292 M. J. Plateau on tlie Figures of Equilibrium 



for this purpose it was necessary to determine, at the tempera- 

 ture of the preceding experiment, the density p and the height h 

 in regard to the glyceric liquid. This I have done, employing 

 every known precaution, and I have found /> = 1*1065 and 

 /i=10'018 millimetres. One has consequently 2 hp = 22 -17, a 

 number that differs but little from 22'56, which experiment has 

 furnished me ; and the agreement appears still more satisfactory 

 when it is remembered that these two numbers are respectively 

 deduced from elements totally different. The formula 



Up 



may therefore be regarded as clearly verified by experiment. 



The accuracy of this formula requires, however, that the film 

 which constitutes the bubble should not have in any of its points 

 a thickness less than twice the radius of appreciable molecular 

 attraction. In fact, the pressure exerted upon the enclosed air 

 is the sum of the two actions due to the curvatures of the faces 

 of the film ; and, on the other hand, it is known that in the case 

 of a full liquid mass the capdlary pressure of the liquid upon 

 itself emanates from all the points of a superficial stratum having 

 for thickness the radius of activity in question. If, then, in all its 

 points the film has a thickness less than twice this same radius, 

 the superficial layers of its two faces have no longer their com- 

 plete thickness, and, the number of molecules contained in one 

 of these layers being thus diminished, these same layers must 

 necessarily exert a weaker action ; hence the sum of the latter, 

 that is to say the pressures on the enclosed air, must be less than 

 is indicated by the formula. 



I shall thence deduce a convenient method which furnishes an 

 approximate value for the radius of activity now under consider- 

 ation, or at least within a limit extremely little below which this 

 radius is found. If, having inflated a small bubble in the orifice 

 of the funnel of my apparatus, it is enclosed in a small glass 

 globe, it exhibits a remarkable phenomenon ; for, after some time, 

 by placing the eye on a level with its centre, one secs'a large 

 space, perceptibly circular, coloured with a uniform tint, and sur- 

 rounded by narrow concentric rings of other colours. One would 

 infer from this that the point has been reached at which the film 

 has thickness appreciably uniform throughout the whole extent 

 of the bubble, except of course the lowest part, where there is 

 always a small accumulation of liquid : the colours of the rings 

 which surround the central part evidently arise from the oblique- 

 ness of the ray3 from them to the eye. This fact respecting 

 thickness has already been noticed by Newton, but only as oc- 

 curring by chance, in the hemispherical bubbles of soapy water. 

 From the moment the bubble assumes this appearance it main- 



