334 THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS 
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sions increases with the resistance; now, the acquired transverse velocities 
causing, in our large divisions, a tendency te persevere in the mode of trans- 
formation impressed by the vibrations, constitute a resistance to any further 
separation. j 
We pass, in the third place, to the double grave octave. Here, each of the 
divisions which would arise under the sole action of the vibrations, would evi- 
dently comprise four of the divisions which would result from the configurative 
forces alone. Now, if these two actions were combined, if would seem that we 
should have four distinct jets; for it is easy to see that in the three constric- 
tions which would then be formed, the conflict would be unequal; that it would 
be stronger for the middle constriction than for the two others, so that each of 
the two dilatations comprised between these three constrictions would receive 
from the two sides unequal quantities of movement, and that the differences, 
in fine, would be greater for the two extreme dilatations, each of which would 
be comprised between a constriction in conflict and a favored constriction. 
But, on the one hand, the vibrations in question having a considerable ampli- 
tude, we can understand that their action must always efface that of the con- 
figurative forces, and, on the other hand, the divisions formed in this manner 
being very long, we equally perceive, from what has been said above, that new 
configurative forces must be generated which would effect the separation ; now, 
by reason of the resistance also indicated above, this separation should here 
yield but three parts at most, which, in view of the distribution of conflicts 
and concurrences, and the regulating action of the vibrations, must convert the 
sheaf into three jets only. 
There remains, in the fourth place, the action of the sounds comprised be- 
tween the grave octave and the fifth below, and between the latter and the 
double grave octave. For these sounds, there is no longer any simple relation 
between the lengths of the divisions which would result respectively from the 
vibrations alone and from the configurative forces alone; but it will be admitted 
without difficulty that, under the influence of those which approach, whether 
above or below, the double grave fifth, and in the case where the effect of the 
vibrations is not completely substituted for that of the configurative forces, the 
divisions due to these forces are a little shortened or elongated, so as to allow, 
at the limits which separate the successive systems of three of these divisions, 
the absolute concurrence of the two kinds of action, and thus to re-establish . 
the simple ratio of 3 to 1 pertaining to the double fifth; whence the resolution 
into three jets. Under this same influence, as under that of the double fifth, 
if the vibrations are preponderant, but not sufficiently so to oppose an ulterior 
development of configurative forces, each large division can be but separated 
into two, so that the discontinuous part of the vein shall present but two jets. 
It will be also admitted that the sounds .nearest to the grave octave will cause 
the mode related to this latter to prevail, and that in this case also the sheaf 
will never change except into two jets. As regards the sounds which do not 
depart too much from the double grave octave, the vibrations have always suf- 
ficient amplitude, and consequently sufiicient action, to overpower the ordinary 
configurative forces, and at the same time the divisions to which they give rise 
are always sufliciently long to admit of each of them subsequently undergoing 
a separation, which divides it at most into three, and may also separate it into 
but two, if it encounters a greater resistance on the part of the vibrations; and 
hence two jets or three. As to the systems of expansions and nodes which 
are observed in each of the jets, they are plainly a consequence of the acquired 
transverse velocities which proceed from the action of the vibrations. 
§ 29. It may be asked why, above the principal sound and between that and 
its grave octave, no sound, with the exception of those which approximate to 
these two last, had occasioned, in the experiments described in § 27, anything 
