488 M. J. Plateau on Jets of Liquid under the 
ally consists in showing, that if, in the first phases of transforma- 
tion, we consider a portion of the cylinder consisting of a con- 
traction and an expansion, the length of which is equal to that 
of a division, everything takes place in this portion in the same 
manner as if its two bases were solid, so that the transformation 
cannot establish itself spontaneously unless the distance between 
the bases be at least equal to the limit of stability; but if the 
transformation cannot of itself commence, in a cylinder actually 
realized between two solid dises, it is evident that it will continue 
of its own accord if it has once been commenced by a foreign 
cause, which has accumulated a certain quantity of liquid near 
one of the dises so as artificially to determine a sufficiently deve- 
loped expansion and contraction; for it is evident, that, on 
passing from one side of the limit of stability to the other, there 
is no sudden transition from instability te an absolute stability. 
On leaving this limit the stability must at first be very feeble, 
since ‘it sets out from zero; consequently at a little distance 
within this limit a deformation, artificially imparted to the cy- 
linder, cannot, unless the same be small, become spontaneously 
effaced: if, on the contrary, it is considerable, it will progress 
spontaneously, and will bring about the disunion of the mass. 
The demonstration just recalled, therefore, cannot be appealed to 
when the nascent contractions and expansions of the jet of liquid 
are formed by energetic vibrations. In this case, if the sum of 
the lengths of one of these expansions and of one of these con- 
tractions, or what is the same, if the length of a division is a 
little less than the limit: of stability, the transformation may 
commence in this abnormal manner; and the more intense the 
vibrations, the more the corresponding note for which the possi- 
bility of the phenomenon exists will be elevated above the prin- 
cipal note. 
If the foreign note has a lower pitch than the principal one, 
and thus tends to give to the nascent divisions a length necessa- 
rily greater than the limit of stability, it will encounter no such 
resistance as that just signalized within this limit, so that the. 
possibility of the phenomenon will be much more extended ; in 
fact, we find from Savart’s experiments, that the same extends 
over an interval of more than an octave. 
- There is also another reason why the phenomenon should be: 
less limited below than above the principal note: in one and the 
same sonorous instrument the amplitude of the vibrations gene- 
rally increases with the gravity of the note ; now it is evident 
that the greater the amplitude of the transmitted vibrations, the 
greater the excess of liquid which each descending vibration 
tends to push into the jet in order to form a nascent expansion, 
and the greater also the withdrawal of liquid which each aseend- 
