Tension of Liquid Films. 



271 



the force of contraction ; a fall, on the contrary, is observed 

 if the liquid film has been burst. The friction is less and the 

 success more certain if KL is replaced by a wire, one bent end 

 of which fits at F in a small hole, while the other end moves on 

 a circular edge replacing E H "*, 



Reflecting on these experiments, I have devised some others, 

 which, at the same time that they show very neatly the force of 

 contraction, acquire a special interest in this respect — that they 

 can be used for certain exact verifications of the theory. Hence 

 I have no hesitation in submitting to the judgment of the Aca- 

 demy these new methods of studying the tension of liquid films. 



I. Equilibrium of a Flexible Thread submitted to the Tension of 

 a Liquid Film. 



Given a plane or curved film produced, for instance, by Pla- 

 teau's glycerine liquid ; it follows clearly from the principle of 

 tension that, by giving to this film a contour one portion of 

 which is perfectly flexible, it will at once be seen to assume the 

 figure corresponding to the least possible extent of the laminar 

 surface. Now this is confirmed by facts in a decisive manner. 



Fig. 2. 



Let us first investigate the pheno- 

 mena in the case of plane films. Let 

 abed (fig. 2) be a horizontal square f 

 of iron wire, in any two points of 

 which (m and n) in one of its sides (ab) 

 are fixed the ends of a perfectly flex- 

 ible and very fine silk or cotton 

 thread; let this arrangement, sup- 

 ported by a hook f 3 also of iron wire, 

 be immersed in the glycerine liquid ; 

 as soon as we withdraw it we obtain a 

 plane film in which the thread mon 

 floats without affecting any regular shape. That being the case, 

 if by means of a point of filter-paper the laminar portion monm 

 be broken, the flexible contour soon assumes the form of a per- 

 fect arc of a circle. It is obvious that the experiment would 

 still succeed even if the portion m n of the solid wire a b were 

 first suppressed. 



This result proves that the residual film amonb cda occupies 

 in fact the least surface possible ; in fact the calculus of varia- 

 tions teaches us that the area comprised between a straight line 

 m n, and a curve mon of given length, is a maximum when this 

 curve is an arc of a circle ; this condition clearly necessitates 



* Ann. de CMm. et de Phys. de Paris, ser. 4. vol. vii. 



t The shape of the plane solid contour is completely arbitrary. 



