influence of Vibratory Motions. 13 
sion passes the contracted section ; but if this coincidence does 
not exist when the vibrations first exercise their influence, a 
struggle will take place between the actions of the forces of figure 
and those of the vibrations; and it is manifest that from that 
moment the transformation of the jet, which, being a pheeno- 
menon of instability, may be displaced by slight causes, will 
cause all the expansions and contractions to advance or recede, 
so as soon to establish the above coincidence, and thus to permit 
the concurrence and full liberty of the two systems of actions. 
§ 8. These principles beig admitted, we proceed to show 
how, one by one, all the modifications suffered by a jet under 
the influence of vibrations follow as consequences. 
We must, in the first place, remember that when the jet is 
abandoned to the sole action of the forces of figure, the velocity 
with which its transformation is effected remains very small up 
to a considerable distance from the contracted section, so that 
the corresponding portion of the jet has a calm and limpid 
aspect ; in the second place, that at a greater distance the ex- 
pausions assuming a more rapid and perceptible development, 
the jet appears to widen up to the point where the masses detach 
themselves ; and lastly, that beyond this point the diameter of 
the jet, which coincides with that of these masses themselves, is 
sensibly uniform*. 
Such a jet being conceived, let the note we have heretofore 
been considering be produced in its proximity. Inasmuch as 
under the influence of this tone each division leaves the con- 
tracted section in a more advanced phase of transformation (§ 5), 
and as the transformation also departs from this phase with a 
greater velocity than it would have had under the sole action of 
the forces of figure (§ 6), it necessarily follows that the trans- 
formation in question will become completed in less time; con- 
sequently each division will attain the condition of a detached 
mass at a less distance from the orifice, and thus the continuous 
part will become shortened. 
And since the expansions are more developed from their origin, 
we see, in the second place, that the apparent thickness of the 
limpid portion of the jet-—which thickness, in each point of the 
length of this limpid portion, is evidently that acquired by the 
expansions when passing the same—will appear augmented. 
Thirdly, the excess of transversal velocity received by the 
transformation from the vibrations, and which continues as ac- 
quired velocity, must necessarily cause the horizontal diameter of 
the successive masses to exceed that of the spheres which these 
masses tend to constitute, so that the said masses will be flat- 
tened in a vertical direction. But, manifestly, this horizontal 
* Second Series, § 70, 
