« PreviousContinue »
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
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 (8 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.
H. R. LUARD.
26 May 1888.
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. These relate to I. The form of the Solid of Least Resistance. Principia,
Lib. II. Prop. 35, Schol.
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.
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.
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.
1. If upon BM be erected infinitely narrow parallelograms BGhb and M Nom and their distance Mb and altitudes MN, BG be
Mm+ Bb given, and the semi sum of their bases
be also given and
Mm - Bb called s and their semi difference
be called a : and if the
2 lines BG, bh, MN, mo, butt upon the curve nNgG in the points n, N, g, and G, and the infinitely little lines on and hg be equal to one another and called c, and the figure mnNgGB be turned about its axis BM to generate a solid, and this solid move uniformly in water from M to B according to the direction of its axis BM :
the summ of the resistances of the two surfaces generated by the infinitely little lines Gg, Nn shall be least when gG? is to nN19 as BGx Bo to MN x Mm. For the resistances of the surfaces generated by the revolution
MN of Gg and Nn are as
that is, if Ggquad Ggquad
BG MN and Nnquad be called p and q, as and
and their summ р
9 BG MN
BGP MNý is least when the fluxion thereof
is р 9
99 nothing, or
99 Now p=Ggquad = Bbquad + ghquad = ss – 2sx + 2x + cc and therefore p=– 28€ + 2xi, and by the same argument ġ
2sac + 2xic and BG x 2sc – 2.cie MN x 2s.c + 2xic BG XS-X MNx8+X therefore PP 99
99 and thence pp is to 99 as BG x 8 – a to MN x 8 + x, that is, gG! to nN99 as BG ~ Bb to MN * Mm.
BG x P
2. If the curve line DnNgG be such that the surface of the solid generated by its revolution feels the least resistance of any solid with the same top and bottom BG and CD, then the resistance of the narrow annular surfaces generated by the revolution of the [infinitely little lines nN] and Gg is less then if the intermediate solid bgNM be removed (along CB without altering Mb, until bg comes [to BG], supposing as before that on is equal to hg,] and by consequence it is the least that can be, and therefore gG99 is to nN99 as BG ~ Bb [is to MN x Mm].
*[Also if) gh be equal to hG so that the angle [gGh is 45degr) then will 4B6 be [to nN" as BG ~ Bb is to] MN x Mm, and by consequence 4BG91 is to GRI as BGA is to MN BR or 4BG! X BR is to GRcub (as GR to MN].
Whence the proposition to be demonstrated easily follows.
But its to be noted that in the booke pag 327 lin. 7 instead of Quod si figura DN FB it should be written Quod si figura DNFGB, and that DNFG is an uniform curve meeting with the right line GB in G in an angle of 135degr.
I have not yet made any experiments about the resistance of the air and water nor am resolved to see Oxford this year. But perhaps the next year I may. I had answered your letter sooner but that I wanted time to examin this Theorem and the Lem. 1 in the 3d Book. I do not see how to derive the resistance of the air from the ascent of water. The reasoning which must be about it seems too complicate to come under an exact calculus, and what allowance must be made for the retardation of the water by the contact of the pipe or hole at its going out of the vessel is hard to know.
LIST OF PROPOSITIONS APPARENTLY INTENDED TO BE INSERTED
IN A 2ND EDITION OF THE PRINCIPIA.
In Theoria Lunae tractentur hae Propositiones.
8 PROP. XXV. PROB. ·V. PAGE 434, PRINCIP. Orbem Lunae ad aequilibrium reducere.
* If the altitude of the frustum of the cone spoken of in the preceding paragraph be infinitely small, the semi-angle of the cone becomes equal to 45°. Hence when the total resistance is a minimum, the curve meets the extreme ordinate GB at an angle of 45°.