Tension of Liquid Films. 



279 



liquid employed would always be about 3 milligrammes per 

 millimetre. 



In fine, as regards plane films, the experiments seem to me 

 to exhibit a sufficient agreement with the three laws deduced 

 from statical principles. An exact and direct verification of these 

 laws in the case of curved films presents serious difficulties. In 

 all the attempts I have made from this point of view, the skew 

 curves which the thread assumed always appeared to have the 

 same radius ; but in order to be quite sure, I must have had 

 recourse to very long and complex calculations. Yet in this 

 case, as in that of plane curves, everything leads to the suppo- 

 sition that observation would confirm theory. 



II. Equilibrium of a Metal Ring suspended to a Liquid Film. 



I have observed, in experiments on the catenoid, that when I 

 moved the upper ring on either side of its normal position, the 

 film would often raise the lower ring — an effect evidently due to 

 the tension of the liquid. I concluded from this fact that, by 

 making the lower ring sufficiently light, I might be able to obtain 

 it suspended to the liquid plate and kept in equilibrium by the 

 force of contraction of the latter. To determine this, I had a 

 ring made of iron wire 53*30 millims. in diameter, and 0*6 mil- 

 lim. in thickness; it rested on three feet, also of iron wire, 25 

 millims. in length, and 0*25 millim. in thickness. This ring, 

 previously well moistened with the glycerine liquid, being placed 

 with its feet on a table, I approached to it the large ring (at- 

 tached to a fork), on which was already a liquid film ; as soon as 

 the two rings had stuck together, I gently raised the forked 

 ring. The portion of the film in the lower ring remained 

 plane; but the annular part was 

 curved, as was to be expected, in 

 the shape of a portion of a catenoid. 

 Raising then the higher ring, a mo- 

 ment was soon reached at which the 

 lower system was also raised,and was 

 then suspended to the liquid film. 

 Fig. 5 represents on a scale of one- 

 half the system in equilibrium; the 

 portion of a catenoid is shaded. 

 I found that the stability of the 

 equilibrium was perfect; for by blow- 

 ing on the circular film with suffi- 

 cient force to make the system de- 

 scend, I saw the portion of a ca- 

 tenoid elongate without breaking ; 

 as soon as I ceased to blow, the 

 small ring quickly ascended. 



