69G THE PRINCIPLES OF SCIENCE. [CHAP. 



It is quite evident that according to the laws of thought 

 even this arrangement is incomplete. The sub-class mam- 

 mifera must either have wings or be deprived of them ; we 

 must either subdivide this class, or assume that none of 

 the mammifera have wings, which is, as a matter of fact, the 

 case, the wings of bats not being true wings in the meaning 

 of the term as applied to birds. Fish, again, ought to be 

 considered with regard to the possession of mammae and 

 wings ; and in leaving them undivided we really imply that 

 they never have mammce nor wings, the wings of the flying- 

 fish, again, being no exception. If we resort to the use of 

 our letters and define them as follows 



A = vertebrata, 



B = having lungs, 



C = having mammee, 



D = having wings, 



then there are four existent classes of vertebrata which 

 appear to be thus described 



ABC ABcD AEcd Ab. 



But in reality the combinations are implied to be 



ABCd = Mammifera, 



ABcD = Birds, 



ABcd = Eeptiles, 



Abed = Fish, 



and we imply at the same time that the other four con- 

 ceivable combinations containing B, C, or D, namely ABCD, 

 AbCD, AbCd, and AbcD, do not exist in nature. 



Mr. Bentham points out 1 that it is really this method of 

 classification which was employed by Lamarck and De Can- 

 dolle in their so-called analytical arrangement of the French 

 Flora. He gives as an example a table of the principal 

 classes of De Candolle's system, as also a bifurcate arrange- 

 ment of animals after the method proposed by Dume'ril in 

 his Zoologie Analytique, this naturalist being distinguished 

 by his clear perception of the logical importance of the 

 method. A bifurcate classification of the animal kingdom 

 may also be found in Professor Eeay Greene's Manual of 

 the Ccelenterata, p. 18. 



The bifurcate form of classification seems to be needless 

 when the quality according to which we classify any group 



1 Essai sur la Nomenclature et la Classification, Paris, 1823, pp. 

 107, 108 



