Notes . 
537 
the actual area of woody wall in a section of Pine, would scarcely 
amount to more than about 0-2 of the cross-section; so that the 
absolute tenacity of the substance of the walls of the tracheides 
probably approximates closely to that of the fibre of Gossypium . 
Now with regard to the stress actually obtaining in the cell- walls 
of the leaf. It will be convenient, in treating of the stresses, to regard 
the cells as cylinders. This assumption is justified by the consideration 
that it is probably only the cell-walls of the cylindrical cells of the leaf, 
e. g. those of the palisade-tissue and those forming sheath surround- 
ing the bundles, which are exposed to this stress ; for it seems probable 
that the walls of the irregularly stellate cells of the spongy parenchyma 
are not exposed to any great distending forces, otherwise they would 
assume a spherical contour ; unless, indeed, we attribute great rigidity 
to their cell-walls. The apparent paradox, that these cells contain 
a pressure of 20-30 atmospheres, while there is no stress in their 
walls, is explained by the fact that it is an osmotic pressure, and is 
not exerted on the enclosing membrane unless there is fluid enough 
present to distend that membrane. This consideration would also lead 
to the conclusion that the rigidity of leaves is due only to the cylindrical 
and more spherical cells, and that those cells with re-entrant angles 
are not normally in a state of turgor. 
When a cylinder is exposed to internal pressure, the stress in the 
wall tending to rupture it may be obtained in the following way : the 
total disruptive force equals the internal pressure acting over an area 
equal to the length multiplied by the diameter of the cylinder. This 
force is exerted on an area of cellulose equal to the thickness of the 
cell-wall multiplied by twice the length and twice the diameter of 
the cylindrical cell. Thus — 
Stress per sq. mm. of cellulose = - 
v 4 2(l + d)t. 
Where P = osmotic pressure, 1 = length, d = diameter of cell, and 
t = thickness of cell-wall. 
In Cytisus Laburnum the cylindrical palisade-cells are about 
•06 mms. long, about -0175 mms. diameter, and their cell-wall is 
•001 mms. thick. The stress per sq. mm. in their cell- walls is 
consequently 
300 x *06 x -0175 
• 155 x -ooi 
R r 
= 2,032 grs. 
