V] 



OF FIGURES OF EQUILIBRIUM 



379 



so nearly that that state of a system which is most likely to occur, 

 or most likely to endure, is precisely that which we call the state of 

 equilibrium. 



For experimental demonstration, the case of the cylinder is the 

 simplest. If we construct a liquid cylinder, either by drawing out 

 a bubble or by supporting a globule of oil between two rings, the 

 experiment proceeds easily until the length of the cylinder becomes 

 just about three times as great as its diameter. But soon afterwards 

 instability begins, and the cylinder alters its form; it narrows at 



Fig. 111. 



the waist, so passing into an unduloid, and the deformation pro- 

 gresses quickly until our cylinder breaks in two, and its two halves 

 become portions of spheres. This physical change of one surface into 

 another corresponds to what the mathematicians call a "discon- 

 tinuous solution" of a problem of minima. The theoretical limit of 

 stability, according to Plateau, is when the length of the cylinder is 

 equal to its circumference, that is to say, when L = Inr, or when the 

 ratio of length to diameter is represented by -n. 



The fact is that any small disturbance takes the form of a wave, 

 and travels along the cylinder. Short waves do not affect the 

 stability of the system ; but waves whose length exceeds that of the 

 circumference tend to grow in amplitude: until, contracting here, 

 expanding there, the cylinder turns into a pronounced unduloid, 

 and soon breaks into two parts or more. Thus the cylinder is a 



