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It was quite easily demonstrated that the greater the distance of the planet from the sun the longer was the time required for its journey. It might have been thought that the time would be directly proportional to the distance. It was, however, easy to show that this supposition did not agree with the fact. Finding that this simple relation would not do, Kepler undertook a vast series of calculations to find out the true method of expressing the connection. At last, after many vain attempts, he found, to his indescribable joy, that the square of the time in which a planet revolves around the sun was proportional to the cube of the average distance of the planet from that body.

The extraordinary way in which Kepler's views on celestial matters were associated with the wildest speculations, is well illustrated in the work in which he propounded his splendid discovery just referred to. The announcement of the law connecting the distances of the planets from the sun with their periodic times, was then mixed up with a preposterous conception about the properties of the different planets. They were supposed to be associated with some profound music of the spheres inaudible to human ears, and performed only for the benefit of that being whose soul formed the animating spirit of the sun.

Kepler was also the first astronomer who ever ventured to predict the occurrence of that remarkable phenomenon, the transit of a planet in front of the sun's disc. He published, in 1629, a notice to the curious in things celestial, in which he announced that both of the planets, Mercury and Venus, were to make a transit across the sun on specified days in the winter of 1631. The transit of Mercury was duly observed by Gassendi, and the transit of Venus also took place, though, as we now know, the circumstances were such that it was not possible for the phenomenon to be witnessed by any European astronomer.

In addition to Kepler's discoveries already mentioned, with which his name will be for ever associated, his claim on the gratitude of astronomers chiefly depends on the publication of his famous Rudolphine tables. In this remarkable work means are provided for finding the places of the planets with far greater accuracy than had previously been attainable.

Kepler, it must be always remembered, was not an astronomical observer. It was his function to deal with the observations made by Tycho, and, from close study and comparison of the results, to work out the movements of the heavenly bodies. It was, in fact, Tycho who provided as it were the raw material, while it was the genius of Kepler which wrought that material into a beautiful and serviceable form. For more than a century the Rudolphine tables were regarded as a standard astronomical work. In these days we are accustomed to find the movements of the heavenly bodies set forth with all desirable exactitude in the NAUTICAL ALMANACK, and the similar publication issued by foreign Governments. Let it be remembered that it was Kepler who first imparted the proper impulse in this direction.

[PLATE: THE COMMEMORATION OF THE RUDOLPHINE TABLES.]

When Kepler was twenty-six he married an heiress from Styria, who, though only twenty-three years old, had already had some experience in matrimony. Her first husband had died; and it was after her second husband had divorced her that she received the addresses of Kepler. It will not be surprising to hear that his domestic affairs do not appear to have been particularly happy, and his wife died in 1611. Two years later, undeterred by the want of success in his first venture, he sought a second partner, and he evidently determined not to make a mistake this time. Indeed, the methodical manner in which he made his choice of the lady to whom he should propose has been duly set forth by him and preserved for our edification. With some self-assurance he asserts that there were no fewer than eleven spinsters desirous of sharing his joys and sorrows. He has carefully estimated and recorded the merits and demerits of each of these would-be brides. The result of his deliberations was that he awarded himself to an orphan girl, destitute even of a portion. Success attended his choice, and his second marriage seems to have proved a much more suitable union than his first. He had five children by the first wife and seven by the second.

The years of Kepler's middle life were sorely distracted by a trouble which, though not uncommon in those days, is one which we find it difficult to realise at the present time. His mother, Catherine Kepler, had attained undesirable notoriety by the suspicion that she was guilty of witchcraft. Years were spent in legal investigations, and it was only after unceasing exertions on the part of the astronomer for upwards of a twelvemonth that he was finally able to procure her acquittal and release from prison.

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