CAPILLARY ACTION. 579 



(1 a.) When the ellipse becomes a circle, the meridian line becomes a 

 straight line parallel to the axis, and the film passes into the form of a 

 cylinder of revolution. 



(1 6.) As the eUipse degenerates into the straight line joining its foci, the 

 contracted parts of the unduloid become narrower, till at last, the figure becomes 

 a series of spheres in contact. 



In all these cases the internal pressure exceeds the external by where 



J a 



a is the semi-transverse axis of the conic. The resultant of the internal pres- 

 sure and the surface-tension is equivalent to a tension along the axis, and the 

 numerical value of this tension is equal to the force due to the action of this 

 pressure on a circle whose diameter is equal to the conjugate axis of the 

 ellipse. 



(2) When the conic is a parabola the meridian line is a catenary (fig. 10), 

 the internal pressure is equal to the external pressure, and the tension along 

 the axis is equal to 2irTm where m is the distance of the vertex from the 

 focus. 



Fig. 9. Unduloid. Fig. 10. Catenoid. Fig. 11. Nodoid. 



(3) When the conic is a hyperbola the meridian line is in the form of 

 a looped curve (fig. 11). The corresponding figure of the film is called the 

 nodoid. The resultant of the internal pressure and the surface-tension is equiva- 

 lent to a pressure along the axis equal to that due to a pressure p acting 

 on a circle whose diameter is the conjugate axis of the hyperbola. 



When the conjugate axis of the hyperbola is made smaller and smaller, 

 the nodoid approximates more and more to the series of spheres touching each 

 other along the axis. When the conjugate axis of the hyperbola increases with- 

 out limit, the loops of the nodoid are crowded on one another, and each 

 becomes more nearly a ring of circular section, without, however, ever reaching 

 this form. The only closed surface belonging to the series is the sphere. 



732 



