12 M. J. Plateau on Jets of Liquid under the 
and will descend with the same velocity, as if the jet were aban- 
doned to the sole action of these forces of figure. 
The same thing will take place with all the other expansions 
and contractions. In virtue of the equality between the time 
employed by each of these portions in passing the contracted 
section and the duration of each vibration, all the expansions 
will coincide with the descending, and all the contractions with 
the ascending vibrations ; the one as well as the other, therefore, 
will preserve their length and their velocity of translation; but 
they will all leave the contracted section in a more developed 
condition, in other words, in a more advanced phase of trans- 
formation than if no vibrations had been produced. 
§ 6. But the action of these vibrations does not cease here. 
In fact, the velocities of the descending and ascending vibrations, 
which, as we have already intimated, change their direction in 
the expansions and contractions in order to produce a greater 
transversal development in the former, and a greater attenuation 
in the latter, cannot destroy themselves in each of these portions 
the moment they have passed the contracted section ; these velo- 
cities, therefore, thus changed into transversal velocities, will 
continue, like acquired velocities, to augment those which result 
from the forces of figure. 
§ 7. In order that the transmitted vibrations may with all 
their intensity exert upon the nascent divisions of the jet the 
action described in the two preceding paragraphs, it is necessary 
that they have a vertical direction at the orifice, as we have above 
imagined. Without doubt it would be difficult to show, @ priori, 
that in propagating themselves to the orifice, the vibrations there 
actually assume this direction ; but Savart, who occupied himself 
so much with the communication of vibrations, implicitly admits 
the fact. Indeed, on the one hand he supposes that these vibra- 
tions merely reinforce those which, according to him, are generated 
by the efflux itself, and which are necessarily vertical; and, on 
the other hand, he nowhere says that, in order to obtain a maxi- 
mum action, it is necessary to give the sonorous instrument any 
particular position. At all events, in case of difficulty it would 
suffice to remark, that whatever may be the actual direction ac- 
cording to which the liquid molecules execute their vibrations in 
passing the orifice, we may always—except in the exceptional 
case where this direction 1s exactly horizontal—conceive each 
vibration divided into two others, of which the one, being hori- 
zontal, will have no influence on the transformation of the divi- 
sions of the jet, whilst the other, being vertical, will exert its 
whole action, 
We have assumed, too, that each descending vibration com- 
mences at the moment when the lower extremity of each expan- 
