XXX.] 



CLASSIFICATION. 



indifferently 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 : 



ABCdE aBCrfE 



ABcde aBcde 



A&CDE abCDE 



AbcDe abcDe 



They are now classified, so that those containing A stand 

 first, and those devoid of A second, but no other property 

 seems to be correlated with A. Let us alter this arrange- 

 ment and group the combinations thus : 



ABCdE A&CDE 



ABcde AbcDe 



aBC<fE a&CDE 



dBcde abcDe 



It requires little examination to discover that in the first 

 group B is always present and D absent, whereas in the 

 second group, B is always absent and D present. This is 

 the result which follows from a law of the form B = d 

 (p. 136), so that in this mode of arrangement we readily 

 discover correlation between two letters. Altering the 

 groups again as follows : 



ABCdE ABcde 



aBCdE aBcde 



A&CDE AbcDe 



a&CDE abcDe, 



we discover another evident correlation between C and E. 

 Between A and the other letters, or between the two pairs 

 of letters B, D and C, E, there is no logical connexion. 



This example may seem tedious, but it will be found 

 instructive in this way. We are classifying only eight 

 objects or combinations, in each of which only five qualities 

 are considered. There are only two laws of correlation 

 between four of those five qualities, and those aws are 

 of the simplest logical character. Yet the reader would 

 hardly discover what those laws are, and confidently assign 

 them by rapid contemplation of the combinations, as given 

 in the first group. Several tentative classifications must 



