264 THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS 



transformation will take place -with perfect regularity, giving rise to isolated 

 spheres exactly equal iu diameter, and at equal distance s apart. This regu- 

 larity will not, however, extend to the two extreme dilatations; for as each of 

 these is terminated on oue side by a solid surface, it will only receive liquid 

 from the constriction which is situated on the other side, and will, therefore, 

 acquire less development than, the intermediate dilatations. Under these cir- 

 cumstances, then, after the termination of the phenomenon, wc ought to find 

 two portions of spheres respectively adherent to two solid bases, each present- 

 ing a slightly less diameter than that of the isolated spheres arranged between 

 them. 



In the second place, wc may admit that the terminal portions of the figure 

 are, one a constriction and the other a dilatation. The liquid lost by the first, 

 not being then able to traverse the solid base, will necessarily all be driven into 

 the adjacent dilatation ; so that, as the latter receives all the liquid necessary 

 to its development on one side only, it will receive none from the opposite side ; 

 consequently all the liquid lost by the second constriction will flow in the same 

 manner into the second dilatation, and so on up to the last dilatation. The 

 distribution of the movements of transport will, the;i'eforc, still.be regular 

 throughout the figure, and the transformation will ensue iu a perfectly regular 

 manner. This regularity will evidently extend even to the two terminal por- 

 tions, at least so long as the constrictions have not attained their greatest 

 depth ; but beyond that point this will not exactly be the case, for independ- 

 ence being then established between the masses, each of the dilatations, except- 

 ing that which rests upon the solid base, will enlarge simultaneously on both 

 sides, so as to pass into the condition of the isolated sphere, by appropriating 

 to itself the two adjacent semi-constrictions, \thilst thfe extreme dilatation can 

 enlarge on one side. Consequently, after the termination of the phenomenon, 

 we should find, at one of the soild bases, a portion of a sphere of but little less 

 diameter than that of the isolated spheres, and at the other base a much smaller 

 portion of a sphere, arising from the semi-constriction which has remained 

 attached to it. 



Lastly, in the third place, let us suppose that the terminal portions of the 

 figure were both constrictions, in which case, after the termination of the phe- 

 nomenon, a portion of a sphere equal to the smallest of the two above would 

 be left to each of the solid bases. In this case, to be more definite, let us 

 Btart from one of these terminal constrictions ; for instance, that of the left. All 

 the liquid lost by this first constriction being driven into the contiguous dilata- 

 tion, and being sufBcient for its development, let us admit that all the liquid 

 lost by the second constriction also passes into the second dilatation, and so 

 on ; then all the dilatations, excepting the last on the right, will simply acquire 

 their normal development; but the right dilatation, which, like each of the 

 others, receives from that part of the constriction which precedes it the quan- 

 tity of liquid necessary for its development, receives in addition the same 

 quantity of liquid from that part of the constriction which is applied to the 

 adjacent solid, so that it will be more voluminous than the others. Hence it is 

 evident, in the case in point, that the opposed actions of the two terminal con- 

 Btrictioiis introduce an excess of liquid into the rest of the figure. Now, what- 

 ever other hypothesis may be made respecting the distribulion of the move- 

 ments of transport, it must always happen cither that the excess of volume is 

 simultaneously distributed over all the dilatations, or that it only augments the 

 dimensions of one or two of them ; but the former of these su])positiona is 

 evidently inadmissible, on account of the complication which it would require 

 in th(; movements of transi)ort ; hence we must admit the second, and then the 

 isolated spheres will not all be equal. Thus this third mode of transformation 

 would necessarily of itself induce a cause of irregularity ; and, moreover, it 

 would not allow of a uniform distribution of the movements of transport, be- 



