BRITISH SPECIES OF THE GENUS MNIUM. "m 
Unfortunately, apart from the longest leaf, this exact method is only 
applicable in exceptional cases, In a stem with 38 leaves, for instance, 
we do not find any leaf at 500°, and there is thus no leaf strictly comparable 
with the two former ones. A similar difficulty very often occurs. 
Therefore, if we want to study the individual variation and to construct a 
variation curve properly so-called, we must content ourselves with collecting 
and measuring the leaves which belong to the same interval in each stem. 
In this way the variation produced by gradation is eliminated, and we may 
consider the obtained variation curve as being governed only by the laws of 
chance. The easiest method is to limit ourselves to the 10th interval. This 
method is not quite accurate, because the leaves which belong to the same 
interval are not exactly at the same degree ; but it is approximate enough for 
our purpose, which is the description of species and the identification of 
specimens, If we wanted to be more accurate for any other purpose, we 
should take in each stem the longest leaf only. 
Remark III.: It is obvious that certain relations exist between the 
Characters of a given leaf and those of all other leaves.— Ewample : In 
Table XII. the leaves in intervals 5 and 10 have almost exactly the same 
breadth. Starting from this equality, we find that 
In interval 10: 
Length —3:96 mm.; breadth of the cells 213 u; number of marginal teeth =29. 
In interval 5: 
Length —1:59 mm.; breadth of the cells —13 u; number of marginal teeth —10. 
The proportions interval 5: interval 10 are 
Breadth: a o tal 0°65:0°64 = 102:100 
Length <.. ieee. ee 1:59:3°96 = 40:100 
Breadth of cells; js 18:18 = 100:100 
Number of teeth 25 1020; = MF T00 
Numerous comparisons of the same kind are possible : the results seem to 
be capricious to such a degree that one would think that any attempt to dis- 
cover any rule whatever would be vain. All similar relations between the 
leaves of a given stem depend, however, on the gradation of the characters 
under consideration. 
If we want to study the correlation between the leaves of several stems of 
the same species, we must compare leaves which belong to the same interval 
(in preference the 10th) or the longest leaf in all the stems, in order to 
eliminate the influence of gradation. The same method enables us to study 
the correlation between the characters of distinct species. 
Tables such as Tables IL., VIIL, XI., XII., and the specific tables B which 
are given in Part IV., are, in a certain sense, correlation tables. Without 
taking into account the principle of gradation, it is hardly possible to make 
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