803 THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS 
THIRD SERIES. 
Theory of the modifications which liquid veins, projected from circular orifices, 
undergo under the influence of vibratory movements. 
§ 1. In the preceding series we deduced from the properties of our liquide 
figures the theoretical explanation of the constitution of liquid veins projected 
from circular orifices and withdrawn from all disturbing influence; it now 
remains to consider, also, under a theoretical, point of view, the curious phe- 
nomena which are produced when vibratory movements are communicated to 
the liquid. Commencing our investigation, as has been already stated, with an 
idea announced by Savart, we shall show how these movements combine their 
effects with those of the configurative forces which determine the gradual 
transformation into isolated masses, and thenceforth all the phenomena in ques- 
tion will be explained in a natural manner. 
After aiming to establish, by help of an ingenious theory, that the disturb- 
ance occasioned in the mass of the liquid of the vessel by the efflux itself may 
excite in that mass vibrations directed perpendicularly to the plane of the 
orifice, Savart has shown that similar vibrations would result in the formation 
of alternate dilatations and constrictions on the surface of the vein, because 
the portion of the latter which would issue during the continuance of a vibra- 
tion, directed from within outwards, would undergo a compression which would 
increase its thickness, while the portion which issued during the continuance 
of a vibration directed from without inwards would undergo, on the contrary, 
a contraction which would attenuate it. Now, as our researches have shown, 
the formation of dilatations and constrictions of the vein is due to quite another 
cause than vibratory movements, namely, to the instability of the equilibrium 
of figure; but when vibratory movements are transmitted from the exterior to 
the liquid of the vessel, and exist, consequently, in reality in that liquid, when, 
for instance, we place in communication with the walls of the vessel a sonorous 
instrument in vibration, then the movements in question must necessarily tend 
to exert on the vein the action supposed by Savart; and if these movements 
are suitably periodical, their action will evidently concur with those of the 
configurative forces. We shall presently examine this more closely; but we 
must first return to a point. of the theory which we have stated in regard to 
veins not submitted to that influence. 
§ 2. As was seen (2d series, §§ 72, 74, and 82) when the flow takes place 
in the direction of the descending vertical, if we imagine the movement of 
translation of the liquid to be exactly uniform, the laws of the transformations 
of cylinders apply clearly to the vein, aud we thence easily deduce the laws 
indicated by Savart, laws which control, we know, the length of the contin- 
uous part and the sound rendered by the impact of the djscontinuous part 
against a stretched membrane. But this case of uniformity in the movement 
of translation cannot be realized; we can only approximate to it by augment- 
ing the discharge, (Idid., §§ 72 and 73,) and, in the whole length of the con- 
tinuous part, the movement of translation is always more or less accelerated ; 
whence it necessarily results that, in the absence of configurative forces, the 
vein would continue to grow narrower indefinitely from above downwards. 
Hence, the liquid figure being no longer exactly cylindrical, the laws of the 
transformation of cylinders could be no longer applicable to it without some 
modification ; and since the volume of the divisions* of a cylinder is propor- 
* Tt will be remembered tl. 1t we designate as divisions of a liquid cylinder the portions 
of that cylinder each of which is converted into an isolated sphere, and that, during the 
transformation, all the divisions are limited by the cireles of the neck (cercles de gorge) of 
the constrictions. 
re BE ne 
