WITHDRAWN FROM THE ACTION OF GRAVITY. 265 



cause there would be opposition in regard to these movements, at least in the 

 terminal constrictions. 



it may, therefore, be regarded as very probabl'.i that the transformation takes 

 place according to one or the other of the two lirst methods, and never accord- 

 ing to the third, i. c, that things will be so arranged that the figure which is 

 transformed may have for its terminal portions either two dilatations, or one 

 constriction and one dilatation, but not two constrictions. In the former case, 

 as we have seen, the movement of the liquid of all the constrictions would 

 ensue on both sides simultaneously ; and in the second this movement would 

 , occur in all in one and the same direction. If this is really the natural arrange- 

 ment of the phenomenon, we can also understand how it will be preserved even 

 when it is disturbed in its regularity by slight extraneous causes. I^ow, this, 

 as we shall see, is confirmed by the experiments relating to the mercurial 

 cylinder. Although the transformation of this cylinder has rarely yielded a 

 perfectly regular system of spheres, I have found in the great majority of the 

 results either that each of the soild bases was occupied by a mass little less in 

 diameter than the isolated spheres, or that one of the bases was occupied by a 

 mass of this kind and the other by a much smaller mass. 



53. For the sake of brevity, let us denominate divisions of the cylinder those 

 portions of the figure each of which furnishes a sphere, whether we consider 

 these portions in the imagination as in the cylinder itself, before the com- 

 mencement of the transformation, or Avhether v/e take them during the accom- 

 plishment of the phenomenon, /.f., during the modifications which they undergo 

 in arriving at the spherical form. The length of a division is evidently that 

 distance which, during the transformation, is comprised between the necks of 

 two adjacent constrictions; consequently it is equal to the sum of the lengths 

 of a dilatation and two semi-constrictions. Let us, therefore, see how the 

 length in question, i. c, that of a division, may be deduced from the result of 

 an experiment. Let us suppose the transtbrmation to be perfectly regular, and 

 let A be the length of a division, I that of the cylinder, and n the number of 

 isolated spheres found after the termination of the phenomenon. Each of these 

 spheres being fuinished by a complete division, and each of the two terminal 

 masses by part of a division, the length I will consist of n times k, plus two 

 fractions of /. To estimate the values of these fractions, Ave must recollect 

 that the length of a constriction is exactly or apparently equal to that of a dila- 

 tation, (§ 46 ;) now, in the first of the two normal cases, (§ 52.) /. c, when the 

 masses remaining adherent to the bases after the termination of the phenomenon 

 are both of the large kind, each of them evidently arises from a dilatation plus 

 half a constrictioi), therefore three-fourths of a division ; the sum of the lengths 

 of the two portions of the cylinder which have furnished these masses is, there- 

 fore, equal to once and a half I, and we shall have in this case / = (« + 1.5) I, 



whence X^=. — . In the second case, i. c, when the terminal masses con- 



n -f 1.5 

 sist of one of the large and the other of the small kind, the latter arises from a 

 semi-constriction, or a fourth of a division, so that the sum of the lengths of the 

 portions of the cylinder corresponding to these two masses is equal to k ; con- 

 sequently we shall have A =: — — — . 



As the respective denominators of these two expressions represent the num- 

 ber of divisions contained in the total length of the cylinder, it follows that 

 this number will always be either simply a whole number, or a whole number 

 and a half. On the other hand, as the phenomenon is governed by determinate 

 laws, we can understand that for a cylinder of given diameter composed of a 

 given liquid, and placed under given circumstances, there exists a normal 

 length which the divisions tend to assume, and which they would rigorously 

 assume if the total length of the cylinder were infinite. If. then, it happens 



