398. THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS 
the principal sound ; in the latter case, in effect, because of the little difference 
of length between the incipient divisions of the two kinds, it is quite probable 
that the configurative forces simply modify their proper action, as has been 
already said in § 15, by elongating or shortening the incipient divisions which 
correspond with them, so as to make them coincide with those which corre- 
spond with the vibrations; but when the sound of the instrument is sufficiently 
erave for the length of these last divisions to surpass considerably that of the 
others, when, for example, the instrument renders the grave octave, and the 
vibrations transmitted are sufficiently intense to impress upon the vein their 
mode of transformation, it must be admitted that the action of the configurative 
forces is completely destroyed, so that there is no longer a modification of the 
first mode, which adapts itself to the second, but an absolute substitution of 
the second for the first. 
§ 23. Experiment fully verifies what has been said above of the variations 
of stability within and near the limit, in a liquid cylinder adhering to solid bases. 
A horizontal cylinder of oil was formed, in the interior of the alcoholic mixture, 
between two disks* whose diameter was 31 millimetres and their distance 87 
millimetres; the ratio of length to the diameter was therefore, in this cylinder, 
equal to 2.8, so that the figure was quite stable; this ratio, we see, deviated 
somewhat more from the limit than that which we found, in the preceding para- 
graph, to pertain to the incipient divisions of a vein of water brought by the 
action of a sonorous instrument to render the sharp fifth of the principal sound. 
In order to alter artificially the cylindrieal form of the mass, the point of the 
small syringe was moved slowly, and at several intervals, along the upper part 
of the liquid figure, starting from one of the disks and stopping at very nearly 
the middle of their interval; the oil thus accumulates in greater quantity towards 
the other disk, and, during this whole operation, the figure ceases not to regu- 
late itself spontaneously in relation to its axis; that is to say, it remains one of 
revolution, so as to present a constriction and a dilatation analogous to those 
which result from a spontaneous alteration. Now, so long as the versed sine 
of the meridian are of the dilatation was less than about 5 millimetres, the mass, 
it left to itself, gradually recovered the cylindrical form; but when the sine 
in question attained 5 millimetres, the mass left free continued spontaneously 
to change its form and ended by disuniting. 
In this experiment, the artificial deformation necessary to determine the spon- 
taneous continuation of the phenomenon is considerable; for when, by approxi- 
mate measurement, the versed sine of the meridian arc of the dilatation was 5 
millimetres, that of the meridian are of the constriction was 8 millimetres, so 
that the respective diameters of the neck of the constriction and of the equator 
of the dilatation were 15 and 41 millimetres; and hence the first was scarcely 
more than the third of the second; but let it be remembered that the ratio be- 
tween the length and the diameter of the cylinder was below that which, in the 
vein, corresponds to the fifth of the principal sound.t Moreover, there are two 
other reasons why the passage of the sound of the vein to the sharp fifth should 
be induced by vibrations which occasion directly a deformation much less de- 
cided. In the first place, from the immediate action of the vibrations, the de- 
formation must increase by the acquired velocities, (§ 6;) and in the second 
place, the divisions, and consequently the constrictions and dilatations, being 
elongated during their descent, (§ 2 42s,) the sum of the lengths of a constric- 
tion and a dilatation, inferior at first to the limit of stability, begins imme- 
* These disks were maintained by a system similar to that represented in Fig. 27 of the 
second series. 
t this ratio, but for an error in the construction of the small apparatus, would have been 
2.92. 
