646 PLATEAU ON THE PHiSiNOMENA OF A FREE LIQUID MASS 



rninal masses by part of a division, the length / will consist of n 

 times \, plus two fractions of X. To estimate the values of 

 these fractions, we must recollect that the length of a constric- 

 tion is exactly or apparently equal to that of a dilatation (§46) ; 

 now, in the first of the two normal cases (§ 52), i. e. when the 

 masses remaining adherent to the bases after the termina- 

 tion of the phaenomenon are both of the large kind, each of 

 them evidently arises from a dilatation plus half a constriction, 

 therefore three-fourths of a division ; the sum of the lengths 

 of the two portions of the cylinder which have furnished these 

 masses is therefore equal to once and a half A,, and we shall have 



in this case l=(n + 1.5) X, whence X = — — ; — -. In the second 

 ^ ' n+l . 5 



case, i. e. when the terminal masses consist 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 X., consequently we shall have \= . 



As the respective denominators of these two expressions re- 

 present the number 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 w hole number and a half. On the 

 other hand, as the phgenomenon is governed by determinate 

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

 composed of a given liquid, and placed under given circum- 

 stances, there exists a noi-mal 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 that the 

 total length of the cylinder, although limited, is equal to the 

 product of the normal length of the divisions by a whole number, 

 or rather a whole number plus a half, nothing will prevent the 

 divisions from exactly assuming this normal length. If, on the 

 other hand, which is generally the case, the total length of the 

 cylinder fulfills neither of the preceding conditions, we should 

 think that the divisions would assume the nearest possible to the 

 normal length ; and then, all other things being equal, the differ- 

 ence w ill evidently be as much less as the divisions are more nu- 

 merous, or, in other words, as the cylinder is longer. We should 

 also believe that the transformation would adopt that of the two 

 methods which is best adapted to diminish the difference in 



