insu dci iia: 
VE Pp ior ae ee ee 
ea a eee Pe ee UIT 
10 PROF, JULIUS MACLEOD ON TEN 
by acell.... The length attained by an internode, on the other hand, depends upon 
several factors: the original length of the internode, the mean velocity and duration 
of its growth." (Phil. Trans. Roy. Soc. ser. B, vol. cc. (1908) p. 96.) 
The question is a very complicated one (see Percy Groom, l.c. pp. 96-101). 
We do not need to discuss it further in the present paper. In any case, we may 
consider all the leaves which belong to one gradation curve as representing one 
continuous (uninterrupted) period of growth (period of gradation), abstaining from 
any reference to a possible connection between the form of the gradation curve 
and the variation of the velocity of growth during that period. 
$5. LEADING CHARACTER.—When we want to study the gradation of 
several characters along the same axis, at first each character must be 
studied separately. But, in order to obtain a general view of the whole, we 
may take one of the characters as a standard or leading character, all the 
others being referred to the standard. The choice of the leading character 
is, in each peculiar case, arbitrary. As a rule, we may take a conspicuous 
character, the gradation of which is distinct. I take in this paper the length 
of the leaves, the curve of which has ordinarily a prominent summit. 
§5a. We may represent the gradation of a given property in four 
different ways, viz., by means of 
1°. A curve of one specimen (specimen curve): this is merely an 
empiric representation of facts. See $$ 2 & 4. 
2°, An interval curve of one specimen (specimen interval curve). 
See $ 6. 
3°. A mean interval curve of several specimens. See $ 7. 
4°, The curves 1^, 2°, and 3° may be brought into the form of percentage 
curves. See $ 8. 
$6. INTERVAL CURVE OF ONE SPECIMEN.—In this paper I limit myself to 
that part of the stem which extends from the lowest leaf to the longest one. 
As the number of leaves is very variable, even within the limits of one species * 
(which makes comparisons diffieult), I divide this part of the stem into 
10 equal intervals : having measured the value of a given character of all 
the leaves, I calculate the mean value of the character in each interval. The 
figures of each interval thus become comparable with the figures of the same 
interval in all the specimens and species. Moreover, as the leaves are 
brought together into groups, the small irregularities produced by chance 
disappear to some extent, especially when the leaves are numerous. 
Example : I take the length of the leaves of the stem of Mnium serratum, 
the figures of which are given in Table II. (fig. 2). From the lowest leaf 
to the longest one, the number of leaves is 25. divide this part of the 
* Examples.—Fertile stem of Mnium punctatum, 7-19 leaves; fertile stem of M. hornum, 
46-64 leaves. 
