270 M. G. Van der Mensbrugghe on the 



EC' = FB, FD; you would have the same impossibility. It 

 follows, therefore, that as the angles A B D, BDC cannot be 

 right or acute, they must be obtuse. Therefore &c. 



Cor. — In a quadrangle, if two opposite sides are equal, and 

 two adjacent angles comprised by them and a third side are right 

 angles, the other two angles also are right angles. 



XXXVI. On the Tension of Liquid Films. 

 By M. G. Van der Mensbrugghe*. 



A FORCE of contraction or tension has long been attributed 

 to the surface-layer of films. If this conception is in 

 conformity with fact, liquid films are in all respects similar to 

 stretched membranes ; it was by starting from this idea that M. 

 Plateau arrived at the enunciation of a general principle f, accord- 

 ing to which, in every laminar system constituting a polyhedral 

 structure, the sum of the areas of all the plates is a minimum. 

 Yet the tension of liquid surfaces was still a simple hypothesis ; 

 but M. Lamarle, in a memoir in which he has brilliantly turned 

 to account the above principle, has shown that in the case of a 

 liquid mass submitted solely to the action of its own parts, the 

 known phenomena of molecular attraction are necessarily accom- 

 panied by a superficial tension J. It merely remained to render 

 manifest this force which had so long remained mysterious. This 

 has been recently effected by Professor Dupre of Rennes : in the 

 second part of his Cinquieme Memoire sur la Theorie M6canique 

 de la Chaleur he gives several ingenious methods of demonstra- 

 ting the contractile effects produced on the surface of liquids. 

 I may be permitted to adduce here one of the experiments which 

 this able physicist describes in regard to a laminar surface. He 

 uses " a very simple apparatus, consisting of a vertical metallic 

 plate (fig. 1) cut out at G F E H, and of 

 another very light one (K L) applied 

 against the first at K and L. The faces 

 opposite each other are moistened with 

 solution of soap ; and when the moveable 

 plate, at first placed at F E, is made to 

 descend, a liquid film fills the interval. 

 The rapid ascent of K L when left to 

 itself is enough to prove the existence of 



* Communicated by the Author, from the Bulletin de VAcademie Roy ale 

 de Belgique, ser. 2. vol. xxii. 



t " Recherches experimentales et theoriques sur les figures de l'equilibre 

 d'une masse liquide sans pesanteur," 6th series, Mem. de VAcad. Roy. de 

 Belgique, vol. xxxiii. 



% " Sur la stabilite des systemes liquides en lames minces ; notions 

 preliminaires, art 1," Mem. de VAcad. Roy. de Belgique, vol. xxxv. 



E 





Fig 



. 1. 



c 





[ 

 F E 





K 



c 





1 







1 





i 



