274 THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS 



cal line which still establishes, for a very short time, the continuity of the cue 

 with the other, (Fig. 28;) this line then resolves itself into partial masses. It 



Ii^.2 



28. 



Fig. 29. 



generally diyicles into three parts, the two extreme ones of which become lost 

 in the two large masses, the intermediate one forming a spherule, some milli- 

 meters in diameter, -which remains isolated in the middle of the interval which 

 separates the large masses ; moreover, in each of the intervals between this 

 ppherule and the two large masses, another very much smaller spherule is seen, 

 which indicates that the separation of the parts of the above line is also effected 

 by attenuated lines. Fig. 29 (PL VIII) represents this ultimate state of the 

 liquid system, 'i'lie same effects arc produced when the resolution of the thin 

 and elongated cylinder of oil of § 47 into spheres occurs, only there is in one 

 or the other of the intervals between the spheres frequently a larger number 

 of spherules, and, besides, the formation of the principal line is less easily 

 observed, in consequence of the more rapid progress of the phenomena. Lastly, 

 in the case of our cylinders of mercury, the resolution into spheres takes place 

 also in too short a time to allow of our perceiving the formation of the lines; 

 but we always find, in several of the intervals between the spheres, one or two 

 very minute spherules, whence we may conclude that the separation is effected 

 in the same manner.* 



* We cannot avoid recognizing an analogy between the phenomenon of the formation ot 

 liquid lines and that ot the formation of lammae. In fact, in the experiment in ^ 23, for 

 instance, the piano layer begins to be formed when the two opposite concave surfaces'are 

 almost in contact with each other at theii' summits ; and in the resolution of a cylinder into 

 spheres, the formation of the lines commences when all the meridional sections of the figmes 

 almost touch each other by the summits of their concave portions. 



When treating of the layers, we have considered their formation as indicating a hind of 

 tendency towards a particular state of eqnillbruim, which results from the circumstance that 

 in the case of the thin part of the liquid system the ordinary law of pressure is nioditied. For 

 the analogy between the two orders of jjhcnomena to be complete, it would, tlicreibre, be 

 necessary liiat excessively delicate liquid lines should connect thick masses, and should thus 

 form with tiiese masses a system in erji^Jibrio, notwithstanding the iucompatibihty of this 

 equilibrium with the ordinary law of pitjssures. Now, we shall show that this equilibrium 

 is in reality possible, at least theoretically. Let us always take as example the resolution 

 of our unstable cylinder iutof)anial masses. When the cylindrical Hues form, their diameter 

 is even then very small in comparison with the dimensions of the thick masses; consequently 

 their curvature in the direction peipendicular to the i.:;;s is very great in comparison with 

 the curvature of these masses. The pressure corresponding to the lines is then originally 

 much greater than tliose corresponding to the thick masses, whence it follows that the liquid 

 must be driven from the interior of the lines towards these same masses, and that the lines, 

 like the layers, ought to continue diminishing. Moreover, their curvatures, and conse- 

 quently their pressure augmenting in proportion as they become more attenuated, their 

 .tendency'to diminish in thickness will go on increasing, and consequently if we disregard 

 the instability of the cylindrical form, we sec that they must become of an excessive tenuity. 

 IJut I say that the augmentation of the pressure will have a limit, bcyt)nd which this pressure 

 will jirogressivcly diminish, so that it may become equal to that which corresponds to the 

 thick parts of tlie liquid system. 



lu fact, without having recourse to theoretical developments, it is readily seen that if the 

 diameter of tiie line becomes less than that of the sphere of the sensible activity of the mole- 

 cular attraction, the law of the pressure must become nioditied, and, the diameter continuing 

 to decrease, the pressure must liuisli by also progressively diminishing, notwithstanding the 

 increase of the cuivatures, in consequence of the diminiuion in the number of attracting 

 molecules. Hence the pressure may diminish indetinitely ; for it is clear that it would 

 entirely vanish, if the diameter of the line became reduced .to the thickness of a single mole- 

 cule. Those geometricians who study the theory of capillary action know that the formulae 



