196 M. G. Van cler Mensbrugshe on the 



CO' 



the outside of the liquid film. This, indeed, should be the case ; 

 for let m (fig. 2) be a point of the Fig. 2. 



thread a b supposed to be straight ; 

 this point is acted on by three forces, a 

 that is, by the two equal and opposite 

 tensions of the thread, and by the 

 resultant mr of all the elementary 

 actions of the tension of the liquid 

 on m, a resultant which is normal 

 to ab. Now it is clear that these forces can never be in equi- 

 librium unless the two former be infinite. As this condition 

 cannot be fulfilled, the two elements terminating in m must 

 necessarily bend towards the film. The same thing takes place 

 at all points of the flexible thread ; the curve obtained should 

 be concave on the exterior of the figure, as I have always ob- 

 served. 



The same reasoning shows, again, why I have not been able to 

 replace the solid skeleton by a stretched cocoon-thread; this, in- 

 stead of remaining straight, always formed a helicoidal line which 

 had an extremely feeble curvature. 



It follows from the preceding that every line of equilibrium 

 formed by a flexible thread and partially bounding a laminar 

 surface must be concave on the outside ; the curves of equili- 

 brium which satisfy this condition are thus the only realizable 

 ones; this remark must never be lost sight of in the present 

 experiments. 



I have effected the formation of a helix of equilibrium in 

 proportion as experiment corresponds to all the restrictions of 

 theory. I work in the following manner : — I begin by seek- 

 ing the length of a spiral which would be traced on a cylinder 

 of 6 millims. radius, for example, and which has the same pitch 

 as the directrix helix of the skeleton I use (this pitch, measured 

 by the cathetometer, is 31*1 millims.); the length in question is 

 then equal to that of the hypothenuse of a right-angled triangle 

 whose two other sides are respectively it x 12 millims. and 31*1 

 millims., that is, to 48*9 millims. Consequently I take a cocoon- 

 thread as exactly of this length as possible when moistened by 

 the glycerine liquid, and by means of a little wax I fix the two 

 ends at 6 millims. from the axis, at two points of the solid wires 

 representing the extreme generators of the helicoid : in this ope- 

 ration care must evidently be taken not to attach the second 

 end of the thread, before having made this describe an entire turn 

 about the solid axis in the direction indicated by that of the 

 director helix. I then immerse the skeleton in the glycerine 

 liquid, and on withdrawing it I obtain a helicoidal film on which 

 floats a cocoon-thread. By means of a point of filtering-paper I 



