aoz THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS 
would be only under the influence of the principal sound that the sheaf would 
be contracted into a single jet, and there would be only two other definite and 
different sounds which would cause to appear respectively two and three dis- 
tinct jets. But the absence of an indication of the relation between these sounds 
and the principal one suffices to show that Savart has not given close atten- 
tion to the phenomena of this kind, and that after having observed them in 
isolated cases, he did not inquire whether they were susceptible of extension. 
§ 28. Let us see now if the theory will account for these phenomena. We 
will begin with the grave octave. For this sound, the duration of a vibration 
is double that of the passage of a constriction or a dilatation at the contracted 
section, whence we may conclude without hesitation that the divisions which 
would originate under the sole action of the grave octave of the principal sound 
would be double the length of those which would be produced by the isolated ~ 
action of the configurative forces. From this we may admit that each of the 
former comprises exactly the sum of two of the latter; for in this way, at all 
the sections which terminate these sums or couples there is evidently an abso- 
lute concurrence between the two kinds of action, the sections in question con- 
stituting at once the centres of the constrictions which would result from the 
vibrations, and centres of the constrictions due to the configurative forces. 
Now, let us examine what will pass, during the transformation, in any one of 
these couples of divisions. The couple being composed of two entire divisions, 
contains two dilatations which comprise between them a constriction, and is 
terminated by two semi-constrictions. Now, while the entire constrictions to 
which these terminations pertain are, as we have seen, favored by the vyibra- 
tions, it is plain that the intermediate constriction is, on the contrary, in con- 
flict, since its middle, which is the middle of the couple, corresponds to the 
middle of the division which the vibrations tend to produce, and consequently 
to the middle of the dilatation of the latter; thus each of the dilatations which 
the configurative forces give rise to in the vein is adjacent to two dilatations 
unequally solicited. Moreover, the constrictions favored by the vibrations must 
be elongated under their influence, since the constrictions which the latter would 
of themselves produce would have a length twice greater, and:as the length 
of each of the couples of divisions above considered remains the same as in the 
absence of the sound of the instrument, it follows that the constrictions inter- 
mediate to the preceding, that is, those which occupy the middle of the couples 
and which are in conflict with the vibrations, must be shortened. We may 
therefore admit that the favored constrictions, although, from the beginning, 
they are more slender than the constriction in conflict, still contain, because of 
their excess of length, more liquid than the latter; and since, for the double 
reason that they are longer and are accelerated by the vibrations, they arrive 
more rapidly at their rupture, we perceive that they will transmit to the dilata- 
tions more matter with more velocity, and consequently a greater quantity of 
movement. All the dilatations will thus be found in the condition analyzed in 
§ 25, and consequently the isolated masses, on abandoning the continuous part, 
will have some a small excess of velocity and the others a small deficit of ve- 
locity. But here the vibrations, imparting their regularity to the phenomena, 
render all the favored constrictions, at their origin, identical among themselves, 
and in like manner render identical among themselves all the constrictions in 
conflict, so that all the masses formed by the dilatations which, in the line of 
the continuous part, have behind them a favored constriction, leave with the same 
excess of velocity and consequently describe the same trajectory, and all the 
masses which proceed from dilatations having a favored constriction before them, 
leave with the deficit of velocity and also describe the same trajectory ; hence, 
under the influence of the grave octave of the principal sound, the sheaf ought 
to be replaced by two separate jets. 
