450 Prof. J. Plateau on the Figures of Equilibrium 



present category the tension is insufficient to cause rupture; 

 and this is supported by a comparison of the respective tensions 

 of water and of our solution of Marseilles soap : the tension of 

 a film of water at the common temperature is 14'6, and that of 

 a film formed by a solution containing one part of Marseilles 

 soap to forty of water is only 5*64*, or between one-half and 

 one-third of the former. 



Nevertheless, in order that a liquid may be capable of exten- 

 sion into bubbles, it is not indispensable that the tension should 

 be absolutely weak, if only it is so in comparison with the vis- 

 cosity of the superficial layers, or, in other words, if the ratio 

 of the superficial viscosity to the tension be sufficiently great. 

 For instance, while the tension of a film of soap-water, as we have 

 just seen, is only 5*64, that of a film of a solution of albumen, 

 made by adding a tenth of its volume of water to white of egg, 

 is 11*42, or twice as great ; but in hemispherical bubbles of soap 

 the colourless phase is at most twenty seconds, while in those of 

 albumen it lasts several hours. Thus when we pass from the 

 first of these liquids to the second, the tension, or the force tend- 

 ing to break the films, becomes double ; but the resistance to rup- 

 ture increases at the same time, in consequence of the greater 

 viscosity of the superficial layers, and thus solution of albumen 

 stretches out into bubbles like soap, but to a less degree. 



Such is the theory which I propose as a solution of the 

 principal question treated of in the present series of these re- 

 searches. In order that a liquid may be capable of forming 

 large and persistent films, and may consequently admit of being 

 blown into bubbles, it is necessary, in the first place, that the 

 viscosity proper to the superficial layers of its films should be 

 great, in order that the diminution of thickness may take place 

 slowly ; it is also needful that the tension should be relatively 

 small, in order that it may not overpower the resistance opposed 

 by the above viscosity to the rupture of the film, when, in con- 

 sequence of superficial movements, a more than ordinary sepa- 

 ration of the molecules occurs. I have shown, however, by rea- 

 soning which is too long to be dwelt upon here, that the ratio 

 between superficial viscosity and tension, which makes the for- 

 mation of bubbles possible, must be greater in proportion as the 

 superficial viscosity is greater. 



I next pass to a series of facts in support of this theory. I 

 have tried, in the first place, to prove by direct experiments the 

 existence of a viscosity peculiar to the superficial layers, and the 

 variations which it presents in different liquids. The following 

 is, in substance, the method of experimenting that I adopted, 

 and which I found perfectly successful. 

 * These tensions are expressed in milligrammes per millimetre of length. 



