134 THE PRINCIPLES OF SCIENCE. [CHAP. 



refraction for light ; and every facet is repeated in. like 

 relation to each of the three axes. Crystals of the system 

 having one principal axis will be found to possess the 

 various physical powers of conduction, refraction, elas- 

 ticity, &c., uniformly in directions perpendicular to the 

 principal axis ; in other directions their properties vary 

 according to complicated laws. The remaining systems 

 in which the crystals possess three unequal axes, or have 

 inclined axes, exhibit still more complicated results, the 

 effects of the crystal upon light, heat, electricity, &c., 

 varying in all directions. But when we pursue induction 

 into the intricacies of its application to nature we really 

 enter upon the subject of classification, which we must 

 take up again in a later part of this work. 



Solution of the Inverse or Inductive Problem, involving 

 Two Classes. 



It is now plain that Induction consists in passing back 

 from a series of combinations to the laws by which such 

 combinations are governed. The natural law that all 

 metals are conductors of electricity really means that in 

 nature we find three classes of objects, namely 



1. Metals, conductors ; 



2. Not-metals, conductors ; 



3. Not-metals, not-conductors. 



It comes to the same thing if we say that it excludes the 

 existence of the class, "metals not-conductors." In the 

 same way every other law or group of laws will really 

 mean the exclusion from existence of certain combinations 

 of the things, circumstances or phenomena governed by 

 those laws. Now in logic, strictly speaking, we treat not 

 the phenomena, nor the laws, but the general forms of the 

 laws ; and a little consideration will show that for a finite 

 number of things the possible number of forms or kinds 

 of law governing them must also be finite. Using general 

 terms, we know that A and B can be present or absent in 

 four ways and no more thus : 



AB, AJb, aB, ab ; 



therefore every possible law which can exist concerning 

 the relation of A and B must be marked by the exclusion 

 of one or more of the above combinations. The number 



