THE METHOD OF MOVEMENT 167 



flow of solution, even though 98 per cent of the volume is 

 water, he is led to doubt whether a cellulose matrix with 

 only 50 per cent water would be less resistant. Crafts 

 suggested that the structure of cellulose, forming perhaps 

 a regular lattice system might offer much less resistance 

 than ordinary colloidal gels. These capillaries, however, 

 are at best submicroscopic and may be of molecular 

 dimension, but even if all the space occupied by water 

 were in the form of fine capillaries with none of the water 

 fixed as water of hydration, the resistance to mass flow 

 must be very great. 



One cannot safely apply Poiseuille's formula to tubes 

 of such fine dimensions, for the formula assumes that the 

 flow takes place chiefly in the free space at a distance 

 from the wall of the capillary, and that the flow is nil at 

 the wall. In capillaries of such fine dimensions there may 

 be no free flow whatever, or at a certain small radius there 

 may be slow but steady flow with no change in rate with 

 further reduction in size. In this latter case the movement 

 is more probably a diffusional one, and the volume rate 

 of flow may not vary as the fourth power of the radius. 

 Assuming, however, that the law does apply at these 

 dimensions, and also assuming that half of the cross sec- 

 tion of the fresh wall is wall material and half is capillary 

 pores, and that the capillaries are of the same dimensions 

 as those calculated for silica gel, namely SmyLt in diameter; 

 then in order to force a 10 per cent sugar solution through 

 the walls of the phloem to a potato tuber at the rate 

 calculated by Crafts, a pressure gradient of 23 million 

 atmospheres per centimeter would be required. With the 

 free space as small as it must be in hydrated phloem walls, 

 movement is probably largely restricted to diffusion. 

 Equally great pressures would be required to cause a 

 diffusional flow at the required rate. 



In his second paper (1932) Crafts calculated the mini- 

 mum diameter of capillaries that would deliver sap at a 

 linear rate of 0.3 cm. per minute, which he estimated to be 

 the normal rate, through a distance of 50 cm. at a pressure 



