i8o THE STOMATAL MECHANISM 



as great as through septum i. Similarly septum lO, with only half the exposed 

 area of septum 9, permits almost as much diffusion to occur as through sep- 

 tum 9. These results indicate that the rate of diffusion of water-vapor 

 through a small aperture is greater than through an equal area of a larger 

 evaporating surface. 



In other experiments, Sayre found that diffusion of water-vapor through 

 small openings of elliptical shape is also more nearly proportional to their 

 perimeters than to their areas. Hence the "perimeter law"' for the diffusion 

 of gases also holds for openings of other than circular shape. An important 

 inference which can be drawn from this finding is that a stomate attains 

 almost its maximum diffusive capacity long before it is fully open, since the 

 perimeter of a stomatal pore does not increase greatly after the aperture be- 

 tween the guard cells has widened perceptibly. 



The fact that the diffusion of gases through sm.all apertures is much 

 more nearly proportional to their perimeters than to their areas is due to the 

 more rapid diffusion of the molecules through an opening at the periphery 

 than through its center. A molecule of the diffusing gas at the rim of the 

 hole is surrounded on all sides by other molecules moving in all directions. 

 The concentration of diffusing molecules is much less in an outward direction 

 from the rim, however, than towards the center of the opening. Further- 

 more, the diffusion gradient is much steeper from the rim outwards than 

 at points above the opening. Hence the number of molecules escaping 

 through the hole from a given point near the rim per unit time interval 

 will greatly exceed the number escaping from a point near the center of the 

 opening. 



Reduction in the area of any circular or elliptical opening results in in- 

 creasing its perimeter relative to its area. Hence in small apertures such a 

 large proportion of the diffusion occurs at the edge of the opening that the 

 effect of any diffusion which occurs through its center is almost if not com- 

 pletely obscured, and measurements show the rate of diffusion through the 

 small apertures to be essentially proportional to their perimeters. In fact in 

 an opening 0.5 cm, in diameter, for example, a large part of the center of 

 the aperture can be entirely blocked off without any very great effect upon 

 the rate of diffusion of a gas through it. 



That the diffusion of gases through small apertures occurs largely at the 

 rim of the hole can be demonstrated visually by means of a simple experi- 

 ment. A cylindrical glass vessel is partly filled with a gelatin sol which is 

 allowed to gel. A small opening is punched through the center of a disk 

 of celluloid which is then inserted into the position on top of the gelatin, 

 the gap between the edge of the disk and the wall of the cylinder being 



