influence of Vibratory Motions. 437 
condition towards the production of this result must evidently 
coexist with the contact between the sonorous instrument and 
the sides of the vessel, because the vibrations are thereby trans- 
mitted more immediately. In fact, whilst in the case of No. 10 
of paragraph 3, the phenomenon can only be realized within an 
interval of a minor third, here, as may be seen by No. 14 of the 
same paragraph, it extends to intervals of a fifth above, and more 
than an octave below the principal note. We may add, that 
Savart no longer expresses himself vaguely as before; he says 
distinctly, that the note of the jet puts itself into unison with 
that of the instrument. 
§ 22. A superior limit elevated to the height of a fifth, appears 
at first sight to be in opposition to certain results in our second 
series ; for, in order that the note of the jet may be elevated 
one-fifth, the number of detached masses which strike the 
stretched membrane in a given time must necessarily increase 
in the ratio 2:3; and the same remark applies also to the 
number of nascent divisions which pass the contracted section 
during the same time (§ 2); and as, under a constant charge, 
the length of the nascent divisions evidently varies inversely as 
the latter number, it follows that from the principal note to its 
fifth the nascent divisions become shortened in the ratio 3: 2. 
But we know* that when a jet of water yields its natural note, 
the length of its nascent divisions is equal to 4°38 times the dia- 
meter of the contracted section + ; if, therefore, by the sole action 
of a sonorous instrument the note of such a jet can be raised 
by a fifth, the length of the nascent divisions will be reduced to 
two-thirds of the above value, that is, to 292 times the diameter 
of the contracted section. Now this number is a little less than 
the limit of stability of liquid cylinders, which limit we know} 
to be comprised between 3 and 3°6; and nevertheless we have 
demonstrated §, that when a liquid cylinder is transformed, the 
length of its divisions cannot be less than this same limit. 
The difficulty is only apparent however. The demonstration 
just cited assumes that the cylinder commences spontancously 
to transform itself, and under this assumption it is rigorously 
correct ; but it does not apply to the case where the contractions 
and expansions are originally formed by a sufficiently energetic 
foreign cause. In fact, the demonstration in question essenti- 
* Second Series, § 83. 
+ Such, at least, is the value of the ratio under moderate or strong 
charges; under a feeble charge, however, the ratio will be less, because ac= 
cording to the hypothesis of paragraph 2, the nascent divisions then assume 
a less volume, and consequently also a less length; but everything leads 
us to believe, that, in the experiment in question, the charge employed by 
Savart was not of the latter description. 
$ Second Series, § 46, § Ibid. § 57. 
