24 THE PRINCIPLES OF SCIENCE. 



and in another when air is absent. The inquiry branches 

 out into two lines, and we ought to try in both cases 

 whether cutting off a supply of heat by conduction pre 

 vents its evolution in friction. Now the same branching 

 out of the inquiry occurs with regard to every circum 

 stance which enters into the experiment. Regarding 

 only four circumstances, say A, B, C, D, we ought to test 

 not only the combinations 



ABCD, ABCd, ABcD, A&CD, BCD, 



but we ought really to go through the whole of the combi 

 nations given in the fifth column of the Logical Abece- 

 clarium. The effect of the absence of each condition should 

 be tried both in the presence and absence of every other 

 condition, and every variety of selection of those conditions. 

 Perfect and exhaustive experimentation would, in short, 

 consist in examining natural phenomena in all their pos 

 sible combinations and registering all relations between 

 conditions and results which are found capable of exist 

 ence. Experimentation would thus resemble the exclusion 

 of contradictory combinations carried out in the Indirect 

 Method of Inference (chapter vi. vol. i. p. 95), except that 

 the exclusion of any combination is grounded not on prior 

 logical premises, but on a posteriori results of actual trial. 

 The reader will readily perceive, however, that such 

 exhaustive investigation is practically impossible, because 

 the number of requisite experiments would be immensely 

 great. Four circumstances only would require sixteen 

 experiments ; twelve circumstances would require 4096, 

 and the number increases as the powers of two. The 

 result is that the experimenter has to fall back upon his 

 own tact and experience in selecting those variations 

 which are most likely to yield him significant facts. It 

 is at this point that logical rules and forms begin to fail 

 in giving aid. The logical rule is Try all possible com- 



