326 THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS 
§ 20. Let us now produce anew a sound which differs from that of the vein, 
still continuing to place the sonorous instrument in contact with the vessel, so 
as to give more energy to the action of the vibrations. We perceive, by No. 
12 of § 3, that in this case the last three conclusions of § 12 are distinctly in 
accordance with the observations of Savart. ‘There may, it is true, seem some- 
thing vague in the words, almost all sounds ; but they cannot be supposed to 
signify that ineffectual sounds alternate with effectual ones. Let us suppose, 
in effect, for an instant, the inefficacy of certain intermediate sounds, and 
imagine that the tone of the instrument goes on deviating in a continuous man- 
ner from that of the vein; then, when we quit one of these inefficacious sounds, 
it will be necessary either that the action on the vein, from being null as it 
was for this sound, increases gradually to a certain point, which would be con- 
trary to the statement of the number cited, accordihg to which the action di- 
minishes in proportion as we depart from unison; or else that this action be- 
comes suddenly energetic, which is scarcely admissible. It is very probable, 
therefore, that the idea of ineffectual sounds, implied in the words, almost all , 
sounds, refers simply to sounds too far remote from that of the vein, which, in 
virtue of the statement in question, must produce but an insensible action. 
§ 21. It was said, § 15, that vibrations differing in period, within certain 
limits, from those of the sound proper to the vein, may predominate over the 
configurative forces in the generation of the incipient constrictions and dilata- 
tions; that the transformation thus commenced is then completed after this new 
manner, and that, consequently, the sound of the vein is reduced to unison 
with that of the instrument. Now, the most favorable condition for the pro- 
duction of this result must evidently be the contact of the sonorous instrument 
with the walls of the vessel, because of the more immediate transmission of 
the vibrations. And, in effect, while in the case of No. 10 of § 3, the phe- 
nomenon can only be realized in an interval of a minor third, here, as we see 
by No. 14 of the same paragraph, it extends to intervals of a fifth above its 
principal sound and of more than an octave below; we may add that Savart 
does not employ here, as in the former case, terms of little precision; he says 
distinctly that the sound of the vein is reduced to unison with that of the in- 
strument. 4 
.§ 22. An upper limit, so high as the fifth, seems, at first glance, to be in 
Opposition with certain results of our second series. In effect, for the sound 
of the instrument to, ascend a fifth, it is necessary that the number of isolated 
masses which strike, in a given. time, against the stretched membrane, should 
increase in the ratio of 2 to 3, and that, consequently, (§ 2,) it should be so 
likewise with the number of incipient divisions which pass, in the same time, 
at the contracted section, and as, under a constant discharge, the length of the 
incipient divisions is evidently in inverse ratio with this latter number, it fol- 
lows that, from the principal sound to its fifth, the incipient divisions become 
shortened in the ratio of 3 to 2; but we know (2d series, § 83) that when a 
vein of water renders the sound proper to it, the length of its incipient divi- 
sions is equal to 4.38 times the diameter of the contracted section ;* if, then, 
by the sole action of a sonorous instrument, the sound of such a vein rises by 
a fifth, the length of its incipient divisions will be reduced to 3 of the above 
value; that is, to 2.92 times the diameter of the contracted section; now, this © 
number is a little inferior to the limit of stability of liquid cylinders, a limit 
which, as has been shown, (2d series, § 46,) is comprised between 3 and 3.6, 
*Such, at least, is the value of the ratio under moderate or strong discharges; under a 
weak one, the meipient divisions taking, in virtue of the hypothesis of § 2, a less volume, 
and cousequently a less length, the ratio would be also less. But we are led to the conclu- 
sion ne an the experiments in question, the discharge employed by Savart was not of this 
tter kind. . 
