26G THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS 



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

 of the normal length of the divifsions by a whole number, or rather a Avholc 

 number plus a half, nothing will pieveut the divisions from exactly assuming 

 this normal length. If, ou the other hand, which is generally the case, the 

 tof.il length of the cylinder fulfils 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 difference will evidently be as much 

 "less as lh(^ divisions are more numerous, 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 dilference in question, 

 and this is also confirmed by experiment, as we shall see presently. Hence, 

 ah hough, as I have already stated, the transformation of the cylinder of mei'- 

 cury almost always ensues in one of the two normal methods, the result is 

 rarely very regular; we must, thert^fore, admit that slight accidental disturbing 

 causes in general render the divisions formed in any one experiment unequal 

 in length ; but then the expressions of A obtained above evidently give in each 

 experiment the mean length of these divisions, or, in other words, the common 

 length which the divisions would have taken if the transformation had occurred 

 in a perfectly regular manner, giving rise to the same number of isolated 

 spheres and to the same state of the terminal masses. 



Lastly, since the third method of transformation presents itself, i. c, since it 

 sometimes happens that each of the bases is occupied by a mass of the small kind, 

 if we would leave out of consideration the particular cause of irregularity inhe- 

 rent in this method, (the preceding paragraph,) and find the conesponding 

 expression of )., it need only be remarked that each of the terminal masses 

 then proceeds from a semi-constriction or the fourth of a division, which will 



evidently give X = -r-z- 



54. I shall now relate the results of the experiments. The diameter of the 

 copper wires, consequently of the cylinder, was 1.05 millimeter. I first gave 

 the cylinder a length of 90 millimeters, and repeated the experiment ten times, 

 noting after each the number of isolated spheres produced, and the state ot the 

 masses adherent to the bases ; I then calculated for each result the correspond- 

 ing value of the length of a division, by means of that of the three formulaj of 

 the preceding ])aragraph which refers to this same result, I afterwards made 

 ten more experiments, giving the cylinder a length of 100 millimeters, and al.io 

 calculated the corresponding values of the length of a division. The table con- 

 tains the results furnished by these cylinders, and the values deduced for the length 

 of a divi.'^ion. I only obtained a perfectly regular result in one case in each series; 

 1 have placed an * opposite the corresponding number of isolated spheres.- 



