Transpiration and the Ascent of Sap. 55 



particles as spheres, the radii of which will equal 0*01 mm; if 

 r = radius of the particle and R = radius of the envelope, we have 



4 7t 



-^- R^ = volume of the sphere formed by the particle and its 

 o 



4 îf 

 envelope and ., r^ = the volume of the particle. 

 o 



Since there is 30 per cent weight of water present in the soil 



this will amount to about 60 per cent by volume, as the specific 



gravity of the particles may be taken about 2. Therefore 



47r_47r 360 47r 3 



3 3 ^ ^ 100 ^ 3 * 



R-i = (1 + 0-6) r" = 1-6 X (10-2)^^ 



R = 1-17 X 10-- = 00117 



Thickness of envelope = R — r = 0*0017 mm. 



But since the particles are not quite spherical their surface will 

 be greater and consequently the envelopes will be thinner than 

 appears from this estimation. 



In a film of this thickness, not much thicker than the cell wall 

 of the root hair, motion could be but very slow, and of course not 

 being supported in any way it cannot transmit tension. 



We must next consider the amount of energy needed to raise 

 the transpiration current as a tensile stream in the wood and 

 ascertain how far the sources available suffice to do the work. 



The work done will be equal to the weight of the water raised 

 from the soil to the leaves, together with the energy expended in 

 overcoming the resistance of the conducting tracts. The available 

 energy is to be found in the energy entering at the evaporating 

 surfaces supported in the cell-walls of the leaves. The surface of the 

 liquid is held there by the capillary forces developed in the sub- 

 microscopic spaces in the substance of the walls, and may be compared 

 to an evaporating surface (composed of innumerable menisci) in 

 porous clay. 



The suitability of evaporating menisci as a mechanism for doing 

 work may be illustrated by a model. ^) See Fig. 7. A light fly wheel is 

 delicately hung in an air-tight chamber. The short limb of a J-shaped 

 glass-tube enters the upper part of this chamber from above, and its 

 end, which is drawn to a fine nozzle, is vertically over the edge of 

 the wheel. The longer limb of the tube dips into a well of water 



*) H. H. Dixon, On the Physics of the Transpiration Current. Notes from 

 the Botanical School, Trinity College, Duhliu, No. 2, 1897, pp. 16 et seq. 



