368 THE PRINCIPLES OF SCIENCE. 



discover, and, if we arrange the classes in any one order 

 rather than another, it must be for the purpose of showing 

 that the combinations are logically complete. It will be 

 obvious that there are three different possible arrange- 

 ments which may be of some use ; firstly, that employed 

 above in which all the combinations containing A stand 

 first, and those devoid of it follow ; secondly, and thirdly, 

 the similar arrangements in which the combinations con- 

 taining B, and C, respectively stand first. 



Suppose now that there are but four kinds of objects 

 possessing the qualities A, B, C, and that these kinds are 

 represented by the combinations ABC, AbC, aBc, abc. 

 The order of arrangement will now be of importance ; for 

 if we place them in the order 



fABC 



[aBc 

 JA6C 

 [abc 



placing the B's first and those which are Us last, we shall 

 perhaps overlook the law of correlation of properties in- 

 volved. But if we arrange the combinations as follows 



JABC 



[AbC 

 faBc 

 [abc 



it becomes apparent at once that where A is, and only 

 where A is, the property C is to be found, B being in- 

 differently present and absent. The second arrangement 

 then would be called a natural one, as rendering mani- 

 fest the conditions under which the combinations exist. 



As a further instance, let us suppose that eight objects 

 are presented to us for classification, which exhibit combi- 

 nations of the five properties, A, B, C, D, E, in the follow- 

 ing manner : 



