Tension of Liquid Films. 281 



end of which I absorb, by means of a piece of filtering-paper, 

 the small mass of liquid which adheres to the lower ring. Placing 

 then sand on the paper disk, I load the system until the tan- 

 gent at the lowest point of the generating curve is but little 

 removed from the vertical, after which I wait five minutes, 

 and remove as soon as possible the fresh quantity of liquid 

 which surrounds the small ring. Taking care, then, always 

 to keep this horizontal, I gradually increase the burden, but 

 by gradually smaller amounts, in proportion as I more closely 

 approach the point at which the tangent to the base of the curve 

 will become vertical. Let us suppose this point attained; the 

 weight suspended is then at its maximum value, and equilibrium 

 should cease to be stable. To understand this, it must be ob- 

 served that when the tangent is exactly vertical, the lower ring- 

 passes by the summit of the meridional chain ; if then,* for any 

 reason, the ring descends by the smallest amount, it passes beyond 

 the summit in question, and hence the tangent should be inclined 

 in a contrary direction. But from this moment a increases, and 

 therefore the action 27rrS cos « of the tension diminishes, so that 

 the weight ought to continue to descend. This is just what ob- 

 servation confirms. As soon as the ring is low enough to rest on 

 the table, I can burst the film without fearing to derange the 

 load and thus alter its weight. In this manner I have made a 

 series often experiments; the following numbers give in milli- 

 grammes the greatest weights successively obtained : — 



1012 I 1005 



1001 1008 



1027 

 1050 

 1011 



1021 

 1001 



1068 



These values are sufficiently close ' to one another, excepting 

 two, which exceed the least by 49 and 67 milligrammes respect- 

 ively. These deviations are probably due to a cause of error 

 which escaped me, — for instance, to a drop of liquid which was 

 added to the load at the time the film was broken. In any 

 case, taking the mean of the ten values, and dividing by 

 27jt= 167*45, we get 1020-4 



S= ^i=6-095. 

 167*45 



Excluding the two greatest values and taking the mean of the 

 other eight, we should have 



S= i™ =6-031. 

 167*45 



These numbers, which give the tension for each millimetre of 

 length of a catenoidal film, differ, as will be seen, but little from 

 the values obtained for S in my experiments on the equilibrium of 



