criticise a train of reasoning may have been equal to that of Kepler or Newton, but the point of view was different. Then, again, new points of view are provided by the invention of new methods in that system of logic which we call mathematics. All that mathematics can do is to assure us that a statement A is equivalent to statements B, C, D, or is one of the facts expressed by the statements B, C, D; so that we may know, if B, C, and D are true, then A is true. To many people our inability to understand all that is contained in statements B, C, and D, without the cumbrous process of a mathematical demonstration, proves the feebleness of the human mind as a logical machine. For it required the new point of view imagined by Newton's analysis to enable people to see that, so far as planetary orbits are concerned, Kepler's three laws (B, C, D) were identical with Newton's law of gravitation (A). No one recognises more than the mathematical astronomer this feebleness of the human intellect, and no one is more conscious of the limitations of the logical process called mathematics, which even now has not solved directly the problem of only three bodies. These reflections, arising from the writing of this History, go to explain the invariable humility of the great mathematical astronomers. Newton's comparison of himself to the child on the seashore applies to them all. As each new discovery opens up, it may be, boundless oceans for investigation, for wonder, and for admiration, the great astronomers, refusing to accept mere hypotheses as true, have founded upon these discoveries a science as exact in its observation of facts as in theories. So it is that these men, who have built up the most sure and most solid of all the sciences, refuse to invite others to join them in vain speculation. The writer has, therefore, in this short History, tried to follow that great master, Airy, whose pupil he was, and the key to whose character was exactness and accuracy; and he recognises that Science is impotent except in her own limited sphere. It has been necessary to curtail many parts of the History in the attempt — perhaps a hopeless one — to lay before the reader in a limited space enough about each age to illustrate its tone and spirit, the ideals of the workers, the gradual addition of new points of view and of new means of investigation. It would, indeed, be a pleasure to entertain the hope that these pages might, among new recruits, arouse an interest in the greatest of all the sciences, or that those who have handled the theoretical or practical side might be led by them to read in the original some of the classics of astronomy. Many students have much compassion for the schoolboy of to-day, who is not allowed the luxury of learning the art of reasoning from him who still remains preeminently its greatest exponent, Euclid. These students pity also the man of to-morrow, who is not to be allowed to read, in the original Latin of the brilliant Kepler, how he was able — by observations taken from a moving platform, the earth, of the directions of a moving object, Mars — to deduce the exact shape of the path of each of these planets, and their actual positions on these paths at any time. Kepler's masterpiece is one of the most interesting books that was ever written, combining wit, imagination, ingenuity, and certainty. Lastly, it must be noted that, as a History of England cannot deal with the present Parliament, so also the unfinished researches and untested hypotheses of many well-known astronomers of to-day cannot be included among the records of the History of Astronomy. The writer regrets the necessity that thus arises of leaving without inention the names of many who are now making history in astronomical work. G. F. August 1st, 1900. CONTENTs PREFACE. . . . . . . . . . . . . . . . . . . . . . . . . e - e. e. e. e. e. e. EMY TO COPERNICUs . . . . . . . . . . . . . . . . . BOOK II . Discovery OF THE TRUE SOLAR SystEM — Tycho BRAHE — KEPLE.R. . . . . . . . . . . . . GALILEO AND THE TELEscoPE – NOTIONS SIR Is AAC NEwton — LAw OF UNIVERSAL . NEwTON's SUCCEssoRs – HALLEY, EULER, LAGRANGE, LAPLACE, ETC. . . . . . . . . . . . . . Discovery of NEw PLAN Ets—HERSCHEL, PIAzzi, ADAMS, AND LE VERRIER. . . . . . PAGE SCOPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . BOOK IV 12. THE SUN. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Io9 |