276 THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS 



of spherules. This figure refers to the case of a very slightly viscid liquid, 

 Buch as water, alcohol, &c., and where the convex surface of the cylinder is 

 perfectly free; consequently, in accordance with the prohable conclusion with 

 which § 60 terminates, the ]noportion of the length of the divisions to the 

 diameter has been taken as equal to 4. 



The phenomenon rf)f the formation of lines and their resolution into spherules 

 is not confuied to the case of the rupture of the equilibrium of liquid cylinders; 

 it is always manifostcd when one of our liquid masses, whatever may be its 

 figure, is divided into partial masses. This is the manner in which, for 

 instance, in § 29 of the preceding memoir the minute masses which Avere then 

 compared to satellites are formed.* The pluniomeuon under consideration is 

 also ])roduced when liquids are submitted to the free action of gravity, although 

 it is then less easily shown. For instance, if the rounded end of a glaf^s rod be 

 dii)j)ed in ether, and then ^'ithdrawn carefully in a perpendicular direction, at 

 the instant at which the small quantity of liquid remaining adhcnmt to the rod 

 separates from the mass, an extremely minute spherule is seen to roll upon the 

 surfacf>of the latter. Lastly, the phenomenon in question is of the same nature 

 as that which occurs when very viscid bodies are drawn into threads, as glass 

 softened by heat, except that in this case the great viscidity of the substance, 

 and moreover the action of cold, which solidifies the thread formed, mahitains 

 the cylindrical forai of the latter tud allows of its acquiring an indefinite 

 length. 



03. To complete the study of the transformation of liquid cylinders into 

 isolated spheres, it still remains for us to discover the law according to which 

 the duration of the phenomenon varies with the diameter of the cylinder, and 

 to endeavor to obtain at least some indications rektive to the absolute value 

 of this dtu-ation in the case of a cylinder of a given diameter, composed of a 

 given liquid, and placed in given circumstances. 



We can understand, a priori, that when the liquid and the external circum- 

 stances are the same, and su])j)Osii)g the length of the cylinder to be always 

 such that the divisions assume exactly their normal length, (§ 53,) the duration 

 of the phenomenon must increase with the diameter; for the greater this is, the 

 greater the mass of each of the divisions, and, on the other hand, the less the 

 curvatures upon which the intensities of the configuring forces depend. It is 

 true that the surface of each of the divisions increases also with the diameter 

 of the cylinder; consequently it is the same with the number of the elementary 

 configuring forces; but this augmentation takes place in a less proportion than 

 tha! of the mass. This we shall proceed to show more distinctly. Under the 

 above conditions two cylinders, the diameters of which are ditl'erent, will be- 

 come divided in the same manner; ?'.«., the pro])ortion of the length of a division 

 to the diameter will be the same in both parts, (§ o5.) Now, it may be considered 

 as evident that the similitude in figure Avill be maintained in all the ])liases of the 

 transfoi-mation ; this is, moreover, confirmed by experiment, as we shall soon see. 

 Hence it follows at each homologous instant of the transformations of the two 

 cylinders the respective surfaces of the divisions will always be to each other 

 as the squares of th;' diameters of these cylinders, whilst the masses, which 

 evidently remain invariable throughout the entire duration of the phcnouK na, 

 will always be to each other as ihe cubes of these diameters. Thus, at each 

 homologous instaiit of the respective transformations, the extent of the- super-, 

 filial layer of a division, consequently the number of the configuring forces 

 which emanate from each of the elements of this layer, change fnjin one figure 

 to the other only in the proportion of the squares of the primitive diameters of 



* It is clear that this mode of fonnatiou is entirely foreign to La Place's cosmogoiiic liypo- 

 tlicsis; therefore we have liad no idea of deduciiipf from this little experiment, which "only 

 relers to I he effects of molecular attractiou, and not to those of gravitation, any argument in- 

 lavor of the liypothesis in question — an hypothesis which, in other respects, we' do not adopt. 



