of a Liquid Mass without Weight. 45 



those described in his first paper, to the attraction of the mole- 

 cules ; but he confines himself to this simple general view of the 

 matter. I explain the facts more precisely by help of the fol- 

 lowing consideration : when a liquid film is curved and its two 

 principal flexures are not in opposite directions, each element of 

 the film exerts, as I have shown in my Fifth Series, a pressure 

 perpendicular to the surface and directed from the concave side. 

 The pressure thus arising, when the velocity of projection of the 

 liquid is sufficiently diminished, increases the meridional cur- 

 vature of the films in question so far as to close them com- 

 pletely. 



In order to complete the theory of these phenomena, it still re- 

 mained to account for the limitation of the films when not closed, 

 as well as for the formation of the drops which escape from their 

 margins. 



M. Hagen, who repeated and varied the principal experiments 

 contained in Savart's second paper, has proposed what appears 

 to be a correct theory of the limitation of the films, and one 

 which leads to the two laws pointed out above. As to the ge- 

 neration of drops, M. Hagen avows that he has not been able to 

 find any satisfactory explanation : and this is just what might 

 have been expected ; for this phenomenon depends upon a prin- 

 ciple propounded in my Second Series, with which it was impos- 

 sible for M. Hagen at that time to have been acquainted. The 

 following is, I am convinced, the exact explanation of the matter. 

 Let us call to mind what happens immediately after the two 

 orifices are opened, and while the disk of liquid is still increas- 

 ing in diameter. This disk evidently constitutes a figure of re- 

 volution whose meridional section presents a very high curva- 

 ture at the equator — that is to say, precisely at the margin of 

 the sheet ; now this high curvature necessarily gives rise to a 

 strong capillary pressure directed along the radius of the disk, 

 but in the opposite direction to the motion of the liquid. Hence 

 at the edges of the disk the liquid is subject to two opposing 

 forces, one of which tends to move it away from the centre, and 

 the other to make it approach the centre, and consequently a 

 lateral motion of the liquid must ensue; in other words, during 

 the growth of the disk, the liquid that is thrown back must form 

 a thickened border all round its circumference. This border, 

 however, having the shape of a sort of cylinder that has been 

 bent round into a ring, forms, as I have shown in my Second 

 Series, an unstable figure, and must as an absolute necessity 

 break up during its development into isolated masses; on the 

 other hand, the border, by virtue of the inertia of its total mass, 

 cannot completely lose its velocity at the same time as the por- 

 tion of the film to which it immediately adheres; the small 



