of a Liquid Mass without Weight. 129 



between the summit of the air-bubble and the surface of the 

 liquid has become very small, these molecular movements are no 

 longer able to take place with a velocity corresponding to that 

 with which the bubble rises. Hence, in order that the air which 

 constitutes the bubble may continue to rise and come above the 

 surface of the liquid, it is plain that the liquid must either part 

 or be raised up. Since the beautiful researches of MM. Donny 

 and Henry, there can, however, no longer be any doubt as to 

 the cohesion of liquids being comparable to that of solids ; ac- 

 cordingly the stratum of liquid which separates the summit of 

 the bubble of air from the surface, at the moment at which we 

 take the phenomenon into consideration, offers, notwithstanding 

 its extreme thinness, a resistance much too great to allow it to 

 be broken. Consequently this layer is raised up, or, in other 

 words, a liquid film is formed. 



I show that, at the end of the phenomenon, this film neces- 

 sarily forms part of a sphere, but can in no case become a com- 

 plete hemisphere, although it approaches thereto the more nearly 

 the larger it is. I verify the last result experimentally : I showthat 

 when the air-bubble is very small, when, for example, its diameter 

 does not exceed 1 millimetre, the film which it produces at the sur- 

 face of the liquid is only a very small part of the sphere to which 

 it belongs; but that in proportion as the volume of air is in- 

 creased the spherical surface approaches more and more nearly 

 to a hemisphere, so that when the diameter of its base exceeds 

 about 3 centimetres it appears to the eye hemispherical. In 

 what follows, I shall always suppose such films to be so large 

 that they may be regarded as sensibly hemispherical. 



^Yhen two hemispherical films formed at the surface of a liquid 

 touch each other at the base, it is well known that they penetrate 

 each other more or less, but so that the quantities of air which 

 they respectively enclose remain separated from each other by a 

 liquid film or partition. I show that this partition also forms 

 part of a sphere, generally of a different curvature from that of 

 the first two films. Starting from the principle that the pressure 

 exercised by a film of liquid of spherical curvature on the air 

 enclosed by it varies inversely as the radius of curvature of the 

 film, and denoting the radii of the larger film, of the smaller 

 film, and of the partition respectively by p, p' } and r } I arrive at 

 the formula 



pp> 



r=: — — 



p-p" 



which gives the radius of the partition when the radii of the two 

 films are known. 



In order to complete the study of such a grouping, we have 



