MOLECULAR MAGNITUDES 271 



film which would just cause them to cease. He found 

 that a layer of approximately 1.6xlO~ 7 cm. was 

 sufficient. Since the layer cannot be less than one 

 molecule in thickness the diameter of a molecule is 

 not greater than this distance. 



Somewhat similar values were obtained by various 

 investigators using soap films. We have all noticed 

 that as a soap bubble drains, its iridescent colors change 

 and a black spot appears at the point where it ultimately 

 breaks. Measurements of this thickness are possible 

 by optical means and another value of the upper 

 limit for the diameter of a molecule has thus been 

 obtained. 



Some of the most consistent values of the number of 

 molecules per mole were obtained by Pen-in. He used 

 small granules of gamboge or of mastic, substances 

 which do not dissolve in water but form emulsions. 

 Such particles he sorted into uniform size by centri- 

 fuging. The average kinetic energy of these is the 

 same l as that of a molecule of the liquid in which they 

 are placed. But it is this energy which accounts for 

 the osmotic pressure and brings about a diffusion of 

 the particles when the liquid is not agitated. 



In a liquid the osmotic pressure will depend at 

 each point upon the concentration of the particles. If 

 there is no external cause like gravity the concentration 

 will be the same at all points when the liquid has 

 reached a state of equilibrium. Because of gravity, 



1 That is, there is an equipartition of k.e. between the particles 

 and the molecules of the liquid. It is this equipartition which 

 makes such Brownian movements so valuable in the study of the 

 invisible molecules. 



