284 THE FIGURES OF EQUILIBRIUM OP A LIQUID MASS 



cacli other, whilst it hecomes thinner ;it the iutermodiate portions, and the length 

 of the dilatations thus Ibrnied is equal, or nearly so, to that of the constrictions; 

 these modilicatious become gradually more marked, ensuing with accelerated 

 rapidity, until the middle of tlie constrictions has become rery thin; then, com- 

 meueiugat the middle, the liquid rapidly retires in both directions, still, however, 

 leaving the masses united two and two by an apparently cylindrical line; the 

 latter then experiences the same modifications as the cylinder, except that there 

 are in general only two constrictions formed, which consequently include a 

 dilatation between them ; each of these little constrictions becomes in its turn 

 converted into a thinner line, which breaks at two points and gives rise to a 

 very minute isolated spherule, whilst the above dilatation becomes transformed 

 into a larger spherule; lastly, after the rupture of the latter lines, the large 

 masses assume completely the spherical form. All these ph(uaomena occur 

 symmetrically as regards the axis, so that, throughout their duration, the figure 

 is always a figure of revolution. 



4. Wc denominate divisions of a liquid cylinder, those portions of the cylinder, 

 each of v/hich must furnish a sphere, whether we conceive these portions to exist 

 in the cylinder itself, before they have begun to be apparent, or whether we take 

 them during the transformation, i. c, whilst each of them is becoming modified 

 so as to arrive at the spherical form. The length of a division consequently 

 measures the constant distance Avhich, during the transformation, is included 

 between the necks of two adjacent constrictions. 



Moreover, by normal length of the divisions, we denominate that which the 

 divisions would assume, if the length of the cylinder to which they belong were 

 infinite. 



In the case of a cylinder which is limited by solid bases, the divisions also 

 assume the normal length when the length of the cylinder is equal to the pro- 

 duct of this normal length by a Avhole number, or rather a whole number and a 

 half. Then, if the second factor is a whole number, the transformation becomes 

 disposed in such a maimer that during its accomplishment the figure terminates 

 on one side with a constriction, and on the other with a dilatation; if the second 

 factor is composed of "a whole number and a half, the figure terminates on eacH 

 side in a dilatation. When the length of the cylinder fulfils neither of these 

 conditions, the divisions assume that length which approximates the most closely 

 possible to the normal length, and the transformation adopts that of the two 

 above dispositions which is most suitable for the attainment of this end. 



5. In the case of a cylinder of a given diameter, the normal length of the 

 divisions varies with the nature of the liquid, and with certain external circum- 

 stances, such as the pi'esence of a surrounding liquid, or the contact of the 

 convex surface of the cylinder with a solid plane. In all the subsequent state- 

 ments we shall take the simplest case, i. e., that of the absence of external 

 circumstances ; in other words, we shall always suppose that the cylinders are 

 produced in vacuo or in air, and that they are free as regards their entire convex 

 surface. 



G. Two cylinders of different diameters, but formed in the sam(; liquid, and 

 the lengths of which are such that the divisions assume in each of them their 

 normal length, become subdivided in the same manner, i. e, the respective 

 normal lengths of the divisions are to each other as the diameters of these cyl- 

 inders. In other Avords, when the nature of the liquid does not chang«3, the 

 normal length of the divisions of a cylinder is proportional to the diameter of 

 the latter. 



The same consequently applies to the diameter of the isolated spheres into 

 which the normal divisions become converted, and to the length of the intervals 

 which separate these spheres. 



7. The proportion of the normal length of the divisions to the diameter of the 

 cylinder always exceeds the limit of stability. 



