2 TRANSPIRATION AND ASCENT OF SAP ch. 



Diffusion through stomata. The beautiful re- 

 searches of Brown and Escombe on diffusion through 

 perforated septa have satisfactorily cleared up this diffi- 

 culty. They showed experimentally that the amount of 

 vapour which diffuses through a perforation in a septum 

 does not diminish proportionally as the cross section 

 diminishes, but only in proportion as its diameter 

 decreases. This result, which is at first sight by no 

 means obvious, has been mathematically explained by 

 both Stephan and Larmor. Brown and Escombe quote 

 both writers ; but as their methods may not be easily 

 followed by all botanists the following simple explanation 

 may be of interest. 



When diffusion, undisturbed by convection currents, is 

 taking place from a perforation which is kept filled with 

 water vapour, or from a surface of water, into a space 

 less rich in water vapour, it is evident that after a time 

 a certain gradient of concentration will establish itself 

 over the aperture. The concentration will be greatest near 

 the perforation and less more remote from it, whilst shells 

 of uniform concentration will be found over-arching the 

 perforation. At a little distance from the aperture, say 

 when the diameter of the shells is about four times that of 

 the perforation, these shells will be approximately hemi- 

 spheres. 



To possess any given concentration p a shell must have 

 an area bearing a definite proportion to the area of the 

 perforation ; because the supply maintaining its concen- 

 tration is derived from the water molecules leaving the 

 aperture, and the number of these will be proportional to 

 its area. 



Let R and A denote the radius and area respectively of 

 the shell having a concentration p, and r and a the radius 

 and area of the perforation. Let p l indicate the concen- 

 tration of water vapour in the perforation. 



A = La or & = lr-. 



