216 



ON SYSTEMATIC ZOOLOGY. 



ceiving this error of the German cryptogamist, and join- 

 ing him in maintaining that no group is natural which 

 does not form a circle, Mr. MacLeay subsequently adopts 

 the plan of M. Fries,, by first dividing his group into 

 two divisions, one of which he terms normal, and the 

 other aberrant. Now, this normal group corresponds to 

 the centrum of M. Fries ; that is, it contains two series, 

 and not one. We may here repeat our author's words, 

 in speaking of the central group of M. Fries, as per- 

 fectly applicable to his own binary division of a typical 

 or normal group. " In the first place, M. Fries lays it 

 down as a rule that he admits no groups whatever to be 

 natural_, unless they form circles more or less complete. 

 Let us, then, apply this rule to what he terms his cen- 

 tral group, and which he makes always to consist of 

 two. Does this form a circle ? If not, the group can- 

 not be natural, according to his own definition." We 

 may, in like manner, enquire, Does our author's admis- 

 sion that every group is a circle, apply to that which he 

 calls his normal group ? If not, this group, any more 

 than the centrum of M. Fries, cannot be natural. Of 

 this, indeed, Mr. MacLeay is perfectly aware ; for he ob- 

 viously merely uses this term to assimilate his normal 

 group with the centrum of Fries, which, as we have 

 already seen, contains the two most typical groups of every 

 circle. The disadvantages of this mode of division are 

 several : first, it has conveyed the impression to others, 

 that Mr. MacLeay's system is, in the first place, binary, 

 and, in the second, quinary. A countenance has been thus 

 given to the binary method, which superficial writers have 

 adroitly used, by appealing to this constant and primary 

 use of the number two, while others insist that there must 

 be always ' ' a great typical group resolvable into two." It 

 likewise gives to the term group two distinct meanings : 

 one as used to denote an artificial division (every na- 

 tural group being a circle) ; and another as denoting a 

 natural, and therefore a circular, division. It is to 

 be hoped this elucidation of Mr. MacLeay's theory, prolix 

 and perhaps tedious as it necessarily has been, will not 



