doubt, however, that Newton was right in thinking that Leibnitz had been shown this MS., since a copy of part of it, in Leibnitz's hand, has been found among the papers of Leibnitz preserved in the Royal Library at Hanover'. It is, of course, possible that at the time when this copy was taken Leibnitz was already acquainted in some degree with the Differential Calculus, but it is difficult to acquit him of a want of candour in never avowing in the course of the long controversy respecting the discovery of Fluxions, that he had not only seen this tract of Newton's, but had actually taken a copy of part of it. He must have seen, also, at the same time, that the MS. was an old one, and although it does not contain the pointed letters which Newton sometimes but by no means invariably employed to denote Fluxions, Leibnitz could hardly fail to see, if he was acquainted with the Differential Calculus, that the principle of Newton's method was the same as that of his own. It is repeatedly stated by Newton that what he claims is the first invention of the method, and that he does not dispute about the particular signs and symbols in which the method may be expressed. Again, he often states that although, in the sense which he employs, the method can have but one inventor, yet the method may be improved, and the improvements belong to those who make them.

In some of these papers relating to the dispute with Leibnitz, Newton gives us some interesting information respecting the times when several of his discoveries were made. Thus in a passage, which has been quoted by Brewster2, he states that he wrote the Principia in seventeen or eighteen months, beginning in the end of December 1684, and sending it to the Royal Society in May 1686, excepting that about ten or twelve of the propositions were composed before, viz. the 1st and 11th in December 1679, the 6th, 7th, 8th, 9th, 10th, 12th, 13th and 17th, Lib. I, and the 1st, 2nd, 3rd and 4th, Lib. 11, in June and July 1684. The following extract will give an idea of Newton's prodigious mental activity at an earlier period of his life.

1 See Gerhardt, Mathem. Schriften Leibnitzens, 1. p. 7.

2 Brewster's Life, Vol. 1. p. 471.

"In the beginning of the year 1665 I found the method of approximating Series and the Rule for reducing any dignity of any Binomial into such a series. The same year in May I found the method of tangents of Gregory and Slusius, and in November had the direct method of Fluxions, and the next year in January had the Theory of Colours, and in May following I had entrance into the inverse method of Fluxions. And the same year I began to think of gravity extending to the orb of the Moon, and having found out how to estimate the force with which [a] globe revolving within a sphere presses the surface of the sphere, from Kepler's Rule of the periodical times of the Planets being in a sesquialterate proportion of their distances from the centers of their orbs I deduced that the forces which keep the Planets in their Orbs must [be] reciprocally as the squares of their distances from the centers about which they revolve: and thereby compared the force requisite to keep the Moon in her orb with the force of gravity at the surface of the earth, and found them answer pretty nearly. All this was in the two plague years of 1665 and 1666', for in those days I was in the prime of my age for invention, and minded Mathematicks and Philosophy more than at any time since. What Mr Hugens has published since about centrifugal forces I suppose he had before me. At length in the winter between the years 1676 and 1677o I found the Proposition that by a centrifugal force reciprocally as the square of the distance a Planet must revolve in an Ellipsis about the center of the force placed in the lower umbilicus of the Ellipsis and with a radius drawn to that center describe areas proportional to the times. And in the winter between the years 1683 and 16843 this Proposition with the Demonstration was entered in the Register book of the R. Society. And this is the first instance upon record of any Proposition in the higher Geometry found out by the method in dispute. In the year 1689 Mr Leibnitz, endeavouring to rival me, published a Demonstration of the same Proposition upon another supposition, but his Demonstration proved erroneous for want of skill in the method."

The above extract has been given here on account of its intrinsic interest, although in writing it so many years after

1 In 1666 Newton was in the 24th year of his age.
2 Probably this should be changed to 1679 and 1680.
3 Probably this should be changed to 1684 and 1685.

the events to which it relates, Newton appears to have made one or two mistakes of date, and probably for this reason has drawn his pen through the entire passage.

Newton's manuscripts on Alchemy are of very little interest in themselves. He seems to have made transcripts from a variety of authors, and, if we may judge by the number of praxes of their contents which he began and left unfinished, he seems to have striven in vain to trace a connected system in the processes described. He has left, however, notes of a number of his own chemical experiments made at various dates between 1678 and 1696. Some of these are quantitative. Those of most interest relate to alloys. He mentions several easily fusible alloys of bismuth, tin and lead, and gives as the most fusible that which contains 5 parts of lead + 7 of tin + 12 of bismuth. He says that an alloy consisting of 2 parts of lead + 3 of tin + 4 of bismuth will melt in the sun in summer. The alloy which goes by his name is not in the proportions of either of these two; but, as he states that tinglas (bismuth) is more fusible than tin, he could not have used pure metal.

The note-book which contains the longest record of his chemical experiments contains also the account of a few optical and other physical experiments and the paper on the decussation of the optic nerve published by Harris and from him by Brewster. Harris, according to Brewster, published from a copy in the Macclesfield Collection; but the copy seems to have been identical with that in this book, except that a paragraph at the end is omitted. Brewster overlooked the paper in this book, though he has quoted from other parts of the book.

The Historical and Theological MSS. cannot be considered of any great value. A great portion of Newton's later years must have been spent in writing and rewriting his ideas on certain points of Theology and Chronology. Much is written out, as if prepared for the press, much apparently from the mere love of writing. His power of writing a beautiful hand was evidently a snare to him. And his fastidiousness as to the expression of what he wrote comes out very curiously in these

papers; thus there are six drafts of the scheme for founding the Royal Society, seven drafts of his remarks on the chronology published under his name at Paris (which made him very angry), many of the Observations on the Prophecies, several of the scheme of mathematical learning proposed for Christ's Hospital,

&c.

The four elaborately bound volumes, containing the Chronology of Ancient Kingdoms Amended,' the Chronicle to the Conquest of Persia by Alexander, Observations on the Prophecies, and the treatise "De Mundi Systemate," are very remarkable specimens of their author's care in writing out his works, and of his beautiful handwriting (§ vii. 2). They are all contained in Horsley's collection.

It is believed that in the present catalogue nothing has been omitted, and that thus a very fair idea may be obtained of what occupied Newton's time throughout his life. The papers date from his earliest time, giving his accounts when first he began college life as a sizar of Trinity College, and his mathematical notes while still an undergraduate: and they continue till his death. All the papers or books which have been returned to Lord Portsmouth are marked with an asterisk* in the catalogue. Of the more important letters, which have not been retained by the University, copies have been taken by the permission of Lord Portsmouth, and these are retained with the portion of the MSS. presented by him to the University. In addition to this a copy of Brewster's Life of Newton has been placed with the collection, in which the letters there given have been carefully collated with their originals; so that practically the student of Newton's works has all the scientific correspondence at his command.

CAMBRIDGE,

26 May 1888.

H. R. LUARD.

G. G. STOKES.

J. C. ADAMS.

G. D. LIVEING.

APPENDIX TO THE PREFACE.

It may be interesting to give a few extracts from the Newton papers on some of the subjects which have been referred to in the above Preface.

I.

II.

These relate to

The form of the Solid of Least Resistance. Principia,
Lib. II. Prop. 35, Schol.

A List of Propositions in the Lunar Theory intended to be inserted in a second edition of the Principia. III. The motion of the Apogee in an elliptic orbit of very small eccentricity, caused by given disturbing forces.

I. ON THE FORM OF THE SOLID OF LEAST RESISTANCE.

LIB. II., PROP. XXXV. SCHOL., p. 326, 1st Ed. Draft of a Letter in Newton's hand, no doubt to Professor David Gregory, and probably written in 1694.

SIR,

I now thank you heartily both for the very kind visit you made me here and for the errata you gave me notice of in my book and also for your care of Mr Paget's business. The Lem. 1 in the third book I could not recover as tis there stated, but I have don't another way with a Demonstration, and altered very much the Proposition which follows upon it concerning the precession of the Equinox. The whole is too long to set down. The figure which feels the least resistance in the Schol. of Prop. xxxv. Lib. II. is demonstrable by these steps.

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