46 Prof. J. Plateau on the Figures of Equilibrium 



masses into which it has been transformed will therefore sepa- 

 rate themselves from the circumference of the film, and will be 

 projected with the slight excess of acquired velocity which they 

 retain. At the same moment the capillary pressure must ra- 

 pidly give rise to a new border, which soon resolves itself, like 

 the first, into isolated masses ; and so the action will go on. 



I have shown in my memoir that this theory agrees with all 

 the details observed by Savart and by MM. Hagen and Magnus ; 

 and it applies equally to the drops projected from the margin 

 of the open films described in Savart's first paper. 



To the class of films of which we have just been speaking, 

 belong also those which M. Magnus obtained by the collision of 

 two liquid veins whose axes form a certain angle with each other. 

 These films exhibit some remarkable peculiarities that are easily 

 accounted for. 



We have seen above that Savart's films, when they assume 

 curved shapes and the velocity of the liquid is sufficiently dimin- 

 ished, close up in consequence of the capillary pressures exerted 

 by all the points of their two surfaces by virtue of their curva- 

 ture. The singular mode of formation of bubbles observed by 

 my son belongs to the same class of phenomena. The experi- 

 ment consists in projecting obliquely into the air soap-water 

 contained in a capsule, so as to spread out the liquid into a thin 

 sheet or film ; this film generally breaks into several pieces, each 

 of which immediately closes so as to form a complete hollow 

 bubble, which descends more or less slowly. The phenomenon 

 is due to the margin of each partial film acquiring a thickened 

 border or hem ; this falls more quickly than the central part, 

 which is opposed by the resistance of the air, so that the film 

 assumes a highly dome-shaped form with its convex side turned 

 upwards ; the rest is done by capillary pressure. 



I mention, in conclusion, a last species of films : they are like- 

 wise formed by a liquid in motion ; but cohesion and viscosity 

 play only a secondary part in their production, since the mole- 

 cular veins of which they may be considered to be made up have 

 no tendency to separate from one another. A film of this kind 

 is formed by a jet of liquid projected downwards from an orifice 

 having the form of a rectilinear slit — a jet whose singular ap- 

 pearance is well known. I made known a long time ago an 

 experiment which seems to me curious, inasmuch as it exhibits 

 visibly a large vertical film of liquid, one of the free edges of 

 which has a thickened border, and has the form of a straight 

 line inclined to the horizon. The experiment consists in making 

 water issue from a vertical and rectilinear slit extending up one 

 side of the vessel from near the bottom to above the surface of 

 the liquid. It is the free upper surface of the film which exhi- 



