356 Prof. J. Plateau on the Figures of Equilibrium 



saturated with aqueous vapour, but only for a few minutes when 

 they are freely exposed to the air. The glycerine-solution not 

 only does not emit vapour, but, on the contrary, absorbs the 

 moisture of the surrounding air; and it is partly because of this 

 that films of this liquid last so long even when exposed to the air. 



In the third place, since gravity constantly causes the liquid 

 to descend towards the base of the films, it is plain that, by get- 

 ting rid of or lessening the action of this force, the duration of 

 the film must be increased. Hence it evidently follows that, 

 other things being equal, a horizontal film will last longer than 

 one which is inclined or vertical. I have made this comparison 

 in the case of films of soap-water formed upon rings of iron 

 wire 7 centims. in diameter and exposed to the air, one being 

 horizontal and the other vertical. The average persistence of the 

 first was 25 seconds, and that of the latter 13 seconds. Hence 

 the position, or, more accurately, the greater or less degree of in- 

 clination, of the film must be reckoned as one of the secondary 

 causes that we are considering. 



In the fourth place, combinations of films always last a much 

 shorter time than figures formed of a single film. This is because 

 the highly concave surfaces of the small masses of liquid which 

 form the liquid edges, and especially those which exist at the 

 points of junction of these edges, produce a continual drain upon 

 the liquid of the films and thus tend powerfully to make them 

 thinner. The combination of films into systems is therefore 

 likewise one of the secondary causes which modify their per- 

 manence. 



In the fifth place, films generally last longer in proportion as 

 they are of smaller size. For instance, if systems of films are 

 produced upon two skeletons of similar shape but of different 

 sizes, the one on the smaller skeleton lasts the longest. 



If the persistence generally diminishes when the size of the 

 films is increased, this is, I think, simply because the greater a 

 film is, the greater is the chance that one point or another will 

 yield to some cause of rupture. Under certain circumstances 

 this effect of size does not show itself; for instance, films of soap- 

 water formed upon rings 10, 7, 2, and 1 centim. in diameter 

 lasted on the average for the same length of time. This last 

 fact may be explained by the consideration that the drain of 

 liquid caused by the great concave curvature of the small quan- 

 tity of liquid which connects the film with the whole of the inner 

 circumference of the ring, tends to make the smaller films last a 

 shorter time, and thus the effects of size and curvature may neu- 

 tralize each other. 



Lastly, it is needful, in the sixth place, to take account of the 

 nature of the solid to which the film adheres, and of the condi- 



