18 M. J. Plateau on Jets of Liquid under the 
preceding expansion, and that the end of this same vibration 
will be in conflict with the lower part of the following expansion. 
It is easy to see that after a certain number of vibrations a 
similar effect will be reproduced, in other words, that the middle 
of an ascending vibration will again coincide with the middle of 
the passage of a contraction, and that this coincidence will occur 
periodically and at equal intervals. For example, if the duration 
of a vibration were five-sixths of that of the passage of a con. 
traction or an expansion, then six double vibrations—each of 
which is composed of an ascending and a descending vibration— 
would be accomplished in the same time as the passage of five 
contractions and five expansions; and if we commence counting 
from one of the above coincidences, another coincidence will 
occur at the end of this interval of time; in our example, coin- 
cidences will occur at intervals equal to the duration of six double 
vibrations. Let us next attempt to discover what takes place 
during each of these intervals, or, in other words, between any 
such coincidence and the next following one. 
For this purpose let us examine what occurs at the termination 
of the first half of one of these intervals. In the above example 
we shall evidently have again arrived at the middle of an ascend- 
ing vibration; but if we consider that the interval commences 
with the passage of the beginning of a division (§ 4), and exactly 
embraces the passage of five whole divisions, we shall recognize 
that the middle of a division, that is to say, the middle of an 
expansion, is just passing the contracted section at the termina- 
tion of the first half of the interval under consideration ; this 
vibration, therefore, will be altogether opposed by the forces of 
figure ; the conflict which is now at its maximum will evidently 
have been on the increase up to this moment, that is to say, it 
will have been occupying greater portions of the successive vibra- 
tions, in order afterwards to diminish by the same degrees. 
These principles being granted, let us notice'the consequences. 
Each of the contractions corresponding to a coincidence will 
leave the contracted section in a more advanced phase of trans- 
formation, and thus each will become ruptured at a less distance 
from the orifice than if no vibrations had been produced ; but 
the following contraction, being already under less favourable 
conditions, will not be so soon ruptured; and the subsequent 
ruptures, up to that of the contraction for which the conflict 
between the two actions has been greatest, will, in a similar 
manner, be effected at increasing distances from the orifice ; 
after this the phenomena will retrograde, that is to say, the 
places of successive rupture will remount until a contraction 
corresponding to a coincidence again returns, when everything 
will recommence in the same order. It appears, then, that 
