104 THE QUANTITATIVE METHOD IN BIOLOGY 



gradually curved in proportion as the weight of the fruit in- 

 creases. The flowering stems of a number of Graminem (and 

 many other plants) are more or less curved (drooping) under the 

 influence of gravity, the degree (and the plan) of curvature 

 being variable according to the intensity (and the direction) of 

 the wind. 



SECOND GROUP : More interesting are the cases in which 

 the curvature, depending on internal causes, is fixed and 

 constitutes a characteristic feature of the object. 



FIRST EXAMPLE: An oblong or oval leaf of a moss 

 (Mnium, Bryum, Tortula, Catharinea, etc.) is Umited on both 

 sides by a curved line (margin), the median nerve being straight. 

 This object is a more or less modified chess-board system, con- 

 sisting of numerous unicellular segments, the axes being NS 

 (longitudinal) and EW (transverse). How can it be ex- 

 plained that the axis NS is straight in the middle and curved 

 along both margins ? Two factors are here at play. 



The first factor depends on gradation. When the cells are 

 counted in the transverse direction at successive levels from the 

 base to the summit (from 5 to N) it is seen that their number 

 increases till the place of the greatest breadth of the leaf is 

 reached. Here we find the maximum. Further towards the 

 summit the number gradually decreases. The property 

 number of cells is thus variable all along the axis NS. A 

 consequence of this gradation is a displacement of the marginal 

 cells, 1 which do not any longer form a straight longitudinal 

 row. Two successive marginal cells, taken at random, are 

 joined by a straight simple axis ; the successive simple axes 

 follow one another in the form of a broken hne, which is a 

 compound axis. 



The second factor depends on the flexibility and elasticity of 

 the ceU waUs. Since all the successive marginal cells are united 

 by their walls, they form a continuous whole, the margin, which 

 is brought into a new state of equilibrium : the margin is 

 curved over its whole length and assumes the form of a con- 

 tinuous curve (the angles between the simple axes being as it 

 were, smoothed out). The form of the curved (marginal) axis 

 depends thus (i) on the relative position and the direction 

 of the simple axes, which direction and relative position depend 

 themselves on gradation ; (2) on the flexibility and elasticity 

 of the cell'-waUs. 



The cells which form one longitudinal row (or several parallel 

 rows) in the middle of the leaf are not displaced : here all the 

 successive simple axes form one straight compound axis. In a 

 leaf considered as a whole the direction of the middle nerve 



1 And, of course, of all the longitudinaljrows of cells, in proportion as they 

 are at a greater distance from the nerve. 



