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established, we are led to the conclusion that the sun was in the past larger and less condensed than now, and by going sufficiently far back into the past we find it in a condition not unlike the primitive nebula which Laplace presupposed, with the exception that it need not have been hot.

320. A new light has been thrown on the possible development of the earth and moon by Professor G. H. Darwin’s study of the effects of tidal friction (cf. § 287 and §§ 292, 293). Since the tides increase the length of the day and month and gradually repel the moon from the earth, it follows that in the past the moon was nearer to the earth than now, and that tidal action was consequently much greater. Following out this clue. Professor Darwin found, by a series of elaborate calculations published in 1879-81, strong evidence of a past time when the moon was close to the earth, revolving round it in the same time in which the earth rotated on its axis, which was then a little over two hours. The two bodies, in fact, were moving as if they were connected; it is difficult to avoid the probable inference that at an earlier stage the two really were one, and that the moon is in reality a fragment of the earth driven off from it by the too-rapid spinning of the earth, or otherwise.

Professor Darwin has also examined the possibility of explaining in a similar way the formation of the satellites of the other planets and of the planets themselves from the sun, but the circumstances of the moon-earth system turn out to be exceptional, and tidal influence has been less effective in other cases, though it gives a satisfactory explanation of certain peculiarities of the planets and their satellites. More recently (1892) Dr. See has applied a somewhat similar line of reasoning to explain by means of tidal action the development of double stars from an earlier nebulous condition.

Speaking generally, we may say that the outcome of the 19th century study of the problem of the early history of the solar system has been to discredit the details of Laplace’s hypothesis in a variety of ways, but to establish on a firmer basis the general view that the solar system has been formed by some process of condensation out of an earlier very diffused mass bearing a general resemblance to one of the nebulae which the telescope shews us, and that stars other than the sun are not unlikely to have been formed in a somewhat similar way; and, further, the theory of tidal friction supplements this general but vague theory, by giving a rational account of a process which seems to have been the predominant factor in the development of the system formed by our own earth and moon, and to have had at any rate an important influence in a number of other cases.

AUTHORITIES AND BOOKS FOR STUDENTS. I. General.

I have made great use throughout of R. Wolf’s Geschichte der Astronomie, and of the six volumes of Delambre’s Histoire de l’Astronomie (Ancienne, 2 vols.; du Moyen Age, 1 vol.; Moderne, 2 vols.; du Dixhuitième Siècle, 1 vol.). I shall subsequently refer to these books simply as Wolf and Delambre respectively. I have used less often the astronomical sections of Whewell’s History of the Inductive Sciences (referred to as Whewell), and I am indebted—chiefly for dates and references—to the histories of mathematics written respectively by Marie, W. W. R. Ball, and Cajori, to Poggendorff’s Handwörterbuch der Exacten Wissenschaften, and to articles in various biographical dictionaries, encyclopaedias, and scientific journals. Of general treatises on astronomy Newcomb’s Popular Astronomy, Young’s General Astronomy, and Proctor’s Old and New Astronomy have been the most useful for my purposes.

It is difficult to make a selection among the very large number of books on astronomy which are adapted to the general reader. For students who wish for an introductory account of astronomy the Astronomer Royal’s Primer of Astronomy may be recommended; Young’s Elements of Astronomy is a little more advanced, and Sir R. S. Ball’s Story of the Heavens, Newcomb’s Popular Astronomy, and Proctor’s Old and New Astronomy enter into the subject in much greater detail. Young’s General Astronomy may also be recommended to those who are not afraid of a little mathematics. There are also three modern English books dealing generally with the history of astronomy, in all of which the biographical element is much more prominent than in this book: viz. Sir R. S. Ball’s Great Astronomers, Lodge’s Pioneers of Science, and Morton’s Heroes of Science: Astronomers.

II. Special Periods.

Chapters I. and II.—In addition to the general histories quoted above—especially Wolf—I have made most use of Tannery’s Recherches sur l’Histoire de l’Astronomie Ancienne and of several biographical articles (chiefly by De Morgan) in Smith’s Dictionary of Classical Biography and Mythology. Ideler’s Chronologische Untersuchungen, Hankel’s Geschichte der Mathematik im Alterthum und Mittelalter, G. C. Lewis’s Astronomy of the Ancients, and Epping & Strassmaier’s Astronomisches aus Babylon have also been used to some extent. Unfortunately my attention was only called to Susemihl’s Geschichte der Griechischen Litteratur in der Alexandriner Zeit when most of my book was in proof, and I have consequently been able to make but little use of it.

I have in general made no attempt to consult the original Greek authorities, but I have made some use of translations of Aristarchus, of the Almagest, and of the astronomical writings of Plato and Aristotle.

Chapter III.—The account of Eastern astronomy is based chiefly on Delambre, and on Hankel’s Geschichte der Mathematik im Alterthum und Mittelalter; to a less extent on Whewell. For the West I have made more use of Whewell, and have borrowed biographical material for the English writers from the Dictionary of National Biography. I have also consulted a good many of the original astronomical books referred to in the latter part of the chapter.

I know of no accessible book in English to which to refer students except Whewell.

Chapter IV.—For biographical material, for information as to the minor writings, and as to the history of the publication of the De Revolutionibus I have used little but Prowe’s elaborate Nicolaus Coppernicus, and the documents printed in it. My account of the De Revolutionibus is taken from the book itself. The portrait is taken from Dandeleau’s engraving of a picture in Lalande’s possession. I have not been able to discover any portrait which was clearly made during Coppernicus’s lifetime, but the close resemblance between several portraits dating from the 17th century and Dandeleau’s seems to shew that the latter is substantially authentic.

There is a readable account of Coppernicus, as well as of several other astronomers, in Bertrand’s Fondateurs de l’Astronomie Moderne; but I have not used the book as an authority.

Chapter V.—For the life of Tycho I have relied chiefly on Dreyer’s Tycho Brahe, which has also been used as a guide to his scientific work; but I have made constant reference to the original writings: I have also made some use of Gassendi’s Vita Tychonis Brahe. The portrait is a reproduction of a picture in the possession of Dr. Crompton of Manchester, described by him in the Memoirs of the Manchester Literary and Philosophical Society, Vol. VI., Ser. III. For minor Continental writers I have used chiefly Wolf and Delambre, and for English writers, Whewell, various articles by De Morgan quoted by him, and articles in the Dictionary of National Biography.

Students will find in Dreyer’s book all that they are likely to want to know about Tycho.

Chapter VI.—For Galilei’s life I have used chiefly Karl von Gebler’s Galilei und die Römische Curie, partly in the original German form and partly in the later English edition (translated by Mrs. Sturge). For the disputed questions connected with the trial I have relied as far as possible on the original documents preserved in the Vatican, which have been published by von Gebler and independently by L’Épinois in Les Pièces du Procès de Galilée: in the latter book some of the most important documents are reproduced in facsimile. For personal characteristics I have used the charming Private Life of Galileo, compiled chiefly from his correspondence and that of his daughter Marie Céleste. I have also read with great interest the estimate of Galilei’s work contained in H. Martin’s Galilée, and have probably borrowed from it to some extent. What I have said about Galilei’s scientific work has been based almost entirely on study of his own books, either in the original or in translation: I have used freely the translations of the Dialogue on the Two Chief Systems of the World and of the Letter to the Grand Duchess Christine by Salusbury, that of the Two New Sciences by Weston (as well as that by Salusbury), and that of the Sidereal Messenger by Carlos. I have also made some use of various controversial tracts written by enemies of Galilei, which are to be found (together with his comments on them) in the magnificent national edition of his works now in course of publication; and of the critical account of Galilei’s contributions to dynamics contained in Mach’s Geschichte der Mechanik.

Wolf and Delambre have only been used to a very small extent in this chapter, chiefly for the minor writers who are referred to.

The portrait is a reproduction of one by Sustermans in the Uffizi Gallery.

There is an excellent popular account of Galilei’s life and work in the Lives of Eminent Persons published by the Society for the Diffusion of Useful Knowledge; students who want fuller accounts of Galilei’s life should read Gebler’s book and the Private Life, which have been already quoted, and are strongly recommended to read at any rate parts of the Dialogue on the Two Chief Systems of the World, either in the original or in the picturesque old translation by Salusbury: there is also a modern German version of this book, as well as of the Two New Sciences, in Ostwald’s series of Klassiker der exakten Wissenschaften.

Chapter VII.—For Kepler’s life I have used chiefly Wolf and the life—or rather biographical material—given by Frisch in the last volume of his edition of Kepler’s works, also to a small extent Breitschwerdt’s Johann Keppler. For Kepler’s scientific discoveries I have used chiefly his own writings, but I am indebted to some extent to Wolf and Delambre, especially for information with regard to his minor works. The portrait is a reproduction of one by Nordling given in Frisch’s edition.

The Lives of Eminent Persons, already referred to, also contains an excellent popular account of Kepler’s life and work.

Chapter VIII.—I have used chiefly Wolf and Delambre; for the English writers Gascoigne and Horrocks I have used Whewell and articles in the Dict. Nat. Biog. What I have said about the work of Huygens is taken directly from the books of his which are quoted in the text; and for special points I have consulted the Principia of Descartes, and a very few of Cassini’s extensive writings.

There is no obvious book to recommend to students.

Chapter IX.—For the external events of Newton’s life I have relied chiefly on Brewster’s Memoirs of Sir Isaac Newton; and for the history of the growth of his ideas on the subject of gravitation I have made extensive use of W. W. R. Ball’s Essay on Newton’s Principia, and of the original documents contained in it. I have also made some use of the articles on Newton in the Encyclopaedia Britannica and the Dictionary of National Biography; as well as of Rigaud’s Correspondence of Scientific Men of the Seventeenth Century, of Edleston’s Correspondence of Sir Isaac Newton and Prof. Cotes, and of Baily’s Account of the Revd. John Flamsteed. The portrait is a reproduction of one by Kneller.

Students are recommended to read Brewster’s book, quoted above, or the abridged Life of Sir Isaac Newton by the same author. The Laws of Motion are discussed in

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