of the Potential Energy of Liquid Surfaces, 433 



by the plane or curved sheets of liquid first described by Sa- 

 vart*, and afterwards studied by Hagenf, Tyndallt, Magnus§, 

 and BoussinesaJ. I quickly recognized some very interesting 

 verifications of my theory in the curious peculiarities mani- 

 fested by those sheets, of which no satisfactory explanation 

 has, to my knowledge, been yet furnished. In order to be 

 able to continue without hurry the experimental control of 

 my theoretic deductions, I will briefly explain how the prin- 

 ciples of thermodynamics account for the effects in question. 



2. It is known from Savart' s observations that, if two veins 

 of water with equal circular sections are impelled with equal 

 and opposite velocities, and meet so that their axes coincide, 

 there is formed, for all pressures sufficiently strong, a plane 

 circular sheet bounded by a rough, agitated, and sonorous 

 zone when the pressure exceeds a certain amount, but which 

 for a less charge becomes perfectly smooth and even through- 

 out its extent. From this it follows that, under favourable 

 conditions, not merely the vis viva of the water after the im- 

 pact of the two veins, but also the effects of gravity are almost 

 completely nullified after a relatively very short course. What 

 can be the cause that destroys so considerable an energy of 

 motion ? and by what is the latter replaced ? 



3. Since 1849 M. Hagen has invoked, as being that cause, 

 the superficial tension of the liquid, which, having constantly 

 to be overcome, gives rise to a retarding force. 



Doubtless the theory of M. Hagen is very ingenious, espe- 

 cially for the time when it was sent forth ; but, besides that it 

 does not clearly show the force which is substituted for the 

 'vis viva in proportion as this is destroyed, it does not make 

 intelligible the various effects ascertained by Savart, except 

 by means of an indispensable complement or, rather, a rectifi- 

 cation. In the actual case the principle of the conservation of 

 energy is verified, owing to the circumstance that the energy 

 of motion of the two veins is almost entirely replaced by the 

 potential energy of the superficial layers of the two faces of 



* "Memoire sur la choc d'une veine liquide lancee contre un plan cir- 

 culaire," Ann. de Chim. et de Phys. de Paris, 1833, fc. liv. p. 55 ; "Memoire 

 sur le choc de deux veines animees de mouvements directement opposes," 

 ibid. t. lv. p. 257. 



t " Ueber die Scheiben, welche sich beim Zusarumenstossen von zwei 

 Wasserstrahlen bilden, und liber die Auflosung einzelner Wasserstrahlen 

 in Tropfen," Pogg. Ann. 1849, vol. lxvii. p. 451. 



% On some Phenomena connected with the Motion of Liquids," Phil. 

 Mag. 1854, ser. 4, vol. viii. p. 74. 



§ " Hydraulische Untersuchungen/' Pogg. Ann. 1855, vol. xcv. p. 1. 



j| Theorie des experiences de Savart sur la forme que prend une veine 

 liquide apres s'etre choquee contre un plan circulaire," Comptes Rendios, 

 1869, t. lxix. pp. 45, 128. 



