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 ove. 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 
