324 THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS 
tion and at a phase still a little more advanced ; and so on, until an impulse 
perceptibly coincides with the termination of such a vibration. — Under these 
repeated impulses, the amplitude of the vibrations of the body will necessarily 
go on increasing, as far as the impulse last cited. But, by virtue of the small 
excess of duration of the intervals, the impulses which follow will oceur during 
the ascending vibrations, and, as before, at phases more and more advanced, so 
that after a number of impulses equal to that of the preceding series, the body 
will again be struck at the instant of the termination of a vibration. Now, this 
second group of impulses will evidently destroy the effects of the first; that is 
to say, will gradually diminish the amplitude of the vibrations and end by an- 
nulling them. A third group of impulses will revive these vibrations, a fourth 
will annul them anew, and so on indefinitely. The sound of the body struck 
will be therefore alternately raised and lowered; on the other hand, the sound 
of the vein will be weaker when the masses reach the body during its descend- 
ing vibrations than when they strike it during its ascending vibrations, on ac- 
count of tbe difference of the relative velocities; and we see, moreover, that this 
latter sound has-its minima during the augmentations of that of the body, and 
its maxima during the diminutions. This being so, if the vibrations of the 
body acquire, in their greatest amplitude, a certain energy, and if the relative 
velocity of the impulses becomes at the same time sufficiently small, the sound 
of the vein will be entirely masked at the moments of greatest intensity of that 
of the body, to reappear and predominate in turn at the intermediate moments; 
and consequently the two sounds will be heard periodically. But if the body 
is capable of executing vibrations of only small amplitude, and if it be held at 
a great distance from the orifice, it may be that the relative velocity of the im- 
pulses shall continue to be always considerable, so that the sound of the vein 
will be perceptibly uniform, and that of the body, in its maxima, not have suf- 
ficient intensity to mask it. In that case, the first will not cease to be perceived, 
and consequently, during the periods of intensification of the second, they will 
be both heard at once. It is doubtless in this sense that we should interpret 
the words, or even simultaneously, which are literally borrowed from Savart. 
§ 17. Let us now revert to the case where a sonorous instrument is made to 
render a sound in exact unison with that proper to the vein. If the instru- 
ment, instead of acting at a distance, is placed in contact with the walls of the 
vessel whence the vein escapes, it is clear that the vibrations communicated to 
those walls and propagated in the liquid will be much more energetic, and that, 
in consequence, the modifications of the vein will be much more decided ; 
moreover, the small irregularities spoken of in § 10 will be then entirely 
effaced. The contents of No. 11 of § 3 are thus explained of themselves. 
§ 18. Proceeding to No. 12 of § 3, we observe, in the axis of the vein, on 
quitting the lower extremity of the continuous part, another system of expan- 
sions and nodes more minute as well as shorter, which is due, as Savart has 
shown, to the spherules which accompany the masses. : 
Here an apparent difficulty presents itself. When the vein is withdrawn 
from all vibratory action, its interrupted part is free from expansions and nodes; 
it would seem, therefore, that under the sole action of the configurative forces, 
the masses arrive at the spherical form without perceptible oscillations, and 
that the oscillations of form take place only in the case in which the configura- 
tive forces are re-enforced by vibrations; now, the mode of production of the 
spherules can in no manner be influenced by the vibrations, for these act di- 
rectly only at the contracted section; lower down than that section, their effect 
is lanited to the acquired velocities, (§§ 6 and 8,) which accelerate the develop- 
ment of the dilatations and the deepening of the constrictions, then to the con- 
version of each of these last into a thread, and this thread is afterwards trans- 
formed, thus furnishing the spherules by the configurative forces alone, which 
arise therein as in every liquid cylinder sufficiently elongated; nevertheless, 
