CAPILLARY ACTION. 



These nguws of revolution have been studied mathematically by Poisson*. 

 Goldschmidtt. Lindeldf and MoignoJ, Delaunayll, Lamarle, Beerl, and Mann- 

 *, and have been produced experimentally by Plateautt in the two different 

 ways already described. 



The limiting conditions of the stability of these figures have been studied 

 both mathematically and experimentally. We shall notice only two of them, 

 the cylinder and the catenoid. 



STABILITY OF THE CYLINDER. 



The cylinder is the limiting form of the unduloid when the rolling ellipse 

 a circle. When the ellipse differs infinitely little from a circle, the 



x 



c is 



equation of the meridian line becomes approximately y = a + c sin - where 



mull. This is a simple harmonic wave-line, whose mean distance from the axis 

 is a, whose wave-length is 2ira, and whose amplitude is c. The internal pres- 



T 

 sure corresponding to this unduloid is as before p = - . Now consider a 



portion of a cylindric film of length x terminated by two equal disks of radius ; 

 und containing a certain volume of air. Let one of these disks be made to 



approach the other by a small quantity dx. The 

 film will swell out into the convex part of an 

 unduloid, having its largest section midway between 

 the disks, and we have to determine whether the 

 internal pressure will be greater or less than before. 

 If A and C (fig. 12) are the disks, and if x the 



Ffe. 13. 



NouvMe Uieorie de Faction capillaire (1831). 



f Ddwrnimitio ttiperficiei minima rolatione curves data duo puncta jungentis circa datum axem 



(Oottingen, 1831). 



} Ltymt da calcttl de* variations (Paris, 1861). 



'8ur U surface de revolution dont la courbure moyenne eat constant*," Liouvitte's Journal, vi. 

 { "TbforiB gfomftrique dea rayons et centres de courbure," Bullet, de CAcad. de Belgigue, 1857. 



* Tractate* de Theoria Mathematica Pfuenomenorum in Liqnidix actione gravitate detractis obter- 



(Bonn, 1857). 

 ** Journal F/nttitut, No. 1260. 

 ft Statique exjxrimentale et theorique dea liquidea. 



