WITHDRAWN FROM THE ACTION OF GRAVITY. 283 



be free, but that tbe divisious formed iu it should acquire the same length as 

 before, the total duration would scarcely be at all diminished. 



There still remains the effect of the elongation of the divisions. The length 

 of the divisions of our cyliuder is equal to 6.35 times the diameter, (§ 56,) 

 whilst, according to the hypothesis of the complete freedom of the convex sur- 

 face, this length would very probably be less than four times the diameter, 

 (§ 60.) Now, in virtue of the principle established in the preceding section, this 

 increase in the length of the divisions necessarily entails a diminution in the 

 duration, which diminution is more considerable iu proportion as it occurs in 

 the vicinity of the limit of stability ; consequently, if it could be managed so that 

 the elongation in question should not exist, the total duration would be very 

 considerably increased. Thus the suppression of the direct action of the con- 

 tact of the plate would only produce a very slight dimiuution of the total dui-ation ; 

 and the annihilation of the elongation of the divisions would produce, on the 

 other hand, a very considerable increase in this same duration. If, then, these 

 two influences Avere simultaneously eliminated, or, in other words, if the entire 

 convex surface of our cylinder were free, the total duration of our transformation 

 would be very considerably greater than the direct result of observation. 



Now, the quantity which we have to consider is' the partial, and not the total 

 duration ; but, under the same circumstances, the first must be but little less 

 than the second; for when the lines are about to break, the masses between 

 which they extend even then approximate to the spherical form ; consequently, 

 iu accordance with the conclusion obtained above, we must admit that the 

 partial duration under our present consideration, i. e., that referring to the case 

 of the complete freedom of the convex surface of the cylinder, would still exceed 

 considerably the total duration observed, i. e., 0".4. 



Iu starting from this value 0".4 as constituting the lower limit corresponding 



to a diameter of 2.1 millimeters, the law of the proportionality of the partial 



duration to the diameter will immediately give the lower limit corresponding to 



any other diameter; we shall find, e.g., that for 6 millimeters this limit would be 



0".4 4- 10 



zzz 1".9, or more simply 2". 



.2.1 ^ ■^ 



If, then, we imagine a cylinder of mercury a centimeter in diameter, 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 transfoa-mation of this 

 cylinder to the instant of the rupture of the lines will considerably 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 stahiHty 

 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 diameter, 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, si^herules of different diameters are jdaced ; 

 except that each of the solid bases retains a portion of a sphere adherent to its 

 surface. 



3. The course of the phenomenon is as follows : The cylinder at first gradually 

 swells at those portions of its length which arc situated at equal distauccs from 



