688 PLATEAU ON THE PHiENOMENA OF A FREE LIQUID MASS 



and of the same liquid which would be formed in the air, and 

 the entire convex surface of which is free ; now in the case of 

 mercury, we know that the proportion of this normal length to 

 the diameter of the cylinder must be less than 4 ; consequently, 

 in our imaginary vein of mercury, the proportion of the length 

 of the divisions to the diameter of the contracted section will 

 also be less than 4 ; but in our state of ignorance of the exact 

 value of this proportion, we will first suppose it to be equal to 

 the above number. If we then denote the diameter of the con- 

 tracted section by k, the diameter of the isolated spheres com- 

 posing the discontinuous part of the vein will be (§ 60) equal to 

 1'82 . k, and the length of the interval between two successive 

 spheres will be 2*18 • k. But the line into which a constriction 

 is converted is necessarily shorter than this interval ; for so long 

 as the rupture does not take place, the two masses united 

 together by the filament must still be slightly elongated ; and, 

 moreover, each of them must present a slight elongation of the 

 line, so as to be connected to the latter by concave curvatures. 

 Judging from the comparison of the aspects presented imme- 

 diately after the rupture of the line, and after the entire com- 

 pletion of the phaenomena, by the figure resulting from the 

 transformation of one of our short cylinders of oil (see figs. 28 

 and 29), I should estimate that for each of the two masses con- 

 nected by a line, the elongation towards the latter plus the slight 

 concave prolongation form about two-tenths of the diameter 

 which these masses acquire after their transition to the state of 

 spheres. To obtain the approximative value of the line belonging 

 to our vein, we must therefore deduct from the interval 2*18 . A:, 

 four-tenths of the diameter 1*82.^, which gives I'Ab .k. On 

 the other hand, if we denote the diameter of the orifice by K, 

 we have (note to the preceding section) very nearly K = 0*8 . K ; 

 whence it follows that the approximate value of the length of 

 our line is equal to 1*45 x 0*8 . K = l-16 K. Lastly, the upper- 

 most point, of rupture of the line must be very near the upper 

 extremity of the latter ; if we suppose it to be at this extremity 

 itself, the quantity i will be half the length of the line, and we 

 shall consequently have 



i=0-58.K. 



Let us pass to the quantity s. We know that the distance be- 

 tween the orifice and the contracted section, although not en- 

 tirely independent of the charge, always differs but little from 



