200 M. G. Van der Mensbrugffhe on the 



on' 



have the same curvature at all points. But the film is then 

 no longer a catenoid; this is at once seen when the length 

 of the line of gorge of the new figure is measured ; I find that 

 this length, which varies with the azimuths, may exceed by 2 

 millims. the diameter of the circle of the original gorge ; the sur- 

 face, therefore, is materially different from a catenoid *. 



It remains now to be seen whether the deformation observed 

 in a film after the breaking of a portion bounded by a flexible 

 thread is simply local, or if it extends to the entire surface. In 

 order to clear up this point, I made the following experiments : — 

 I tied the ends of a moistened cocoon-thread so as to produce 

 a closed contour 92 millims. in length ; I laid it on a catenoidal 

 film the diameter of the circle of the gorge of which I had found 

 to be equal to 54'60 millims. Having then broken the inner 

 film of the cocoon-thread, I saw it arrange itself in the direction 

 of a skew curve, one part of which was very near the line of the 

 gorge. I placed then the plane of symmetry of this curve suc- 

 cessively in different azimuths, and noted each time, after mea- 

 suring with a horizontal cathetometer, the breadth of the line 

 situated in the plane of the circle of the original gorge. The fol- 

 lowing are the results obtained in this manner (the azimuth « 

 of the plane of symmetry of the curve is reckoned from the ver- 

 tical plane passing through the axis of the telescope of the ca- 

 thetometer, and I denotes the corresponding breadth): — 



a. I. 



millims. 



54-80 



45 54-95 



80 55-25 



100 55-15 



155 54-90 



180 54-75 



These numbers show very clearly that the deformation of the 

 catenoidal surface is very considerable in the immediate neigh- 

 bourhood of the cocoon-thread, and that it becomes less the 

 greater the distance from this thread. This fully agrees with 

 the experiments already described in reference to the skew he- 

 licoid. 



It follows thence that, when a laminar portion limited by 

 a flexible thread is broken, a new minimum surface is formed, 



* I said in my former research that by the presence of a silk thread 

 submitted to the tension of a catenoidal film, the surface did not seem al- 

 tered ; I had not made accurate measurements ; moreover, if I had then 

 observed a deformation, I should have attributed it, as I have already said, 

 at any rate in part, to the weight of the moistened thread. 



