If the views upheld in this work be correct, all inductive investigation consists in the marriage of hypothesis and experiment. When facts are in our possession, we frame an hypothesis to explain their relations, and by the success of this explanation is the value of the hypothesis to be judged. In the invention and treatment of such hypotheses, we must avail ourselves of the whole body of science already accumulated, and when once we have obtained a probable hypothesis, we must not rest until we have verified it by comparison with new facts. We must endeavour by deductive reasoning to anticipate such phenomena, especially those of a singular and exceptional nature, as would happen if the hypothesis be true. Out of the infinite number of experiments which are possible, theory must lead us to select those critical ones which are suitable for confirming or negativing our anticipations.
This work of inductive investigation cannot be guided by any system of precise and infallible rules, like those of deductive reasoning. There is, in fact, nothing to which we can apply rules of method, because the laws of nature must be in our possession before we can treat them. If there were any rule of inductive method, it would direct us to make an exhaustive arrangement of facts in all possible orders. Given the specimens in a museum, we might arrive at the best classification by going systematically through all possible classifications, and, were we endowed with infinite time and patience, this would be an effective method. It is the method by which the first simple steps are taken in an incipient branch of science. Before the dignified name of science is applicable, some coincidences will force themselves upon the attention. Before there was a science of meteorology observant persons learned to associate clearness of the atmosphere with coming rain, and a colourless sunset with fine weather. Knowledge of this kind is called empirical, as seeming to come directly from experience; and there is a considerable portion of knowledge which bears this character.
We may be obliged to trust to the casual detection of coincidences in those branches of knowledge where we are deprived of the aid of any guiding notions; but a little reflection will show the utter insufficiency of haphazard experiment, when applied to investigations of a complicated nature. At the best, it will be the simple identity, or partial identity, of classes, as illustrated in pages 127 or 134, which can be thus detected. It was pointed out that, even when a law of nature involves only two circumstances, and there are one hundred distinct circumstances which may possibly be connected, there will be no less than 4,950 pairs of circumstances between which coincidence may exist. When a law involves three or more circumstances, the possible number of relations becomes vastly greater. When considering the subject of combinations and permutations, it became apparent that we could never cope with the possible variety of nature. An exhaustive examination of the possible metallic alloys, or chemical compounds, was found to be out of the question (p. 191).
It is on such considerations that we can explain the very small additions made to our knowledge by the alchemists. Many of them were men of the greatest acuteness, and their indefatigable labours were pursued through many centuries. A few things were discovered by them, but a true insight into nature, now enables chemists to discover more useful facts in a year than were yielded by the alchemists during many centuries. There can be no doubt that Newton was an alchemist, and that he often laboured night and day at alchemical experiments. But in trying to discover the secret by which gross metals might be rendered noble, his lofty powers of deductive investigation were wholly useless. Deprived of all guiding clues, his experiments