436 On the Potential Energy of Liquid Surfaces. 



limited at the equatorial section (I thus name the section the 

 plane of which passes through the points where the tangent 

 to the generatrix is vertical). 



I have, in fact, ascertained that, if the operation is conducted 

 with a constant charge, there is never any sudden rising fol- 

 lowed by the formation of a surface concave upwards ; no 

 more is there such when the charge, instead of diminishing, 

 goes on increasing ; and, finally, there is none when, from any 

 cause whatever, the sheet presents an aperture. 



(b) While the gradual development of potential energy in 

 the upper portion of the sheet gives rise to a retarding force, 

 there is developed, on the contrary, in the lower portion an 

 accelerating force, due not merely to gravity, but also to the 

 diminution of the potential energy of the liquid rings, which 

 are incessantly narrowing right to the axis. It is owing to 

 the increase of the velocity of the liquid that the water- threads, 

 after encountering the axis, scatter in little drops. A Savart 

 closed sheet thus presents a striking example of the transfor- 

 mation of kinetic into potential energy, and of potential energy 

 into energy of motion. 



(c) If while the sheet is closed the kinetic energy diminishes, 

 either gradually or abruptly, the retarding force arising from 

 the increase of potential energy in the upper part increases, 

 either continuously or suddenly, and then struggles against 

 the accelerating force that animates the lower part of the sheet. 

 For this reason the film is strongly stretched : there is some- 

 times delineated a projecting ridge ; and immediately after- 

 wards the sheet rises, becoming concave upwards ; but then 

 the retarding force which dominates the concave portion is 

 directed downward, like gravity and the accelerating force of 

 the lower part — which immediately brings back the sheet to 

 its primitive form, but with smaller dimensions. 



While Savart generally operated only with charges decreas- 

 ing in a continuous manner, I have verified the preceding 

 theoretic consequence by abruptly diminishing the charge 10 

 centims. I thus saw, after a few seconds, the singular figure, 

 concave upward, formed which so much preoccupied the 

 French physicist. 



(d) According to my formula 



d Q=Atcl(s§), 



which gives the variation of heat dQ corresponding to an in- 

 crement <iS of the surface S, having the potential energy T, 

 and absolute temperature t, the variation dQ must vanish with 



