This declaration of principles met, at the time, with the hostility of all astronomers of any reputation, but it has become the starting-point of the discovery of the laws on which the whole edifice of astronomy reposes. Had Kepler, however, been left to depend entirely on his own resources, he might, perhaps, have never completed his task. A fortunate circumstance brought him an unexpected ally. Tycho, having taken refuge in Bohemia, sent for the young astronomer (Kepler then was but twenty-nine years old), to assist him in the composition of the "Rudolphine Tables."[74] "This," says Kepler, "was a providential interposition. I repaired to Bohemia early in the year 1600, in the hope of learning the correction of the eccentricities of the planets. Perceiving that Tycho made use of a mixed system (which made Mercury and Venus revolve around the sun, and all these planets, with their companions, around the earth), I asked his permission to follow out my own ideas. It was the will of Providence again, that we should occupy ourselves with Mars. My whole attention, therefore, was directed to this planet: and it is through the movements of Mars we must obtain our insight into the secrets of astronomy, or remain ignorant of them for ever (_ex Martis motibus omnino necesse est nos in cognitionem astronomiæ arcanorum venire aut ea perpetuo nescire_)."[75] Why this preference given to Mars? In the first place, because, among all the planets then known, it was Mars which, in its movement round the sun, departed most from the circle; next, its orbit approaches nearest to the earth's; the earth is very near to Mars when she passes between that planet and the sun,--that is to say, when she is in _opposition_, while she retires from it triple the distance when in _conjunction_,--that is, when the sun is between her and Mars. Hence arise certain variations of aspect, particularly adapted to make manifest the form of the orbit, and the law of the real movement of the "red planet, Mars." As for the other planets, as far as they were then known, their orbits differ so little from the circle, that the nature of the curve which they describe in reality would never have been exactly recognised by any inexperienced star-gazer. For these reasons Kepler regarded as providential the choice he had been led to make of Mars at the outset of his astronomical career. Before the close of 1601, Tycho died, bequeathing to his young fellow-worker a treasury of observation. Thenceforth Kepler undertook to finish without assistance the famous Rudolphine Tables. They cost him five-and-twenty years of assiduous labour. Looking upon Tycho's observations, because of their exactness, as "a gift from the Divine Goodness," he employed them, in the first place, as a test of the old hypotheses of planetary orbits and movements. Let us do our best to grasp the range and bearing of this part of his work. * * * * *