TRANSACTIONS OF SECTION K. 719 



of the University of Manchester. On the suggestion of Prof. Lang, I took mosses of 

 the genus 3Inium. I limited myself to the study of the leaves of the fertile stem 

 of seven species of that genus, the material being obtained from the Barker Collection 

 of British Mosses. 



^Vhen we measure, for instance, the length of the successive leaves from the l)ase 

 to the summit of a fertile stem of a Mnium, we see that the length increases up to a 

 maximum and then cUmiuishes. Example : 



Tiihlc a : Mnium punctatiim, a stem with 10 leaves, in mm. 



This curve represents the period of growth of the character under consideration 

 along the axis ; it is something quite difl'erent from a variation-curve properly so 

 called. The seven species of Mnium agree in this respect with Table a. 



In this paper I limit myself (except in one case) to that part of the stem which 

 extends fi-om the lowest leaf to the longest one. As the number of leaves is variable 

 (between 8 and 56), I have divided this part of the stem into ten intervals, measuring 

 the minimal, median, and maximal value of each character in the leaves of each 

 interval. The figures of each given interval thus become comparable with the figines 

 of the same uiter\-al m all the stems and species. Followmg this method, we find 

 that the period.s of all the measured characters of the seven species may be brought 

 under three types : 



1. The character iiicrea.ses from the base to the longest leaf and decreases beyond 

 this. The curve m Table a is an example of this type. 



2. The character reaches its maximum below the longest leaf, the position of the 

 maximum being to a certain degree variable. Example : The breadth of the leaves 

 of Mnium cuspidatum (Table P) ; the maximum here falls about the hiterval 4, 

 the longest leaf being here the narrowest ! 



Table y8 (mm.). 



3. The character reaches its highest value in the leaves Avhich are above the longest 

 loaf. Example : In Mnium punctatum, the nerve is sliorl and never reaches the summit 

 of the leaf in the three lirst intervals ; in the intervals 4-10 it grows longer and 

 approaches the summit more and more ; in the leaves above the longest one in all the 

 specimens the nerve reaches the summit. 



These three types are more or less variable along different luies. The increase 

 of a character from one interval to the following is more or less rapid. In several 

 cases the hicrcase is rapid in the first intervals and sloAver further on. Example : 

 The number of cells in the transverse direction at the place of the greatest breadth 

 in Mnium cuspidatum (Table 7) ; 



Some characters have the value 0, i.e., they do not exist in the first intervals ; 

 they show their period in the followmg intervals. 



The knowledge of the period of a certain number of characters a, h, c, . . . . 

 enables us to make clear the variability of the leaves of the same stem. The value 

 of the characters a, b, c. .... of each leaf depends on the position of the leaf. In 

 other words, a leaf which belongs to the ji'^ interval will have the values of the curves 

 of the characters a, b, c in that interval. .46- each character has its own inde- 

 pendent curve, and as much diversity exists among the curves, the result is a practically 

 unlimited number of combinations. Each leaf shows such a combination. It is 

 impossible to analyse this form of variability by any other method. 



By the knowledge of the periods and by the division of the axis mto a certain 

 number of intervals (1 have managed with ten), we are enabled to study the correlation 

 which exists or may exist : 



(,a) Between the characters of the leaves of one stem ; 



