Walter Stiles 
176 
during the intake of water by the vacuole, the former of the two 
equations just given becomes 
P Z V Z (1 - P) = P (V - pv z ), 
or, if v is the degree of turgor stretching, 
P = P 1 
z v-p 
the form in which the relation is given by Hofler. 
Should the volume of the protoplasm also change with increasing 
turgor of the cell, this equation has to be further modified. In the 
absence of information on this point, however, further elaboration 
of this question is scarcely profitable. 
It is to be observed that the relations given above only hold 
within the limits of elasticity of the cell wall. It must be admitted 
that we know very little about the elasticity of the cell wall. 
Schwendener and Krabbe (1893) immersed cylinders of young pith 
cells in water with the result that they swelled so that the length 
increased 25 to 30 per cent. On plasmolysis they contracted to the 
same length as that of similar cylinders plasmolysed immediately 
after their isolation from the plant without any immersion in water 
before plasmolysis. According to Pfeffer (1873) the staminal fila¬ 
ments of Cynareae can be stretched to double their normal length 
without the limits of elasticity being exceeded. On the other hand, 
some cells, including bast fibres, are incapable of elastic stretching 
exceeding 0-5 to 1*5 per cent, of their normal length (Pfeffer, 1903). 
Although a considerable amount of work has been done on the 
question of the elasticity of the cell wall, yet owing to the complex 
systems which constitute plant tissues, such work is full of difficulties 
and the results obtained open to considerable criticism. A discussion 
of this is out of the question here, but it maybe pointed out that after 
considerable stretching the cell wall may take some time to return 
to its original shape, recovery being gradual (Detlefsen, 1884, 1888), 
while the modulus of elasticity will vary with the water content of 
the cell wall (Pfeffer, 1903). It is clear that relations involving as¬ 
sumptions with regard to the elasticity of the cell wall should be 
accepted with caution. 
Isotonic Solutions and Isotonic Coefficients 
A solution having the same osmotic concentration as the cell sap 
is said to be isotonic with it, a solution of greater concentration than 
the cell sap is described as hypertonic, and one of lower concentra¬ 
tion than the cell sap as hypotonic. 
