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 pre-eminently 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 wellknown 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 mention the names of many who are now making history in astronomical work.

August 1st, 1909.

G. F.

Book I.

THE GEOMETRICAL PERIOD

1. Primitive Astronomy and Astrology.

THE growth of intelligence in the human race has its counterpart in that of the individual, especially in the earliest stages. Intellectual activity and the development of reasoning powers are in both cases based upon the accumulation of experiences, and on the comparison, classification, arrangement, and nomenclature of these experiences. During the infancy of each the succession of events can be watched, but there can be no à priori anticipations. Experience alone, in both cases, leads to the idea of cause and effect as a principle that seems to dominate our present universe, as a rule for predicting the course of events, and as a guide to the choice of a course of action. This idea of cause and effect is the most potent factor in developing the history of the human race, as of the individual.

In no realm of nature is the principle of cause and effect more conspicuous than in astronomy; and we fall into the habit of thinking of its laws as not only being unchangeable in our universe, but necessary to the conception of any universe that might have been substituted in its place. The first inhabitants of the world were compelled to accommodate their acts to the daily and annual alternations of light and darkness and of heat and cold, as much as to the irregular changes of

weather, attacks of disease, and the fortune of war. They soon came to regard the influence of the sun, in connection with light and heat, as a cause. This led to a search for other signs in the heavens. If the appearance of a comet was sometimes noted simultaneously with the death of a great ruler, or an eclipse with a scourge of plague, these might well be looked upon as causes in the same sense that the veering or backing of the wind is regarded as a cause of fine or foul weather.

For these reasons we find that the earnest men of all ages have recorded the occurrence of comets, eclipses, new stars, meteor showers, and remarkable conjunctions of the planets, as well as plagues and famines, floods and droughts, wars and the deaths of great rulers. Sometimes they thought they could trace connections which might lead them to say that a comet presaged famine, or an eclipse war.

Even if these men were sometimes led to evolve laws of cause and effect which now seem to us absurd, let us be tolerant, and gratefully acknowledge that these astrologers, when they suggested such "working hypotheses," were laying the foundations of observation and deduction.

If the ancient Chaldæans gave to the planetary conjunctions an influence over terrestrial events, let us remember that in our own time people have searched for connection between terrestrial conditions and periods of unusual prevalence of sun spots; while De la Rue, Loewy, and Balfour Stewart' thought they found a connection between sun-spot displays and the planetary

I Trans. R. S. E., xxiii. 1864, p. 499, On Sun Spots, etc., by B. Stewart. Also Trans. R. S. 1860-70. Also Prof. Ernest Brown, in R. A. S. Monthly Notices, 1900.