PREFACE An attempt has been made in these pages to trace the evolution of intellectual thought in the progress of astronomical discovery, and, by recognising the different points of view of the different ages, to give due credit even to the ancients. No one can expect, in a history of astronomy of limited size, to find a treatise on practical" or on "theoretical astronomy," nor a complete "descriptive astronomy," and still less a book on " speculative astronomy." Something of each of these is essential, however, for tracing the progress of thought and knowledge which it is the object of this History to describe. The progress of human knowledge is measured by the increased habit of looking at facts from new points of view, as much as by the accumulation of facts. The mental capacity of one age does not seem to differ from that of other ages; but it is the imagination of new points of view that gives a wider scope to that capacity. And this is cumulative, and therefore progressive. Aristotle viewed the solar system as a geometrical problem; Kepler and Newton converted the point of view into a dynamical one. Aristotle's mental capacity to understand the meaning of facts or to 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 |