vague ideas as to the properties of metals and the geometrical relations of the regular solids.  Above all, his reasoning was penetrated by the supposed astrological influences of the stars and their significant relation to human fate.  Under the influence of such a farrago of notions, Kepler resolved to make all sorts of trials in his search for the connection between the distance of a planet from the sun and the time in which the revolution of that planet was accomplished.

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.