2 M. J. Plateau on Jets of Liquid under the 
alternate expansion and contraction of the diameter of the 
jet; because the portion of the latter which issued during 
the continuance of a vibration directed from within outwards, 
would suffer a compression which would augment its thickness, 
whilst the portion which issued during the continuance of a vi- 
bration directed from without inwards would, on the contrary, 
suffer a traction which would attenuate it. According to our 
former researches, however, the formation of these expansions 
and contractions is due, not to vibratory motions, but to the 
instability of the equilibrium of the figure; nevertheless, when 
vibrations are communicated from without to the liquid in the 
vessel, and consequently really exist in this liquid, when, for 
instance, a sonorous instrument in a state of vibration is put in 
communication with the sides of the vessel, then the vibrations 
in question must necessarily tend to exert upon the vein an 
action of the kind conceived by Savart ; and if these vibrations 
have a suitable period, there will necessarily be a concurrence 
between their actions and those of the forces of figure. 
Before examining the subject more closely, we must refer to a 
point in our theory concerning jets not submitted to the above 
influence. 
§ 2. In the second series, §§ 72, 74 and 82, we have seen that 
if, when a jet of liquid issues vertically downwards, we imagine 
the motion of translation to be perfectly uniform, the laws of the 
transformation of cylinders apply exactly to the jet; and from 
them may be deduced the laws of Savart governing the length 
of the continuous portion, and the tone produced by the shock 
of the discontinuous portion against a stretched membrane. 
But this uniformity in the motion of translation cannot be real- 
ized ; it can only be approached by augmenting the charge*, 
and throughout the length of the continuous part the translatory 
motion is always more or less accelerated ; whence it results, that 
in the absence of the forces of figure the jet would necessarily 
become more and more attenuated at greater distances from the 
orifice. Hence the liquid figure being no longer exactly cylin- 
drical, the laws of the transformation of cylinders cannot, with- 
out some modifications, be applicable ; and we were of opiniony, 
that, since the volume of the divisions} of a cylinder is less the 
less the diameter of the latter, the divisions of a jet ought during 
their descent to suffer a gradual diminution of volume bearing a 
certain relation to the above-mentioned attenuation. But, not- 
* Second Series, §§ 72 and 75. + Ibid. § 76. 
¢ It will be remembered that the term divisions was given to those por- 
tions of a oe cylinder each of which became converted into a detached 
here; and that during the transformation, the limits of all divisions are 
the circular sections at the most contracted parts of the jet. 
