446 M. J. Plateau on. Jets of Liquid unider the 
the vibrations, must be-shortened.. We may assume, therefore, 
that the favoured contractions, although from their origin more 
attenuated than those im conflict, contaim, nevertheless, more 
liquid than the latter because of their greater length ; and since, 
being at once longer, and activated by the vibrations, they arrive 
more rapidly at their rupture, it is evident that they will transfer 
to the expansions more matter with greater velocity, and hence 
also a greater quantity of motion. All the expansions there- 
fore will be in the condition analysed in paragraph 25, and con- 
sequently some of the detached masses on leaving the continuous 
part will have a small excess, and others a small defect of velo- 
city. But here, inasmuch as the vibrations impart their regu- 
larity to the phenomena, they render all the favoured contrac- 
tions identical at their origin, and similarly all the contractions 
in conflict identical amongst themselves; so that all the masses 
formed from the expansions which, during the course of the con- 
tinuous part, had a favoured .contraction in the rear, will leave 
that part with the same excess of velocity, and hence describe 
the same trajectory ; and all the detached masses which result 
from the expansions which were preceded by the favoured con- 
tractions, when traversing the continuous part, will leave the 
latter with the same defect of velocity, and consequently describe 
another unique trajectory different from the former. Under the 
influence of the octave below the principal note, therefore, the 
sheaf should be replaced by two separate jets. 
Nevertheless, it would not be impossible for the note under 
- consideration to cause the sheaf to disappear; in fact, this note 
having already a very low pitch—at least with respect to the jet 
upon which I operated—its vibrations have a large amplitude, 
and they may act (§ 22) with sufficient energy to prevent the 
formation of the contractions in conflict, and thus leave only 
those divisions in the jet which they themselves tend to produce, 
in which case all the detached masses would necessarily have the 
same normal velocity. 
Let us examine, in the second place, the influence of the fifth 
below the preceding note, or in other words, of the second fifth 
below the principal note. The vibrations of this note being 
three times less rapid than those of the principal note, we easily 
conclude that each of the divisions which they themselves tend 
to determine in the jet comprise exactly three of the divisions 
due to the forces of figure. It is clear, too, that of the three 
expansions contained in this group of ‘divisions, the last has 
behind it a favoured contraction, and before it a ‘contraction in 
conflict ; that the first, on the contrary, is preceded by a fayoured 
contraction and followed by one in conflict ; and lastly, that the 
intermediate one is situated between two contractions in conflict 
