992 THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS 
the law becomes modified, it must approximate towards that of Savart in pro- 
portion as the value given to this charge is greater. 
75. We said (note to § 72) that we should return to the closely approxima- 
tive principle of equality between the length of the continuous part of an 
imaginary vein and the Shae dewey distance D, in order to establish this 
principle more clearly ; we shall now do this. 
Let L be the length of the continuous part, and C the portion common to 
this length and the distance D; let also s be the interval between the origins 
of the lengths L and D, ¢. e., the small distance comprised between the orifice 
and the contracted section ; and, lastly, let z be the interval between the ter- 
minations of these same lengths, z e., the distance comprised between the up- 
permost point of the rupture of the line and the middle of this line; we shall 
then have 
L=C.-+s, 
D=C+z; 
consequently 
- L—D=s-7; 
whence 
ee dls 1) 
D> Dovrrrreesrssst (7, 
Let us now first approximatively value the quantity 7 in the case of some par; 
ticular liquid, and let us again take mercury. After what was shown at the 
commencement of the preceding section, the length of the divisions of an imagi- 
nary vein is equal to the normal length of those of a cylinder of the same 
diameter and of the same liquid which would be formed in the air, and the en- 
tire 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 contracted section by 4, the diameter of the 
isolated spheres composing the discontinuous part of the vein will be (§ 60) equal 
to 1.82.4, and the length of the interval between two snecessive spheres will 
be 2.18.%. 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 com- 
parison of the aspects presented immediately after the rupture of the line, and 
after the entire completion of the phenomena, 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 connected 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 .4, four-tenths of the diameter 
1.82.4, which gives 1.45.4. 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 appro<imate value of the length of our line is equal 
to 1.45 0.8.K=1.16 K. Lastly, the uppermost 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 ¢ will be half the length of the line, and we 
shall consequently have 
i=0.58.K. 
