448 M. J. Plateau on Jets of Liquid under the 
clude that in every more or less analogous liquid figure the 
length of the divisions increases with the resistances; but the 
acquired transversal velocities, which in our large divisions deter- 
mine a tendency to persevere in the mode of transformation im- 
parted by the vibrations, constitute a resistance to an ulterior 
division. 
Let us proceed, in the third place, to the second octave below 
the principal note. Here each of the divisions which would be 
generated under the sole action of the vibrations evidently com- 
prises four of the divisions which would result from the forces of 
figure alone; but if these two actions combined together, it 
would appear that four distinct jets ought to result; for it is 
easy to see that the conflict would be unequal in the three con- 
tractions which would then form themselves, that it would be 
greater for the middle than for the two other contractions, so 
that each of the two expansions comprised between these three 
contractions would receive at its two sides unequal quantities of 
motion; and finally, that the differences would be greater for 
the extreme expansions, each of which would be situated between 
a favoured and opposed contraction. But, on the one hand, the 
vibrations in question having a considerable amplitude, it is clear 
that their action ought always to efface that of the forces of 
figure ; and, on the other hand, the divisions thus formed being 
very long, it is also evident from what has been above said, that 
new forces of figure must arise to cause their subdivision. Again, 
in consequence of the resistance, also above indicated, this sub- 
division can at most give three parts, which, in consequence of 
the distribution of the conflicts and concurrences, and the re- 
gularity imparted by the vibrations, will convert the sheaf into 
three jets only. 
We have still to consider, in the fourth place, the action of 
the notes included between the octave below the principal note 
and the fifth below the former, as well as those between this fifth 
and the second octave below the principal note. For these notes 
there is no longer any simple relation between the divisions 
which would result respectively from the vibrations alone and 
from the forces of figure alone; but it will without difficulty be 
admitted, that under the influence of the notes a little above or 
a little below the second fifth, and in the case where the effect 
of the vibrations does not entirely efface that of the forces of 
figure, the divisions due to these forces will be lengthened or 
shortened a little so as to permit the absolute concurrence of the 
two kinds of action at the limits which separate the successive 
systems of three of these divisions, and hence also the re-esta- 
blishment of the simple ratio of 3 to 1 corresponding to the second 
fifth ; hence the resolution into three jets. Under this influence, 
