THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS 259 



which they yield, and dividing by the density of the liquid, that the first of the 

 above two actions would be equivalent to a difference of level of 10""". 21 ; while, 

 even supposing the absence of the little annular mass, the second would evi- 

 dently proceed only from a difference of level equal to the radius of the air 

 bubble — that is, to 0'"™.5. With our small volume of air and a hemispherical 

 film, equilibrium, then, is impossible; that it should exist, it would be necessary 

 that the bubble of air should remain almost entirely beneath the level of the 

 liqirid, and hence should give rise to a film scarcely at all elevated and of very 

 feeble curvatin-e; then, in effect, the slight hydrostatic pressure which tends to 

 cause the bubble of air to rise will be equivalent to the minute weight of a vol- 

 ume of liquid a little less than that of this bubble, and the light pressure (>x- 

 erted by the exterior face of the film, in virtue of its feeble curvature, will suffice 

 to counterbalance it. 



Experiment again fully verifies this deduction of theory. Having poured, to 

 a certain height, glyceric liquid into the vessel with plane glass walls which 

 served for experiments on the masses of oil, and slightly agitated the liquid in 

 order to prodiice small bubbles of air, I chose one of these about 1"^"* in diam- 

 eter, and sufficiently near to one of the walls, and observed it by successively 

 placing the eye a little below and then above the level of the liquid. In this 

 way I perceived that the little bubble appeared spherical, and was so fiir im- 

 mersed that its projection above the level was very inconsiderable. 



§ 5. From this it is clear that if we form successive films on the surface of 

 soap-water or glyceric liquid, beginning with a diameter of one decimetre, fol- 

 lowed by others progressively smaller, a limit will be reached below which the 

 films Avill exhibit a sensible depression, or appear, in other words, to constitute 

 less than a hemisphere. In order to determine this limit approximately in regard, 

 to the glyceric liquid, I deposited the bubbles, as was indicated in the preceding 

 paragraph, on the surface of the liquid contained in a salver a little more than 

 full, and ascertained that they appear hemispherical only for diameters greater 

 than about 3 centimetres; below that value the bubbles form segments sensibly 

 less relatively to the entire sphere, and this diminution is the more decided as 

 the diameter of their base is smaller. 



§ 6. Although a film of spherical curvature thus formed at the surface of a 

 liquid be in equilibrium of figure, still absolute repose does not exist : it slowly 

 becomes thinner until it bursts. The principal causes of this have been long 

 since indicated: they are, firstly, evaporation, in the case of liquids which are 

 susceptible of it; and secondly, the action of gravity which causes the liquid 

 constantly to descend from the summit of the film towards its base. And here 

 again viscosity has a great influence : if this be very weak, it is plain that the 

 gliding of the molecules towards the base of the film will be effected with great 

 rapidity, and consequently the film will have scarcely any persistence; hence, 

 when we succeed in forming films with pure water, they scarcely subsist at all. 

 This remark concerning the agency of viscosity in the duration of films had 

 already been presented, though in a somewhat different manner, by Professor 

 Henry,* in regard to bubbles of soap compared with those of pure water. 



§ 7. Let us suppose now that a second bubble of air rises from the bottom of 

 the vessel, and that at the moment when it has nearly reached the surface, it 

 happens to be partly under the first film; it will thus occasion the formation of 

 a film which will necessarily lift up the former on one side, so that the two 

 quantities of air respectively imprisoned by these two films will be separated by 

 a portion of the second, as by a liquid partition. But this partition will not 

 observe the curvature of the rest of the second film, as I shall proceed to show. 



In virtue of their liquid nature, films can evidently not meet under angles with 

 linear edges: for continuity it is necessary that, along the whole line of junc- 



*See the article cited in 3d note of section 1. 



