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PREFACE.

IT:
T has been long known that Sir Isaac Newton left, at his

death, a large mass of papers, consisting partly of copies of his works written out or corrected for the press, partly of notes relating to the various subjects in which he was interested, and of an extensive correspondence with English and Foreign mathematicians. These came immediately on his death into the possession of Mr Conduitt, who married Catharine Barton, Newton's favourite and accomplished niece. By the marriage of their only child to the first Lord Lymington, they passed into the hands of the first Lord Lymington, and we find them in October 1751 in the hands of Mr Saunderson of Sheer Lane, for Lord Lymington'. Since that time they have remained in the possession of the Portsmouth family.

Several years ago the present Earl of Portsmouth expressed a wish to present to the University all that portion of the papers and correspondence which related to science, as he felt that these would find a more appropriate home in the Library of Newton's own University than in that of a private individual. Lord Portsmouth entrusted the whole collection of papers to the University, and the present syndicate was appointed to examine, classify, and divide them. This has proved a lengthy and laborious business, as many of the papers were found to be in great confusion-mathematical notes being often inserted in the middle of theological treatises, and even numbered leaves of MSS. having got out of order. Moreover a large portion of the collection has been grievously damaged by fire and damp. The

i See Stukeley's Memoirs (Surt. Soc., 1887) iii. p. 15.

correspondence, however, is in a very fair condition throughout, and had been arranged in an orderly manner.

On receiving a preliminary report on the contents of the collection, Lord Portsmouth expressed a wish that the papers relating to Theology, Chronology, History, and Alchemy, should be returned to him at Hurstbourne, where they would be carefully preserved. On account of his connection with the Newton family, Lord Portsmouth also naturally wished to have returned to him all the papers relating to private, personal, and family matters. These, however, are comparatively few, and not of much interest, with the exception of a short note from Newton's mother, written to him when a boy at College.

Although till the present time the papers have never been thoroughly examined, they have been looked at and partially used by various persons since Newton's death. When that occurred (in 1727) Dr Pellett was appointed by the executors to examine them and to select such as he deemed fit for publication. A rough catalogue of the papers is appended to a bond given by Mr Conduitt to the administrators of Newton's estate, in which he binds himself to account for any profit he may make by their publication. This list, with some remarks of Dr Pellett, will be found in Hutton's Mathematical Dictionary. All which Dr Pellett deemed fit to be printed were An Abstract of the Chronology in 12 half-sheets folio, and The Chronology of Ancient Kingdoms Amended in 92 half-sheets folio; and these were printed in 1728 under the care of Mr Conduitt.

The whole collection was inspected by Dr Horsley, who edited in 1779 the well-known edition of Newton's works in five quarto volumes. He left a few unimportant remarks on some of the papers, but he made no use of them in his edition.

It was again placed in the hands of Sir David Brewster, for his second and elaborate life of Newton in 1855; he made some use of the scattered mathematical notes and papers, and printed a considerable portion of the correspondence.

The character of the collection will be made clear by the catalogue which is now put forth. It divides itself (excluding the correspondence) into the heads of Mathematics, Chemistry and Alchemy, Chronology, History, and Theology. Many of the Mathematical papers contain Newton's preparations for the Principia, and notes which spring out of questions that were started by his correspondents. It must be recollected that Newton practically gave up his mathematical studies after 1696, even the superintendence of the second edition of the Principia being given to Cotes, and thus that after this date there is little of value in these subjects; and as most of what is contained in them, especially all that relates to the revision of the Principia, has been published, there is little to be found beyond what has already appeared.

The case is different, however, with respect to the papers referring to three subjects, viz. 1st, the Lunar Theory, 2nd, the Theory of Atmospheric Refraction, and 3rd, the Determination of the Form of the Solid of Least Resistance,

It is expressly stated by Newton himself that the Lunar Theory as given in his Principia is a mere specimen or fragment of the subject, intended to show how some of the more prominent lunar inequalities could be traced to the disturbing action of the Sun, and how their amounts could be calculated approximately by theory.

The only part which is developed with any fulness of detail is that relating to the inequality called the variation, and also that which treats of the motion of the node and the change of inclination of the orbit to the ecliptic.

In a short scholium given in the first edition of the Principia, Newton mentions that by similar computations he has found the motion of the moon's apogee, and he states some of the numerical results which he has obtained, but he does not give the calculations themselves, as he considers them too complicated and not sufficiently accurate.

In the second edition this short scholium is replaced by a long one, in which Newton states many of the principal results of the Lunar Theory, partly as found from theory alone and partly as deduced by combining his theory with observation; but he confines himself to results alone, and does not give the method by which these results have been obtained. Unfortunately also, the statement given in the first edition, as to the result which he had found by theory for the motion of the moon's apogee, is omitted in the new scholium.

It is interesting to find among the papers on the Lunar Theory a good many containing Newton's calculations relating to the inequalities which are described in the above scholium. These papers are unfortunately very imperfect, and they have greatly suffered from fire and damp, but there is enough remaining to give a general idea of Newton's mode of proceeding. The most interesting of these papers relate to the motion of the moon's apogee. Two lemmas are first established which give the motion of the apogee in an elliptic orbit of very small eccentricity due to given small disturbing forces acting, (1) in the direction of the radius vector, and (2) in the direction perpendicular to it.

These lemmas are carefully written out, as if in preparation for the press, and they were probably at first intended to form part of the Principia.

Next follows the application of the lemmas to the particular case of the Moon, in which the supposition that the disturbances are represented by changes in the elements of a purely elliptic orbit of small eccentricity would lead to practical inconvenience, and consequently Newton is led to modify that supposition. In the Principia he shows that if the moon's orbit be supposed to have no independent eccentricity, its form will be approximately an oval with the earth in the centre, the smaller axis being in the line of syzygies and the larger in that of quadratures, the ratio of these axes being nearly that of 69 to 70. Now when the proper eccentricity of the orbit is taken into account, supposing that eccentricity to be small, Newton assumes that the form of the orbit in which the moon really moves will be related to the form of the oval orbit before mentioned, nearly as an elliptic orbit of small eccentricity with the earth in its focus is related to a circular orbit about the earth in the centre. He then attempts to deduce the horary motion of the moon's apogee for any given position of the apogee with respect to the sun, and his conclusion is that if C denote the cosine of double the angle of elongation of the sun from the moon's apogee, then the mean hourly motion of the inoon's apogee when in that position is to the mean hourly motion of the moon as

1+ 4C : 238%. The investigation on this point is not entirely satisfactory, and from the alterations made in the MS. Newton evidently felt doubts about the correctness of the coefficient { which occurs in this formula.

From this, however, he deduces quite correctly that the mean annual motion of the apogee resulting would amount to 38° 51' 51", whereas the annual motion given in the Astronomical Tables is 40° 411'.

The result stated in the scholium to the 1st Edition appears to have been found by a more complete and probably a much more complicated investigation than that contained in the extant MSS.

The papers also contain a long list of propositions in the Lunar Theory which were evidently intended to be inserted in a second edition, upon which Newton appears to have been engaged in 1694. This list, together with the two lemmas on the motion of the apogee mentioned above, will be found in the Appendix.

Halley inserted in the Philosophical Transactions of 1721 a Table of Refractions by Newton, without giving any idea of the method of its formation,

Kramp, in his Analyse des Réfractions, published in 1799, investigates by a new and powerful analytical method the law of atmospheric refraction for rays in the neighbourhood of the horizon.

On comparing his theoretical results with Newton's Table, he finds a remarkably close agreement, which is enough to show that the Table was also the result of theory, and therefore that Newton must have had some method of his own of solving the difficult problem of horizontal refraction.

Nothing was known of this method, however, until the publication of the correspondence between Newton and Flamsteed by Mr Baily in 1835. In a letter to Flamsteed, dated December 20th, 1694', Newton tries to explain the foundation of

Baily's Flamsteed p. 145.

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