Tension of Liquid Films . 201 



which obeys all the conditions of equilibrium previously enun- 

 ciated, and sensibly coincides, at a greater or less distance, with 

 the original surface. 



I should have greatly liked to be able to apply the experi- 

 mental proof to other surfaces, of mean zero curvature, but I 

 have been prevented from this by the extreme complexity of the 

 calculations; yet the examples investigated above will justify 

 the following conclusions : — 



Whenever a laminar surface bounded either wholly or par- 

 tially by a flexible thread is broken, the original surface of the 

 film is markedly altered when the asymptotic lines have not the 

 same curvature at all points; this alteration takes place even 

 when we try to make this thread coincide with an asymptotic 

 line. 



If, on the contrary, the asymptotic lines have everywhere the 

 same radius of curvature, and the thread can moreover fold 

 itself in their direction, the film undergoes but a very slight defor- 

 mation, which appears to arise from the fact that the thread, not 

 being extensible, yields a little to tension and ceases to coincide 

 exactly with the asymptotic line. 



In all cases the thread forms a curve whose radius of curva- 

 ture appears on inspection to be the same at all points. 



In terminating this note I may be permitted to point out a 

 very curious effect of the tension of liquid films. 



A plane liquid film is produced in -p- 4 



a ring provided with a suspender, 

 and this is pjaced in a vertical plane ; 

 a very thin hollow glass bulb, 8 to 

 12 millims. in diameter, and weigh- 

 ing 10 to 20 milligrammes, is then 

 moistened with glycerine liquid ; it 

 is gently placed in contact with the 

 lower part of the film ; this imme- 

 diately advances in the direction of the bulb and forms a curved 

 surface, which rests on one side on the ring, and on the other on 

 a small circle of the sphere parallel to the plane of this ring. 

 The centre of the bulb is gently moved towards this plane ; as this 

 takes place, the film moistens the sphere on a continually increas- 

 ing circumference, which finishes by being the circumference of 

 a large circle. If the bulb be allowed to rest on the solid contour 

 and be left to itself, it remains perfectly in equilibrium (fig. 4). 

 The ring may even be rapidly turned about its axis without 

 bursting the film or detaching the hollow sphere. 



If the bulb is ellipsoidal instead of being spherical, the ellip- 

 soid turns until it is cut by the plane of the film in the direction 

 of its maximum section, which, once plunged in this film, re- 



Phil. Mag. S. 4. Vol. 34. No. 229. Sept. 1867. P 



