320 THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS 
of a division, and, consequently, of the middle of a dilatation ; hence, for this 
entire vibration there will be opposition with the configurative forces ; this will 
be the maximum of the conflict, and it is obvious that this conflict will, till 
then, have gone oh augmenting; that is to say, occupying greater and greater 
portions of the successive vibrations, to diminish afterwards by the same de- 
grees. These principles being granted, let us see what can be deduced from 
them. 
Each of the constrictions for which a coincidence shall exist will quit, the 
contracted section in a more advanced phase of transformation, and hence will 
be broken at a less distance from the orifice than if vibratory movements had 
not been produecd; but the following constriction, which is under less ad- 
vanced conditions, can only be broken a little further on, and the subsequent 
ruptures will, in like manner, be effected further and further from the orifice, 
until the rupture of the constriction in regard to which the conflict between 
the two actions is at its maximum; after which things will proceed in an in- 
verse order; that is, the successive places of rupture will reascend till there 
recurs anew.a constriction with a coincidence, when all will recommence in the 
same order as at first. It appears then that, in such a vein, the continuous 
part has different lengths, which succeed one another periodically; but the 
shortest of these lengths must be regarded as being that of the real continuous 
part of the vein, since the continuity is there persistent, and it is necessarily 
smaller than wold be the continuous part of the same vein not subjected to 
the influence of a sonorous instrument. Still the shortening will not be so 
great as in the case of unison. In effect, if the sound of the instrument is 
sharper, the most complete concurrence between the two kinds of action only 
takes place, as has been said above, with the middle portion of the constric- 
tions upon which it falls, and there is conflict in the extreme portions. If the 
sound of the instrument is graver, the concurrence extends, indeed, to the 
whole of the constriction, but the conflict then exists in the adjacent portions 
of the two dilatations between which this constriction is comprised, and these 
portions admitting with less facility the liquid which is driven towards them, 
the constriction cannot obey with entire freedom the two actions which tend 
to narrow it. 
In the second place, from what has been just said, the shortening should be 
proportionably less as the sound of the instrument deviates more from unison ; 
for the more it is above this, the less is the portion of the constriction for which 
a concurrence exists; and the more it is below, the further does the conflict 
extend over the two neighboring dilatations. And since in the constrictions 
for which coincidence exists, and to a certain distance on both sides of each of 
them, the action of the vibrations favors, more or less, that of the configurative 
forces, the vein will present, in an analogous but less decided manner, the other 
modifications which unison determines; hence the limpid portion will still 
appear a little thickened, and the interrupted part will have expansions and 
nodes; but these modifications will be the less decided as the interval between 
the sound of the instrument and consonance is greater. 
We may, therefore, so far as the complexity of the subject permits it, pro- 
nounce substantially the four following conclusions: When, at a certain dis- 
tance trom the apparatus, a sound is produced sharper or graver than that 
which is proper to the vein, first, the continuous part will assume periodically 
diffcrent lengths ; second, the shortest of these lengths, which is that of the 
true continuous part, will be less than was the length of the sole continuous 
part before the action of the instrument, but this curtailment will not be so 
great as in the case of unison; third, the vein will present, in a manner analo- 
gous to that which takes place under the action of unison, but at the same 
time less decidedly, a smull increase of thickness in the limpid portion and a 
system of expansions and nodes in the interrupted part; fourth, all these phe- 
