54 PLANT GROWTH SUBSTANCES 



As a matter of fact we do not know whether the wall thickness 

 remains constant. It is possible that it decreases during this first phase, 

 which would cause an increasing tension in the wall even if its structure 

 remains unchanged. On such an assumption the real increase in the 

 elasticity should not amount to more than a doubling. These are mini- 

 mum figures and those of Frey-Wyssling are maximum values for the 

 loosening of the wall structure. 



There cannot be merely a loosening of the wall structure, however. 

 Assuming a constant amount of wall material and taking into account 

 the fact that the cell wall maintains its micellar structure during the 

 whole elongation process, there must be some factor responsible for this 

 organized translocation of material within the wall. Assuming with 

 Frey-Wyssling that the wall maintains its thickness from the start of 

 the elongation, it follows that there must be from the very onset a 

 considerable formation of new wall material. In neither case is there 

 reason for believing that the initial phase of the elongation is only a 

 loosening of the wall structure. Although such a change occurs and plays 

 a prominent role, we must always also consider some mechanism estab- 

 lishing the fixed structure of the wall. 



All these computations have been carried out under the assumption 

 of a proportionality between pressure and tension of the wall, but this 

 is erroneous as is shown by Figure 3. Tamiya (13) has deduced formulae 

 of wall pressure and suction in relation to turgor tension which include a 

 factor for the rigidity of the cell wall. The formula reads: 



Tension = ^^ 



/C, - 1 + e-^^' 



where d denotes the osmotic value and f the rigidity of the wall. 

 If his formulae are applied to elongating cells it is found that the rigidity 

 factor/is remarkably constant in spite of the very large variations in the 

 elasticity as computed according to the ideal physical formulae. This 

 is shown by Figure 4. The cause of this disagreement is that in this case 

 the cell walls are assumed to obey ideal laws of mechanics, whereas the 

 rigidity is computed with attention paid to the empiric formulae of the 

 osmotic conditions (13). The two graphs of Figure 4 are constructed 

 from one series of measurements. 



Obviously there are several ways of computing the elastic properties 

 of the wall, and difterent results can be obtained. We have certainly 



