448 Prof. J. Plateau on the Figures of Equilibrium 



not happen till after several seconds, sometimes not till after 

 two minutes. It evidently follows from this that in this cate- 

 gory, on the contrary, the diminution of thickness is very slow. 



Again, we have seen that the films of the third category have 

 generally a long colourless phase, and that the coloration that 

 appears afterwards never changes quickly. It follows from this 

 that in the third category, as in the first, the diminution of 

 thickness takes place very slowly. 



This great difference in the rapidity with which films of the 

 second category diminish in thickness as compared with those of 

 the other two, cannot, be attributed to ordinary viscosity ; for 

 the fat oils and lactic acid, for instance, which belong to the 

 second category, are much more viscous than most of the liquids 

 belonging to the first and second; oil of turpentine^ again, 

 which belongs to the second category, is more viscous than 

 water, which belongs to the first, &c. Now the distinguishing 

 character of a film is the great extent of its surfaces in proportion 

 to its volume ; we are consequently forced to recognize here an 

 effect depending on the faces of the film, and to look for the 

 cause of the great difference in question in a viscosity peculiar 

 to the superficial layers, and independent, or nearly so, of the 

 internal viscosity, and which is very weak in the liquids of the 

 second category, but, on the contrary, is very strong in those of 

 the first and third. 



This principle being admitted, let us apply it to the pheno- 

 mena. Take a hemispherical bubble at the moment of its for- 

 mation, and let us fix our attention upon one of the two faces 

 of the film, on the convex face, for example, and let us imagine 

 it divided into horizontal molecular rings from the summit to 

 the base. All these rings descend, and consequently each of 

 them goes on always increasing in diameter; this implies that 

 its molecules separate further from each other, and that other 

 molecules belonging to the subjacent layer come and place them- 

 selves in the intervals, so as to reestablish a uniform arrange- 

 ment. This must evidently apply also to the concave face. Let. 

 us now consider one of these molecular rings at the moment of 

 its departure from the summit ; it is clear that for any small 

 space traversed there is a great increase of the distances between 

 the molecules of this ring ; and it will be easily admitted be- 

 sides that these movements are not performed with mathematical 

 regularity, and hence that in the same ring the intervals between 

 the molecules are not all absolutely equal. This being admitted, 

 let us suppose that from some cause or other an obstacle inter- 

 feres with the free arrival of the subjacent molecules into the 

 intervals; one or other of these will in this case soon become so 

 great that the attraction of the molecules which it separates 



