xxx] CLASSIFICATION. 693 



iiidiirerently present and absent. The second arrangement 

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

 fest tlie 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, 1), E, in the follow- 

 ing manner: — 



ABCt^E aBCWE 



ABcde aBcde 



A6CDE ahCDE 



AbcDe ahcDe 



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- 

 uieut aud group the combinations thus : — 



ABCt/E A5CDE 



ABcde AhcDe 



aBCdE . ahCDE 



aBcde 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 : — 



ABC^/E ABcde 



aBCclE . aBcde 



AbCDE AbcBe 



abCDE 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 wav. We are classifying oulv 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 M-ould 

 hardly discover wjiat those laws are, and confidently assign 

 them by rapid contemplation of the combinations, as given 

 in the first grou}). Several tentative classifications umst 



