230 THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS 
quantities of movement which have been supplied, in the other direction, by 
the’ posterior constriction, and that hence this mass will quit the continuous 
part with the velocity exactly corresponding to the general movement of trans- 
lation. . But it is clear that the compensation will be no longer entire if the 
two constrictions differed in their inception; if, for example, they were unequal 
in length: it results from the less duration of the transformation when the 
divisions are longer, (2d series, § 66,) and when, consequently, the constric- 
tions are longer, that the more elongated of the constrictions in question will 
deepen more rapidly than the other, and as, in virtue of its excess of length, 
it comprises more liquid, it will convey into the dilatation a greater afflux of 
material with greater velocities, and consequently a greater quantity of move- 
ment. If, then, this constriction is the posterior one, the mass will quit the 
contracted section with an excess of velocity, and if the anterior, with a defect 
of velocity. Thus, slight differences of length in the incipient constrictions 
will result in establishing small inequalities in the velocities of the successive 
isolated masses; but these masses will then, necessarily, traverse parabolas 
of unequal amplitude, and will, consequently, be spread out in a vertical plane, 
thus forming the sheaf. 
This explanation supposes that the disturbing causes do not produce, in the 
constrictions, any irregularity in directions perpendicular to the axis of the 
vein; and we are led, in effect, to conclude, from the experiment of § 23, that 
the constrictions and dilatations tend with great force to a symmetry in rela- 
tion to the axis, and that hence irregularities in a direction perpendicular to 
this latter cannot be persistent. It is clear, also, from this explanation that 
there are two extreme limits for which the dispersion is necessarily null, 
namely, when the vein is ejected vertically from above downwards and verti- 
cally from below upwards, since, in these two cases, all the isolated masses 
perform the same rectilinear trajectory ;* if, therefore, we pass from the first 
to the second by gradually varying the direction in which the jet is thrown, 
the sheaf cannot begin to show itself in a very distinct manner except on 
attaining a certain angle between that direction and the descending vertical, 
and it will cease to be very distinguishable beyond a certain other angle. 
Moreover, so long as the vein is thrown in directions descending obliquely, and 
even in a horizontal direction, it will be readily conceived that at the extremity. 
of its continuous part, a part which is generally of quite considerable length, 
it will already approach too nearly to the vertical to allow a very clearly 
marked sheaf, so that the first direction which will begin to render the sheaf 
distinct will be one ascending obliquely. All these conclusions are in accord- 
ance with the facts of the number we are considering. 
We admit, it will be seen, that the inequalities. between the incipient con- 
strictions do not depend on the direction in which the jet is thrown; and there 
is no plausible reason, in effect, for attributing these inequalities to the ascend- 
ing obliquity of the jet. If we have not spoken of them in treating of veins 
descending vertically, it is because, in the latter veins, they cannot give rise 
to any appearance of a peculiar kind; they then do no more than evidently a 
little augment, in the axis of the vein, the inexactness of the superposition of 
the individual systems of expansions and nodes, and thus simply constitute an 
influence to be added to those mentioned in § 10. As to the nature of the dis- 
turbing causes which produce the inequalities in question, it would doubtless 
be difficult to discover it; but, whatever it be, the dispersion of the discon- 
tinuous part in veins directed under a suitable angle reveals to us the presence 
of those causes. 
* In a vein ejected vertically from below upwards, the liquid scatters, it is true, in falling 
back, but I need not remark that this latter dispersion is owing to a wholly different cause, 
and has nothing in common with the phenomena we are considering. 
