the Philosophy of System, 371 



ult would be tedious to multiply such instances which at 

 every step are continually occurring ; they have not been over- 

 looked by naturalists, and many schemes have been devised 

 for their improvement ; hence, had we Bonnet's chain of 

 nature, — hence the dichotomous ascent proposed by several 

 authors, — hence the occasional continuous lines terminating in 

 themselves, and forming potential circles, as by Blainville,» 

 Green, and others ; and hence has resulted the quinary circles 

 of Mac Leay, with the osculant groups between them. Watts 

 in his Logic has observed, that dichotomies and trichotomies 

 in system are absurd ; and when nature is forced into any pre- 

 fixed number, it certainly is so ; but it would be very conve- 

 nient as an assistant to the memory, if such a distribution 

 could be naturally found out. Flemming and many other sys- 

 tematists have adopted the No. 2, always pursuing a binary 

 analysis. Mac Leay prefers the No. 5, and Kirby 7. Mr. 

 Field, myself, and many others, have found the No. 3 

 more generally to prevail. On this subject Kirby writes, that 

 " the No. 5 assumed by Mr. Mac Leay for one basis of his 

 system as consecrated by nature, seems to him to yield to the 

 No. 7, the abstract idea of which he states to -be completion^ 

 fulness, perfection.^^ But without entering into any abstract 

 speculations, it may easily be shewn how •* the quinaries are 

 resoluble into septenaries," and how both are but imperfect 

 analyses of the ternary scheme — for the fives result merely 

 from the analysis of one of the threes, the other two remaining 

 unanalyzed, and the sevens from the single one being left un- 

 divided, and often being indivisible. (See Tables.) 



JaniariJi; . ,— "• — I- 



?.9bihnQH J*»^ — [Z equal -_ or — ^ equal — - 



-lOJ »rt! — {- . 



Whereas the analysis should be, as in the former figures, arrived 

 at in two separate stages. 



" To test this point, although the number 3 is not, and never 

 has been assumed as an essential part of the connecting 

 scheme, and only pursued so far as nature has presented trine 

 distributions, and the convenience might be adopted without 

 violating natural alliances, let us briefly examine the quinary 



