influence of Vibratory Motions. 445 
These facts are less restricted than those enunciated in No. 16 
of paragraph 3; in fact, according to this No., in which the 
meaning of Savart’s expressions is reproduced, it is only under 
the influence of the principal note that the sheaf should become 
reduced to a single jet, and there should only be two other de- 
terminate and different notes capable of causing the appearance 
of two and three jets respectively. But the absence of any indi- 
cations with respect to the relations between these notes and the 
principal one, is sufficient to show that Savart did not bestow 
his whole attention on phenomena of this kind, and that after 
having observed them in isolated cases, he did not investigate 
their susceptibility of extension. 
§ 28. Let us now inquire whether theory can account for these 
same phenomena. Let us begin with the octave below the prin- 
cipal note. The period of a vibration corresponding to this note 
is double that of the passage of a contraction or an expansion at 
the contracted section, whence we conclude that the divisions 
which would be produced under the sole influence of the octave 
under consideration would be twice as long as those determined 
under the isolated action of the forces of figure. Hence we may 
admit that each of the first exactly embraces two of the second; 
for in this manner, at all the sections in which these pairs ter- 
minate, there is evidently an absolute concurrence between the 
two kinds of action, the sections in question constituting at once 
the middles of the contractions which would result from the vibra- 
tions, and the middles of the contractions due to the foreesof figure. 
Let us now examine what ought to take place in any one of these 
pairs of divisions during transformation. As this pair consists 
of two entire divisions, it contains two expansions together with 
the intervening contraction, and is terminated by two semi- 
contractions ; now whilst the whole contractions to which these 
terminations belong are, as we have seen, favoured by the vibra- 
tions, it is evident that the intermediate contraction is, on the 
contrary, in conflict, since its middle, which is the middle of the 
pair, corresponds to the middle of the division which the vibra- 
tions tend to produce, and hence to the middle of the expansion 
of the same; each of the expansions which the forces of figure 
produce in the jet is consequently adjacent to two unequally 
solicited contractions. Moreover, the contractions favoured by 
the vibrations must be also elongated by their influence, because 
the contractions which the latter would themselves produce would 
be twice as long; and as the length of each of the pairs of divi- 
sions above considered remains the same as it was in the absence 
of the note of the instrument, it follows that the contractions 
intermediate between the preceding, that is to say, those which 
occupy the iniddles of the pairs, and which are in conflict with 
