influence of Vibratory Motions. 441 
part detached themselves in exactly the same manuer, and if all 
the masses left this point with precisely the velocity which cor- 
responds to the translatory motion of the liquid in the same, 
these masses would all describe exactly the same trajectory, and 
hence the discontinuous part could not become dispersed or 
present the appearance of a sheaf; there must, therefore, as 
Savart remarked, be irregularities in the emission of the detached 
masses from the extremity of the continuous part ; these irregu- 
larities, however, must be very small, for the sheaf has not a 
great width. At first I thought that these irregularities resulted 
from the same causes as those considered in paragraph 10; but 
if this were the case, the suppression of foreign actions ought to 
cause the sheaf to disappear, and thus to reduce the whole to a 
single jet. But experiment does not confirm this; for by em- 
ploying the means used by Savart in the case of jets descending 
vertically, that is to say, by receiving the discontinuous part 
upon a thick plank suitably inclined, and by placing soft bodies 
under the vessel whence the jet issues, under that which receives 
it, and under the supports, 1 have not been able to cause any 
notable diminution in the sheaf. One would infer from this that 
the irregularities are not due to vibratory motions, and conse- 
quently that they affect the action of the forces of figure themselves. 
It is manifest, in fact, from the nature of the phenomenon of 
transformation, that even slight disturbing causes must have an 
influence upon the perfect identity of all the divisions generated 
one after another at the contracted section ; for instance, in the 
experiments of the paragraphs 50 to 55 of the Second Series, we 
have seen an external cause alter the equality in the lengths of 
the divisions of a cylinder. This granted, we will show that 
small differences of this kind in the nascent divisions of a jet 
issuing at a suitable inclination must necessarily cause the dis- 
continuous part to be dispersed to some extent. 
Let us consider more minutely two contractions, together with 
the expansion between them. As we know, each of these two con- 
tractions, very feebly indicated on leaving the contracted section, 
becomes gradually developed in traversing the continuous part 
by sending the half of its liquid into the expansion; the latter, 
therefore, receives in front the liquid sent thither in a direction 
contrary to the movement of translation, and in the rear the 
liquid driven thither in the same direction as that of translation, 
so that its velocity of translation tends to be diminished by the 
one afflux, and to be augmented by the other. Now although 
these two opposite actions are in general unequal, because at 
every moment the contraction in front is in a somewhat more 
advanced phase of transformation than that in the rear, never- 
theless if the two contractions were perfectly identical at their 
