434 Prof. Gr. Van der Mensbrugghe on a new Application 



the sheet. On the other hand, the principles of thermody- 

 namics require that the kinetic energy shall diminish, not only 

 because the concentric rings widen, but moreover because, 

 precisely on account of the superficial enlargement on the two 

 faces, the tension and with it the retarding force are more and 

 more augmented. This last point follows as a consequence 

 from my deductions already confirmed by a former series of 

 experiments, which are described in my recent memoir. 



4. Applying my theory to Savart's plane films, I arrived at 

 the following results : — 



(a) The retarding force due to the augmentation of poten- 

 tial energy goes on increasing in proportion as the liquid 

 travelling over the disk removes further from the axis. 



(6) As we have e= — nearly, € being the thickness of the 



film at any point, C a constant, v the velocity at that point, r 

 the distance from the axis, we conclude that, starting from 

 the axis, e continually diminishes, since r increases more ra- 

 pidly than v lessens. This gradual diminution of e will cease 

 when vr no longer sensibly changes ; but soon the velocity 

 decreases faster than r increases, and from that time the thick- 

 ness must go on increasing by degrees until it attains a 

 maximum. 



(c) When the velocity shall have become sufficiently reduced, 

 e may pass through a series of maxima and minima, so that 

 there will be formed, for sufficiently strong pressures, a series 

 of circular waves joined to one another by cross striae, which 

 will give rise to the production of minute drops, taking away 

 from the outermost zone its transparence and its regularity of 

 form. 



(d) If the velocity of the liquid, after the impact, increases 

 in a certain ratio, the retarding force increases in a greater 

 ratio — which explains the remarkable fact that the liquid disks 

 may become less in diameter when the charge is increased. 



These theoretic results are verified in all points by the ex- 

 periments of the French physicist, and by the measurements 

 furnished by them to M. Hagen. 



5. If my theory is susceptible of useful applications in the 

 study of plane liquid sheets, it finds still more curious appli- 

 cations in relation to curved ones. According to Savart, such 

 a sheet is obtained, for instance, by letting a liquid vein, shot 

 through an orifice of 12 millims., under a sufficient pressure, 

 fall upon the centre of a horizontal brass disk fixed at the dis- 

 tance of 20 millims. beneath. After impact the liquid spreads 

 out in all azimuths, and gives rise to a curved film bounded 

 by an indented margin. For a pressure of 2 metres the 



