THE MECHANISMS OF ORIENTATION AND GROWTH 183 



being given to such a hypothesis. On the other hand a second type 

 of suggestion has been made more recently both by Castle in America 

 and van Iterson in Holland. 



The suggestion starts from the known distribution of stress in the 

 walls of a hollow cylinder submitted to uniform pressure from within. 

 We can perhaps take up the ideas most easily by considering the case 

 of a gas cylinder containing gas under pressure. It is well known that if 

 such a cylinder bursts on dropping, then the wall does not usually 

 splinter nor is one end blown off; instead, the cylinder splits down 

 the middle like a pea-pod. Evidently, since the tensile properties of the 

 metal wall are the same in every direction, this implies that the trans- 

 verse stress in the wall is greater than the longitudinal stress. It is easy 

 to calculate that the stress is indeed twice as great transversely as 

 longitudinally. 



Thus consider a cylinder containing fluid under pressure P, and 

 consider first the equilibrium conditions of a septum inserted trans- 

 versely (horizontal area shaded in Fig. 61); the upward force acting on 

 the septum is na-P. The balancing force directed downwards is derived 

 from the tension in the wall, and this amounts to InaTj, where Ti is the 

 longitudinal tension per unit of the wall periphery. Hence 



7ia^P=27iaTi, 

 so that 



' 2a 



Considering now a longitudinal septum (the longitudinal shaded area 

 in Fig. 61), the two balancing forces are now 2aLP and 2LT, where 

 Tf is the transverse tension per unit wall length. Hence, 



2aLP^2LT, 

 so that 



If 



a 



Thus the transverse tension is twice the longitudinal tension. Now the 

 suggestion is that, since in a cylindrical growing cell the tension trans- 

 versely is twice as great as longitudinally, it is for this reason that the 

 cellulose chains come to be oriented transversely. 



Unfortunately such a mechanical explanation will hardly bear 

 examination and a good deal of criticism has been forthcoming. These 

 criticisms may be classed under three headings: (a) the difficulty of 

 connecting stress alone with orientation and the inadequacy of the 



