396 PLATEAU ON SOAP-BUBBLES. 



deduced from the known fact that there is a difference in energy between a 

 liquid and its vapour, combined with the hypothesis, that as a milligramme of 

 the substance passes from the state of a liquid within the liquid mass, to that 

 of a vapour outside it, the change of its energy takes place, not instantaneously, 

 but in a continuous manner. 



M. van der Waals, whose academic thesis, Over de Continuiteit van <//< 



en Vlocutofloestand*, is a most valuable contribution to molecular physics, 



has attempted to calculate approximately the thickness of the stratum within 



which this continuous change of energy is accomplished, and finds it for water 



about 0*0000003 millimetre. 



Whatever we may think of these calculations, it is at least manifest that 

 the only path in which we may hope to arrive at a knowledge of the size 

 of the molecules of ordinary matter is to be traced among those phenomena 

 which come into prominence when the dimensions of bodies are greatly reduced, 

 as in the superficial layer of a liquid. 



But it is in the experimental investigation of the effects of surface-tension 

 on the form of the surface of a liquid that the value of M. Plateau's book is to 

 be found. He uses two distinct methods. In the first he prepares a mixture 

 of alcohol and water which has the same density as olive oil, then introducing 

 some oil into the mixture and waiting till it has, by absorption of a small 

 portion of alcohol into itself, become accommodated to its position, he obtains a 

 mass of oil no longer under the action of gravity, but subject only to the 

 surface-tension of its boundary. Its form is therefore, when undisturbed, 

 spherical, but by means of rings, disks, &c., of iron, he draws out or com- 

 presses his mass of oil into a number of different figures, the equilibrium and 

 stability of which are here investigated, both experimentally and theoretically. 



The other method is the old one of blowing soap-bubbles. M. Plateau, 

 however, has improved the art, first by finding out the best kind of soap and 

 the best proportion of water, and then by mixing his soapy water with 

 glycerine. Bubbles formed of this liquid will last for hours, and even days. 



By forming a frame of iron wire and dipping it into this liquid he forms 

 a film, the figure of which is that of the surface of minimum area which has 

 the frame for its boundary. This is the case when the air is free on both 

 sides of the film. If, however, the portions of air on the two sides of the film 



* Leiden: A. W. Sijthoff, 1873. 



