vigorous one. Fertility of imagination and abundance of guesses at truth are among the first requisites of discovery; but the erroneous guesses must be many times as numerous as those which prove well founded. The weakest analogies, the most whimsical notions, the most apparently absurd theories, may pass through the teeming brain, and no record remain of more than the hundredth part. There is nothing really absurd except that which proves contrary to logic and experience. The truest theories involve suppositions which are inconceivable, and no limit can really be placed to the freedom of hypothesis.
Kepler is an extraordinary instance to this effect. No minor laws of nature are more firmly established than those which he detected concerning the orbits and motions of planetary masses, and on these empirical laws the theory of gravitation was founded. Did we not learn from his own writings the multitude of errors into which he fell, we might have imagined that he had some special faculty of seizing on the truth. But, as is well known, he was full of chimerical notions; his favourite and long-studied theory was founded on a fanciful analogy between the planetary orbits and the regular solids. His celebrated laws were the outcome of a lifetime of speculation, for the most part vain and groundless. We know this because he had a curious pleasure in dwelling upon erroneous and futile trains of reasoning, which most persons consign to oblivion. But Kepler’s name was destined to be immortal, on account of the patience with which he submitted his hypotheses to comparison with observation, the candour with which he acknowledged failure after failure, and the perseverance and ingenuity with which he renewed his attack upon the riddles of nature.
Next after Kepler perhaps Faraday is the physical philosopher who has given us the best insight into the progress of discovery, by recording erroneous as well as successful speculations. The recorded notions, indeed, are probably but a tithe of the fancies which arose in his active brain. As Faraday himself said—“The world little knows how many of the thoughts and theories which have passed through the mind of a scientific investigator, have been crushed in silence and secrecy by his own severe criticism and adverse examination; that in the most successful instances not a tenth of the suggestions, the hopes, the wishes, the preliminary conclusions have been realised.”
Nevertheless, in Faraday’s researches, published in the Philosophical Transactions, in minor papers, in manuscript note-books, or in other materials, made known in his interesting life by Dr. Bence Jones, we find invaluable lessons for the experimentalist. These writings are full of speculations which we must not judge by the light of subsequent discovery. It may perhaps be said that Faraday committed to the printing press crude ideas which a friend would have counselled him to keep back. There was occasionally even a wildness and vagueness in his notions, which in a less careful experimentalist would have been fatal to the attainment of truth. This is especially apparent in a curious paper concerning Ray-vibrations; but fortunately Faraday was aware of the shadowy character of his speculations, and expressed the feeling in words which must be quoted. “I think it likely,” he says,1 “that I have made many mistakes in the preceding pages, for even to myself my ideas on this point appear only as the shadow of a speculation, or as one of those impressions upon the mind, which are allowable for a time as guides to thought and research. He who labours in experimental inquiries knows how numerous these are, and how often their apparent fitness and beauty vanish before the progress and development of real natural truth.” If, then, the experimentalist has no royal road to the discovery of the truth, it is an interesting matter to consider by what logical procedure he attains the truth.
If I have taken a correct view of logical method, there is really no such thing as a distinct process of induction. The probability is infinitely small that a collection of complicated facts will fall into an