418 THE PRINCIPLES OF SCIENCE. [CHAP. 



relations between conditions and results which are found 

 capable of existence. It would thus resemble the exclusion 

 of contradictory combinations carried out in the Indirect 

 Method of Inference, except that the exclusion of com- 

 binations is grounded not on prior logical premises, but 

 on a posteriori results of actual trial. 



The reader will perceive, however, that such exhaustive 

 investigation is practically impossible, because the number 

 of requisite experiments would be immensely great. Four 

 antecedents only would require sixteen experiments ; twelve 

 antecedents 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 select- 

 ing those experiments 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 combinations; but this being impracticable, 

 the experimentalist necessarily abandons strict logical 

 method, and trusts to his own insight. Analogy, as we 

 shall see, gives some assistance, and attention should be 

 concentrated on those kinds of conditions which have been 

 found important in like cases. But we are now entirely 

 in the region of probability, and the experimenter, while 

 he is confidently pursuing what he thinks the right clue, 

 may be overlooking the one condition of importance. It is 

 an impressive lesson, for instance, that Newton pursued 

 all his exquisite researches on the spectrum unsuspicious of 

 the fact that if he reduced the hole in the shutter to a 

 narrow slit, all the mysteries of the bright and dark lines 

 were within his grasp, provided of course that his prisms 

 were sufficiently good to define the rays. In like manner 

 we know not what slight alteration in the most familiar 

 experiments may not open the way to realms of new 

 discovery. 



Practical difficulties, also, encumber the progress of the 

 physicist. It is often impossible to alter one condition 

 without altering others at the same time ; and thus we 

 may not get the pure effect of the condition in question. 

 Some conditions may be absolutely incapable of alteration ; 

 others may be with' great difficulty, or only in a certain 

 degree, removable. A very treacherous source of error is 

 the existence of unknown conditions, which of course we 



