Tension of Liquid Films. 197 



then break the laminar portion comprised between the axis and 

 the cocoon-thread, so that the concavity of the curve obtained 

 shall be on the outside of the film ; tension is then exerted 

 along the entire length of the thread, which folds itself in a helix 

 that appears perfect (fig. 1). 



To ascertain if in this operation the remaining part of the sur- 

 face is altered, I attach the stem of the skeleton to a support, 

 and before breaking the film, and thus producing the helix, I 

 arrange the flame of a candle so that by the reflexion of the 

 rays on a point at a distance of 7 or 8 millims. from the axis 

 I obtain a brilliant image in the focus of the telescope of a ca- 

 thetometer. When this image is exactly in the centre of the 

 cross wires, I form the helix as above and again observe the image 

 of the flame ; I observe that it is displaced, but to so small an 

 extent that the deformation can be ascribed to the slight exten- 

 sibility of the thread, which slightly mars the regularity of the 

 curve. If, on the contrary, one of the ends of the cocoon-thread 

 be ever so slightly removed to or from the axis without touching 

 the other end, the image of the flame undergoes a considerable 

 displacement, showing clearly that the film has undergone a very 

 marked deformation. Hence I conclude that on a skew helicoid 

 the only curves of equilibrium of tension at all realizable by ex- 

 periment are helices (traced on cylinders) the common axis of 

 which coincides with that of the surface in question. 



I will here make two remarks. In the first place, I take the 

 point where the rays of the candle impinge at 7 or 8 millims. from 

 the axis (that is, close to the helix produced), so that, after break- 

 ing the laminar portion between the axis and the thread, I may 

 be better able to ascertain the ultimate deformation of the surface : 

 this precaution is necessary ; for, as I shall afterwards show, the 

 alteration of figure is greater the nearer we approach the cocoon- 

 thread. In the second place, if, instead of bursting the portion 

 of the film between the axis and the flexible thread, we break 

 that between the latter and the director helix, we observe the 

 thread suddenly thrown along the axis of the figure : this effect 

 clearly arises from the fact that the tendency of the residual 

 film to present the least possible surface can then be freely ex- 

 erted at the moment the film is destroyed. 

 "; After having investigated the lines produced with cocoon- 

 threads whose ends are fixed to two points of the solid skeleton, 

 it may be proposed to produce in a helicoidal film an aperture 

 bounded by a thread and forming a closed contour : the experi- 

 ment always succeeds when the thread is not too long — though 

 the film then no longer represents a helicoid, as can easily be 

 ascertained by the method described above. It is proved in this 

 manner that the deformation undergone by the film is the 



