WITHDRAWN FROM THE ACTION OF GRAVITY. 673 



surface of the cylinder, would still exceed considerably the total 

 duration observed, i. e. 0"*4. 



In starting from this value 0"*4 as constituting the lower limit 

 corresponding to a diameter of 2*1 millims., the law of the pro- 

 portionality of the partial duration to the diameter will imme- 

 diately give the lower limit corresponding to any other diameter ; 

 we shall find, e. g. that for 6 millimetres this limit would be 



0"-4xl0 ,„„ • , „/i 



— — =i"-9, or more simply 2". 



If, then, we imagine a cylinder of mercury a centimetre in dia- 

 meter, formed in vacuo or in air, of sufficient length to furnish 

 several spheres, entirely free at its convex surface, and of such a 

 length that its divisions assume their normal length, the time 

 which will elapse from the origin of the transformation of this 

 cylinder to the instant of the rupture of the lines will consider- 

 ably exceed two seconds. 



68. It will not be superfluous to present here a resume of 

 the facts and laws which the experiments we have described 

 have led us to establish with respect to unstable liquid cylinders. 



1. When a liquid cylinder is formed between two solid bases, 

 if the proportion of its length to its diameter exceeds a certain 

 limit, the exact value of which is comprised between 3 and 3*6, 

 the cylinder constitutes an unstable figure of equilibrium. 



The exact value in question is that which we denominate the 

 limit of stability of the cylinders. 



2. If the length of the cylinder is considerable in proportion to 

 its diameter, it becomes spontaneously converted, by the rupture 

 of equilibrium, into a series of isolated spheres, of equal dia- 

 meter, equally distant, having their centres upon the right line 

 forming the axis of the cylinder, and in the intervals of which, 

 in the direction of this axis, spherules of different diameters 

 are placed ; except that each of the solid bases retains a portion 

 of a sphere adherent to its surface. 



3. The course of the phacnomenon is as follows : — The cylinder 

 at first gradually swells at those portions of its length which are 

 situated at equal distances from each other, whilst it becomes 

 thinner at the intermediate portions, and the length of the dila- 

 tations thus formed is equal, or nearly so, to that of the constric- 

 tions ; these modifications become gradually more marked, en- 

 suing with accelerated rapidity, until the middle of the constric- 

 tions has become very thin ; then, commencing at the middle. 



