44 Prof. J. Plateau on the Figures of Equilibrium 



table, when the films become horizontal. In the detailed me- 

 moir I likewise explain the production of such films as these by 

 the cohesion and viscosity of the liquid. 



These films present some remarkable properties : they last 

 for an astonishing length of time, and their interference-tints 

 even reach blackness ; a film of this kind, formed in a bottle of 

 about 7 centims. diameter, lasted for eighteen days, and had 

 become black all over. 



There is a special class of liquid films upon which I dwell 

 longer, namely those due to the spreading out into a sheet of 

 a liquid in motion. Attention was called to these films by two 

 beautiful papers by Savart, published in the Annates de Chimie 

 et de Physique for 1833. 



In the first paper this distinguished physicist investigates 

 more particularly the phenomena which arise when the continu- 

 ous portion of a liquid vein, projected vertically downwards, 

 strikes perpendicularly against the centre of a small solid disk. 

 Under these circumstances the liquid spreads out into a sheet or 

 film, which, when everything else remains the same, takes dif- 

 ferent forms, according to the velocity with which it flows : with 

 a moderate head of liquid, the vein on striking the disk spreads 

 out all round into a perfectly unbroken film, shaped like a large 

 inverted capsule, whose free slightly serrated edge throws out a 

 great number of small drops, which start from the salient angles 

 of the teeth ; with a smaller head, the film becomes more and 

 more curved, and at last closes up completely below. 



In his second paper Savart investigates the effects produced 

 by the mutual impact of the continuous parts of two liquid veins 

 projected from circular openings, in directions which are exactly 

 opposite to each other at the point where the veins meet. With 

 equal heads and openings of the same size, the liquid spreads out 

 into a disk whose plane is perpendicular to the common tangent 

 to the axes of the two veins. Under a common head of mode- 

 rate amount, the liquid disk is surrounded by a small thick- 

 ened border, from which a multitude of little drops are thrown 

 out. 



Savart's observations led him, for moderate heads of liquid, 

 to the two following laws : — with the same-sized openings, the 

 diameter of the sheet is sensibly proportional to the head simply ; 

 and with the same head, it is sensibly proportional to the area of 

 the openings. 



He further shows that, with openings of different sizes, and a 

 common head of considerable amount, the film is conical ; and 

 that if the head is sufficiently diminished, the base of the conical 

 film contracts, and at last closes completely. 



Savart attributes the closing up of these films, as well as of 



