influence of Vibratory Motions. 11 
the vibration, would, for contrary reasons, give rise to a depressed 
wave on the surface of the jet, of the same length as the elevated 
one, and the former would follow the latter with the same velo- 
city. Afterwards would come a new elevated wave followed by 
a new depressed one, and so on as long as the communication of 
vibrations continued. 
But, in consequence of the instability of the cylindrical figure, 
and of the tendency of the jet to become transformed into de- 
tached masses, quite different results take place. Let us imagine 
that the lower extremity of one of the expansions which would 
be formed under the sole action of the forces of figure, due to 
instability, passes the contracted section precisely at the moment 
when a descending vibration commences in the liquid. Then 
inasmuch as the forces of figure push continuously an excess of 
liquid into this portion of the jet, which expands the latter with- 
out its having any tendency to return to its former shape, it is 
_ evident that the quantity of liquid brought at the same time by 
the additional velocity, due to the descending vibration, may 
spread itself out laterally and contribute to the formation of the 
expansion without having to surmount a contrary tendency. 
Besides, since the duration of the vibration is equal to the time 
employed by the portion of the jet, converted into a nascent ex- 
pansion by the forces of figure alone,—in passing the contracted 
section, the upper extremity of this portion will pass the con- 
tracted section precisely at the expiration of the vibration, so 
that the immediate action of the latter will have been exercised 
upon the whole portion in question and upon this portion only. 
Lastly, since the expansion produced by the combined actions 
above alluded to has no tendency to efface itself, neither will it 
be propagated to the subjacent strata, and hence it will not give 
rise toa wave. Thus the portion of the jet under consideration 
will, from the beginning, be more expanded than it would have 
been in the absence of vibrations; but it will have the same 
length, and will descend with the same velocity as in the latter 
case. 
The descending vibration will be followed by an ascending 
one; and as the latter diminishes the velocity of passage at the 
contracted section, there will result, as we have already intimated, 
a diminution of volume in the portion of the jet under its influ- 
ence, so that the same will tend to become thinner; but as the 
forces of figure tend to make a contraction of this portion, the 
attenuating action of the vibration will again be unopposed, and 
consequently no wave will be formed. We see, therefore, that, 
like the expansion which preceded it, the contraction thus formed 
by the double action of the forces of figure and of the vibration 
will be more developed, though it will have the same length, 
