“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.

Such is the regular march of thought.  An hypothesis has no right to be brought forward until it has passed into the condition of a law, by being duly confirmed.  There are minds, however, endowed with a sort of divination, which feel as by instinct the truth of a discovery, even before it has been confirmed.  It is told of Copernicus, that having discovered, or re-discovered, the true system of planetary motion, he encountered an opponent who said to him:  “If your system were true, Venus would have phases like the moon; now she has none, and therefore your system is false.  What have you to reply?”—­“I have no reply to make,” said Copernicus, (the objection was a serious one in fact); “but God will grant that the answer shall be found."[165] Galileo appeared, and by means of the telescope it was ascertained that Venus has phases like the moon;—­the confidence of Copernicus was justified.  The scientific career of M. Ampere, the illustrious natural philosopher, supplies an analogous fact.  Trusting, like Copernicus, to a kind of intuition of truth, he read one day to the Academy of sciences the complete description of an experiment which he had never made.  He made it subsequently, and the result answered completely to his anticipations.  Genius is here raised to the second power, since it possesses at once the gift of discovery and the just presentiment of its confirmation; but these are exceptional cases, and in general we must say, with Mithridates, that—­