— — — — e — o 
BRITISH SPECIES OF THE GENUS. MNIUM. 9 
I have studied the gradation of twelve characters of the leaves in ten 
species : the figures are given in the description of the species, Part IV. 
The general conclusion is that in each species each character has its own 
gradation, different from all others. (There is, however, often a certain 
analogy between certain gradation curves. See Types of gradation, § 11.) 
nel 
HU 
Ex 
5 10 a. 90 
Fie. 2.—Mnium serratum. Gradation Curves of the length and the breadth of the leaves 
of one fertile stem. o, Base of the stem; x, Summit of the stem; 1,...5,... 27, 
Successive leaves; B, Breadth; Z, Length. See the figures in Table II.—In these 
curves the fortuitous irregularities produced by chance are more conspicuous than in 
fo ale 
$4«a. PERIOD or Grapation.—So long as I was acquainted only with the 
gradation of the length, I thought that there was a relation between gradation 
and the so-called grand period of growth, the development of the longest leaf 
synchronising with the period of greatest velocity of growth. But the faet that 
each character has its own independent gradation and that there is no coincidence 
between the highest values of several characters of the same stem, makes it very 
difficult to admit such a relation. The suggestion that a connection really exists 
between the variation of a character along an axis and the variation of the 
velocity of growth along the same axis, can only be accepted when we admit that 
each character has its own grand period coinciding with the summit of its 
gradation curve. According to this view, we should no longer speak of one 
grand period, but of as many grand periods as there are characters. 
Percy Groom, discussing the question of a possible connection between the 
grand period of growth and the normal curve of a main axis of a herb (gradation 
of the length of the internodes) has pointed out that : “What Sachs describes as the 
grand period of growth of a cell involves merely a kinetic conception dealing exclu- 
sively with the velocity or rate of growth of a cell. The proposition in question . . 
does not define or treat of the duration of growth or the ultimate dimensions attained 
at 
