CH. xxin.] THE USE OF HYPOTHESIS. 505 



are taken in an incipient branch of science. Before the dig- 

 nified name of science is applicable, some coincidences will 

 force themselves upon the attention. Before there was a 

 science of meteorology observant persons learned to asso- 

 ciate 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 know- 

 ledge 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 cir- 

 cumstances 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 me- 

 tallic 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 al- 

 chemists. Many of them were men of the greatest acute- 

 ness, 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 deduc- 

 tive investigation were wholly useless. Deprived of all 



