BRITISH SPECIES OF THE GENUS MNIUM. 15 
their breadth. In the intervals 1-6 the curves Ve (number) and Be (breadth of 
the cells) are both ascending; the increase of Blin those intervals depends on 
the two mentioned factors. In the intervals 6-9, the increase of Be being less 
rapid, the influence of this factor on the increase of £7 becomes smaller and this 
increase depends almost exclusively on Ve. In the intervals 9-10 Be is invariable ; 
therefore the variation (negative increase) of B? depends merely on the variation 
of Ne. 
The relations between B? and the factors Be and We ave thus variable all along 
the axis. Moreover, those relations are not the same in all the species. If we try 
to study those relations by taking a number of leaves at random, we may be brought 
to contradictory results, and general conclusions drawn from such fragmentary 
observations may be rather illusory. It is merely by the study of the gradation 
curves in a sufficient number of species that we may hope to discover general rules 
governing the relations between the dimensions of an organ, the number of its 
constituent cells, and their dimensions *. 
We see from this example that the knowledge of the gradation may have a 
certain importance for the solution of certain physiological, and morphological 
problems—apart from its significance for the study of species and their variation. 
$11. Types or GnApATION.—The gradation curves of twelve characters of 
the leaves of the fertile stem in ten species of Mnium may be brought roughly 
under five types :— 
Type I. : The character under consideration increases from the lowest leaf 
to the longest one, and decreases beyond this. This is, of course, the case 
with the length of the leaves (leading property) in all the species, and also in 
some other cases (examples: figs. 1 & 2; L and Bein fig. 35 Mn. rostratum 
and subglobosum in Table LX.). 
Tyrer II.: The character, incréasing from the lowest leaf, reaches its 
maximum (summit of the curve) below the longest leaf, the position of the 
maximum being very variable. See, for instance Ve and Bl in fig. 3. More 
examples are given in Table IX.; in this table the summit of the curve of 
the same character (breadth of the leaves at their base) has a different position 
according to the species. Two species have their summit in interval 10: 
these belong thus to Type I. The eight other species (hornum is doubtful) 
belong to Type lI., the summit being situated below the longest leaf. 
A comparison between the curves in Table IX. is the occasion of some interesting 
remarks. We see, for instance, that in two species (rostratum, subglobosum) 
the longest leaves have the broadest base, but in four other species (afine, cuspi- 
datum, undulatum, punctatum) the longest leaves have the narrowest base. In 
subglobosum the shortest leaves (intervals 1, 2) are much narrower at their base 
than the longer ones (intervals 9, 10) ; in punctatwm we see rather the inverse. 
This is interesting, because these two species resemble each other in many other 
characters. 
* See Percy Groom, Phil. Trans. Roy. Soc. London, ser. B, vol. cc. (1908) pp. 96-98. 
