132 THE PRINCIPLES OF SCIENCE. 



inductive method, it would direct us to make an ex- 

 haustive arrangement of facts in all possible orders. 

 Given a certain number of specimens in a museum, we 

 might arrive at the best possible classification by going 

 systematically through all possible classifications, and, 

 were we endowed with infinite time and patience, this 

 would be an effective method. It doubtless is the method 

 by which the first few simple steps are taken in every 

 incipient branch of science. Before the dignified name 

 of science is applicable, some coincidences will chance 

 to force themselves upon the attention. Before there 

 was a science of meteorology, or any comprehension of the 

 true conditions of the atmosphere, all observant persons 

 learned to associate a peculiar 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 

 doubtless a considerable portion of our knowledge which 

 must always bear 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 very 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 illus- 

 trated in pp. 146-154 of the first volume, 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 4950 

 pairs of circumstances between which a coincidence may 

 exist. When a law involves three or more circum- 

 stances, the possible number of coincidences becomes 

 vastly greater still. When considering, again, the subject 



