"After I had found the real dimensions of the orbits, thanks to the observations of Brahe and the sustained effort of a long course of labor, I at length discovered the proportion of the periodic times to the extent of these orbits. And if you would like to know the precise date of the discovery,--it was on the eighth day of March in this year 1618 that,--first of all conceived in my mind, then awkwardly essayed by calculations, rejected in consequence as false, then reproduced on the fifteenth of May with fresh energy,--it rose at last above the darkness of my understanding, so fully confirmed by my labor of seventeen years upon Brahe's observations, and by my own meditations perfectly agreeing with them, that I thought at first I was dreaming, and making some _petitio principii_; but there is no more doubt about it: it is a very certain and very exact proposition."[164] All the logic of discoveries is laid down in these lines; and these lines are a testimony rendered by one of the most competent of witnesses. You see in them the conditions of a good hypothesis: Kepler has long studied the phenomena of which he wishes to find the law; he has studied them by himself, and by means of the discoveries of his predecessor Brahe. The law has presented itself to his mind at a given moment, on the eighth of March, 1618. But he does not yet know whether it is a true light, or a deceptive gleam. He seeks the confirmation of his hypothesis; he does not find it, because he makes a mistake, and he rejects his idea as useless. The idea returns; a new course of labor confirms it; and so the hypothesis becomes a law, a certain proposition.