290 THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS 
and the charge necessarily follows from the properties of liquid cylinders. To 
discover whether this law is also true when weaker charges are employed, we 
must start from other considerations ; but it is evident, so far, that if in the lat- 
ter case the law is different, it must at least necessarily converge towards the 
proportionality in question, in proportion as the charge increases. 
We must remark here, that in the case of a given liquid, the charge with 
which the vein begins to exist under the condition which we have determined 
must be as much less as the diameter of the orifice is smaller. In fact, since, 
all other things being equal, the transformation of a liquid cylinder occurs with 
a rapidity proportionate to the diminution in size of the diameter of the cylinder, 
it follows that the value of @ will diminish with the value of the orifice; and 
therefore the smaller the latter is, so much the less will the value of 2 become 
to allow of the term g@ in the expression V2eh+g0, placed at the commence- 
ment of this section, being neglected in comparison with the term Y2gh, and 
consequently for the vein to exist under the condition in question. ; 
Moreover, as the time @ varies with the nature of the liauid, the same will 
necessarily apply to the charge under consideration. 
74. Let us now investigate the second law, namely, that which establishes 
the approximative proportion of the length of the continuous part of the vein 
and the diameter of the orifice, when the charge remains the same. 
Let us resume, for an instant, the imaginary case of an absolutely uniform 
movement of transference. The vein, leaving its divisions out of considera- 
tion, will then constitute a true cylinder commencing at the contracted section, 
(§72,) which cylinder will be formed in the air, and the entire convex surface 
of which will be free; moreover, as the movement of transference of the liquid 
does not exert any influence upon the effect of the configuring forces, (§ 72,) 
and as there is no extraneous cause tending to modify the length of the divi- 
sions, the latter will necessarily assume their normal length. It is evident, 
therefore, that excepting that the formation of its divisions is not simultaneous, 
(§ 69,) our imaginary vein will exist under exactly the same circumstances as 
the cylinders to which the laws recapitulated in section 68 refer; consequently, 
if we consider in particular one of the constrictions of this vein, it must pass 
through the same forms, and accomplish its modifications in the same time, as 
any one of the constrictions which would result from the transformation of a 
cylinder of the same diameter as the vein, formed of the same liquid, and 
placed under the conditions in question. 
Now, in the case of a cylinder of mercury, the time comprised between the 
origin of the transformation and the instant of the rupture of the lines is, in 
accordance with one of our laws, exactly or apparently in proportion to the 
diameter of the cylinder; and it is clear that this law is equally applicable to 
any one of the constrictions in particular, or even simply to its neck, as to the 
entire figure. If, then, we suppose our imaginary vein to be formed of mercury, 
the time which the neck of each of its constrictions will occupy in arriving at 
the instant of the rupture of the line will be exactly or apparently in propor- 
tion to the diameter which the vein would possess if the divisions in it were 
not formed, z.e., to that of the contracted section. Now, as the cylindrical 
form of the vein, supposed to exist without divisions, only begins at the con- 
tracted section, it is only from this part that the configuring actions arising 
from the instability of this cylindrical form commence. We must, therefore, 
admit that the liquid section, which constitutes the neck of a constriction, does 
not begin to undergo the modifications which result from the transformation 
* until the instant at which it passes the contracted section; thus the interval 
under consideration commences at this very instant. 
But this interval, comprised between the instant at which the liquid section 
of which the neck of a constriction is formed passes the contracted section, 
and the instant of the rupture of the line into which this constriction becomes 
