280 M. G. Van der Mensbru™he on the 



DD* 



This experiment not only demonstrates in an elegant man- 

 ner the tension of liquid films, but renders it possible to find 

 approximately the intensity of this force. In fact, knowing 

 the mean diameters* and the vertical distance of the rings, the 

 portion of a catenary can be found which would, by its revolu- 

 tion round the line of the centres of the two circumferences, 

 produce the surface obtained; from this the angle a can be 

 calculated, which the tangent to the lowest point of the genera- 

 ting curve makes with the vertical. Now this tangent gives 

 exactly the direction in which the tension S of the film acts on 

 the suspended ring to keep it at rest. This being granted, it is 

 clear that the sum of the vertical components of this tension along 

 the lower ring holds in equilibrium the weight of the system sup- 

 ported. Hence, calling this weight p, and r the mean radius of the 

 lower ring, we have 2 7rrS cos a =p, 



whence S=t^ — • 



Airr cos a 



This formula shows us now why the equilibrium of the ring 

 is very stable. In fact, as the system is made to descend the 

 angle a diminishes, cos a increases, as well as the resulting 

 action 27rrScosa directed upwards; the ring ascends therefore, 

 and passes its position of equilibrium, to return quickly to it, 

 for the weight p then preponderates. 



The investigation of the angle a gives rise to pretty long cal- 

 culations ; to avoid them I attempt to make a as little differ- 

 ent from as possible ; with this view, I load the lower ring 

 until the tangent at the lowest point is almost, if not exactly, 

 vertical. By this means an approximate value of S may be ob- 

 tained by dividing the weight of the system suspended by the 

 circumference of the smaller ring. The experiment is made in 

 the following manner. I take for the upper contour, not a 

 forked ring, but a ring supported by three legs of about 5 cen- 

 tims. in length (fig. 6) ; to the legs Fig. 6. 



of the smaller ring is attached a 

 disk of paper intended to receive the 

 load. A liquid film having been 

 formed with the upper ring, I place 

 it horizontally on its supports, and 

 carefully raise the lower ring so as 

 to effect its contact with the film ; 

 I then carefully let go the lower 

 system, which remains suspended 

 to the laminar surface. That 

 being done, the circular film is 

 burst, and I wait five minutes, at the' 



* By mean diameter of a ring I intend half the sum of the external 

 and internal diameters. 



