60 PHYSICAL CHEMISTRY 



that of water. If the soap solution is allowed to drop slowly 

 from a stalagmometer it shows a lower' surface tension than if 

 dropped fast. The rate of flow from a stalagmometer is reduced 

 by a piece of capillary tubing forming part of the outflow tube, 

 but the more viscous the fluid the slower it will flow. In order 

 to reduce errors from this source, Traube uses three stalag- 

 mometers for solutions of different viscosity and selects one de- 

 livering less than one drop per second. The error in using the 

 stalagmometer, due to lack of diffusion equilibrium, is less than 

 the error in the methods used on old surfaces, due to the forma- 

 tion of haptogen membranes. It should be remembered, how- 

 ever, that the stalagmometric data are merely comparative, and 

 only those results should be compared where the flow is slow and 

 its rate approximately the same in each case (see Harkins and 

 Humphrey, 1916). 



Fig. 22. Scheme showing that surface tension is located in a film whose 

 thickness equals the diameter of the sphere of molecular attraction. 



In order to understand the relation between surface tension 

 and osmotic pressure certain theoretical considerations are neces- 

 sary. Surface tension is a molecular phenomenon. The thick- 

 ness of the surface film equals the radius of the sphere of 

 molecular attraction. In Fig. 22, suppose m to represent a mole- 

 cule in the interior, M a molecule on the surface of a liquid, and 

 the circles around them to define the spheres of molecular attrac- 

 tion. The sphere of m is entirely within the liquid, hence m 

 attracts and is attracted equally on all sides by all molecules in 

 this sphere. On the contrary, only the hemisphere of M is within 

 the liquid and, hence, M is attracted laterally and downward, but 

 not upward. This attraction which the molecules in the surface 

 film have for one another puts the film under a tension — surface 

 tension. 



