7a M 



or I 



190 THE MOLECULAR ARCHITECTURE OF PLANT CELL WALLS 



where q is the Youngs modulus of the winding and n the torsional 

 rigidity. Strictly speaking, this relation holds only in cases where the 

 winding is isotropic, but since we are considering here the value oiq for 

 extensions parallel to the winding only, and of « in a plane at right 

 angles to this, then the errors involved are presumably quite small. 

 There is naturally some hesitation in comparing such a static model 

 with the dynamic state in the growing sporangiophore, but there are 



grounds for thinking that these two are not so 

 dissimilar as might at first appear. We notice 

 first the following qualitative points: 



(1) The relation is satisfactory in that it 

 throws the weight of the explanation on the 

 wall, where it undoubtedly belongs. The spor- 

 angiophore is known to be under hydrostatic 

 pressure from within, and the impact of this on 

 the closed end corresponds to the axial weight 

 in the model. 



(2) Elongation and rotation go always to- 

 gether, rotation stopping when elongation 

 ceases, and resuming immediately growth begins 

 again. 



(3) The rate of rotation can be very variable 

 since it depends not only on the rate of elonga- 

 tion but also on the value of a, q and n. The 

 latter two factors are known to vary widely in 

 substances of this kind. 



The relation is equally satisfactory in a semi- 

 quantitative sense. Thus the following comparisons with observational 

 data have been made: 



(1) From observed rates of elongation per unit elongation (A^jAL) 

 and the known value of a it has been calculated that nlq=0-22. This 

 lies well within the range of values recently found for the chitin of the 

 mature sporangiophores (62), and agrees with the several estimates 

 which have been given for cellulose. While no particular stress can 

 at the moment be placed upon this correspondence until growing walls 

 have been investigated, it is nevertheless satisfactory that the value of 

 njq required to explain spiral growth quantitatively is of the correct 

 order of magnitude. 



(2) Castle has observed the externally applied torque required just to 

 stop rotation. He found that the torque varied rapidly with cell dia- 

 meter. The present theory predicts that it should vary with a^ and gives 



Fig. 64. For explanation, 

 see text. 



