xxx.] CLASSIFICATION. 697 



of things admits of numerical discrimination. It would 

 seem absurd to arrange things according as they have one 

 degree of the quality or not one degree, two degrees or not 

 two degrees, and so on. The elements are classified accord- 

 ing as the atom of each saturates one, two, three, or more 

 atoms of a monad element, such as chlorine, and they are 

 called accordingly monad, dyad, triad, tetrad elements, and 

 so on. It would be useless to apply the bifid arrangement, 

 thus : 



Element 



Monad not-Monad 



r 



Dyad not-Dyad 



Triad not-Triad 



I 



Tetrad not-Tetrad. 



The reason of this is that, by the nature of number (p. 157) 

 every number is logically discriminated from every other 

 number. There can thus be no logical confusion in a nume- 

 rical arrangement, and the series of numbers indefinitely 

 extended is also exhaustive. Every tiling admitting of a 

 quality expressible in numbers must find its place some- 

 where in the series of numbers. The chords in music 

 correspond to the simpler numerical ratios and must admit 

 of complete exhaustive classification in respect to the 

 complexity of the ratios forming them. Plane rectilinear 

 figures may be classified according to the numbers of their 

 sides, as triangles, quadrilateral figures, pentagons, hexagons, 

 heptagons, &c. The bifurcate arrangement is not false when 

 applied to such series of objects; it is even necessarily 

 involved in the arrangement which we do apply, so that 

 its formal statement is needless and tedious. The same 

 may be said of the division of portions of space. Eeid 

 and Kames endeavoured to cast ridicule on the bifurcate 

 arrangement 1 by proposing to classify the parts of England 

 into Middlesex and what is not Middlesex, dividing the 

 latter again into Kent and what is not Kent, Sussex and 



1 George Bentham, Outline of a New System of Logic, p. 115. 



