BRITISH SPECIES OF THE GENUS MNIUM. 21 
margin of error, because the REAL specific limits are probably not yet reached 
in this FIRST ATTEMPT of construction of minimum and maximum tables *. 
We may conclude that the stem æ is probably cuspidatum, perhaps 
hornum. 
We take now 
Tabie XXXI. (number of cells of the border) : no more species excluded. 
Table XXXII. (number of marginal teeth) : no more species excluded. 
Table XXXIII. (number of double teeth at the margin) : the exclusion of 
hornum is confirmed by the minimum table. 
The stem æ belongs thus to the species Mnium cuspidatum. 
One may perhaps think that we aseribe too high a significance to the 
figures when we conclude, from rather small differences between the figures 
of specimen w and the figures in the tables, that æ does not belong to such 
or such a species. One must realize, once for all, that each figure in the 
tables is a Limir deduced from a series of measurements, and has thus 
a significance quite different from that of a figure given by one specimen 
taken at random. 
We may, moreover, identify specimen æ a second time, taking the tables 
in the reverse order and beginning with 
Table XXXVIII. (number of fruits): the minimum table excludes 
perhaps spinosum and undulatum ; no species are excluded by the maximum 
table. 
Table XX XVII. (number of leaves): the minimum table excludes hornum ; 
no species are excluded with certainty by the maximum table. 
Table XXXVI. (tooth at the summit of the longest leaf) exeludes sub- 
globosum. 
Table XXXV. (length of the nerve) excludes no more species. 
Table XXXIV. (teeth on the nerve at the back of the leaf): the minimum 
table excludes hornum (already excluded) and probably spinosum. No species 
are excluded by the maximum table. 
Table XXXIII. (number of double teeth at the leaf-margin) excludes 
serratum and orthorrhynchum, brings confirmation of the exclusion of spinosum 
and excludes kornum (already excluded). No species are excluded by the 
maximum table. 
Table XX XII. (number of marginal teeth) : the minimum table confirms ° 
the exclusion of undulatum. The maximum table excludes punctatum, and 
also subglobosum and serratum (both previously excluded). 
Table XX XI. (number of cells of the border) does not exclude more 
species. 
* The figures in the tables are approximate enough to demonstrate the use of the 
method, but they want to be verified and corrected by more measurements. It may be 
remembered that many constants, used by physicists and chemists, were at the beginning 
only approximate. They have been corrected later on—often at the cost of long labour. 
