WITHDRAWN FROM THE ACTION OF GRAVITY. 327 
and yet it was demonstrated (2d series, § 57) that when aliquid cylinder is 
transformed, the length of its divisions cannot be less than that limit. © 
_ The difficulty is but apparent. The demonstration cited supposes that the 
transformation.of the cylinder commences spontaneously, and then it is strictly 
true; but it does not apply to the case in which the constrictions and dilata- 
tions are originally formed by an extraneous cause sufficiently energetic. In 
effect, the demonstration in question consists essentially in showing that if, in 
the first phases of the transformation, we consider the sum of a constriction and 
a dilatation—a sum whose length is equivalent to that of a division—all passes 
m that portion of the cylinder as if its two bases were solid, so that the trans- 
formation cannot be established spontaneously without a separation of those 
bases at least equal to the limit of stability; but if, in a cylinder realized be- 
tween two solid disks whose distance is a little less than the limit of stability, 
the transformation could not commence of itself, it is clear that it will continue’ 
of itself if it has commenced from an extraneous cause which has accumulated 
the liquid in a certain quantity towards one of the disks, so as to occasion arti- 
ficially a dilatation and a constriction sufficiently decided, for evidently, at the 
limit of stability, and in passing from beyond to within it, there is no sudden 
transition from instability to an absolute stability. When that limit is passed, 
the stability must at first be very feeble, since it parts from zero; consequently, 
at but little distance within the limit, a deformation impressed artificially on 
the cylinder can only be effaced spontaneously if it be small; if the deforma- 
tion be considerable, it will proceed, 6n the contrary, spontaneously, and will 
produce the disunion of the mass. The demonstration which we have recalled 
can, therefore, be no longer cited when, in a liquid vein, the incipient constric- 
tions and dilatations are formed by energetic vibrations. ‘Then, if the sum of 
the lengths of one of these constrictions and one of these dilatations, or its 
equal, the length of a division, is a little inferior to the limit of stability, the 
transformation can commence after that anomalous mode, (?) and the more in- 
tense the vibrations, the more will the last sound for which the possibility of 
the phenomenon exists be elevated above the principal sound. If the extra- 
neous sound is below the principal sound, and thus tends to give to the incipi- 
ent divisions a length necessarily superior to the limit of stability, it will not 
encounter the kind of resistance which has just been indicated within that 
limit, so that the possibility of the phenomenon will extend much further; we 
see, in effect, that in the experiments of Savart it embraces an interval of 
more than an octave. 
There is still another reason why the phenomenon should be less limited 
below the principal sound than above: in the same sonorous instrument, the 
amplitude of the vibrations increases generally with the gravity of the sound ; 
but the more considerable the amplitude of the vibrations transmitted, the. 
greater is the excess of liquid which each descending vibration tends to drive 
into the vein to form an incipient dilatation, and the greater also is the with- 
drawal of liquid which each ascending vibration tends to effect and thus.deepen 
an incipient constriction. If, then, in proportion as the sound of the instru- 
ment departs from the principal sound, whether below or above, the length of 
the incipient divisions which the vibrations tend to form becomes more and 
more superior or more and more inferior to that of the incipient divisions which 
the configurative forces tend on their part to form, and if thence there evi- 
dently arises a conflict of progressive intensity with these latter forces, on the 
other hand, below the principal sound, the vibrations act mor2 and more ener- , 
getically to cause the new mode of transformation to prevail, and this augmen- 
tation of action must more or less countervail the augmentation of the conflict. 
We may remark here, that in the case of a sound very grave relatively to 
the principal sound, the new mode of transformation is not established after 
the same manner as in the case of a sound which does not much deviate from 
