692 PLATEAU ON THE PHiENOMENA OF A FREE LIQUID MASS 



But there is a cause which acts in an opposite manner upon 

 the divisions. If we imagine the divisions of the continuous 

 part to be suddenly effaced, the small portion of the vein thus 

 modified which replaces, at this instant, any given division, will 

 be smaller in proportion as the division in question is more 

 distant from the contracted section. Consequently we may con- 

 sider each of the divisions which at a determinate instant are 

 arranged upon the entire length of the continuous part, as arising 

 respectively from the transformation of a different cylinder ; and 

 as the minute portion of the vein which replaces, in the above 

 hypothesis, any given division would continue slightly diminish- 

 ing in thickness from above downwards, we should exactly 

 obtain the diameter of the corresponding cylinder by taking 

 the mean diameter of this portion. Now we know that for any 

 liquid, the normal length of the divisions of a cylinder supposed 

 to be formed in the air, and the entire convex surface of which 

 is free, is in proportion to the diameter of this cylinder ; con- 

 sequently if nothing opposed the action of the configuring forces 

 upon the vein, the proportion of the length of a division to the 

 above mean diameter corresponding to it would be the same for 

 all the divisions ; and as this mean diameter diminishes at each 

 division from the top to the bottom of the continuous portion, 

 it follows that the length of the divisions would continue to de- 

 crease in the same proportion. If then the cause with which we 

 are engaged were alone in action, each division would gradually 

 diminish in length and volume in proportion as it descended in 

 the continuous portion. But then the divisions starting from 

 the contracted section with the velocity of the liquid, would 

 necessarily follow in their movement of transference a different 

 law. We shall show that this movement would be retarded, so 

 that the liquid, which descends on the contrary with an accele- 

 rated velocity, must pass from one division to the other, and 

 that the latter must simply constitute, upon the surface of the 

 vein, a sort of undulation, which would be propagated according 

 to a particular law. 



Let us assume the hypothesis of the entirely free action 

 of the configuring forces, and let us commence with the mo- 

 ment at which tae section of the surface of the vein which con- 

 stitutes the neck of a constriction passes to the contracted 

 section. After a brief interval, another superficial section, 

 corresponding to the next neck, will pass in its turn, and 



