influence of Vibratory Motions. 9 
into two distinct jets, each possessing regularly formed ventral 
segments and nodes; sometimes, indeed, with a different deter- 
minate note the sheaf becomes replaced by three jets ; lastly, 
there is always one note which reduces the whole to a single jet, 
presenting a perfectly regular system of ventral segments and 
nodes, and this is the note which also produces the greatest 
shortening of the continuous part. 
No. 17. With one and the same charge and orifice, the num- 
ber of vibrations corresponding to the note which produces the 
greatest effect upon the length of the continuous part, and upon 
the dimensions of the ventral segments of the jet, is less the 
greater the angle between a descending vertical line through the 
orifice and the direction in which the jet issues. The difference 
between the numbers of these vibrations in the two cases where 
the jet falls vertically and where it issues horizontally is incon- 
siderable, but the same becomes very great when the latter case 
is compared with that where the jet ascends vertically. 
§ 4. In proceeding to the explication of these curious pheeno- 
mena, we shall devote all paragraphs between this and the 24th 
to the consideration of jets descending vertically. 
Experiment has shown us*, that, in the transformation of a 
cylinder of liquid, the length of a contraction is exactly, or at 
least very nearly, equal to that of an expansion ; and, as we then 
asserted, we shall demonstrate in the sequel that this equality is 
rigorous at the commencement of the phenomenon. Now this 
result is evidently applicable to the nascent contractions and ex- 
pansions of a jet, whence it follows that the respective durations 
of the passages of one of these contractions and of one of these 
expansions at the contracted section are equal. On the other 
hand, a division of a cylinder or of a jet being comprised between 
the middles of two successive contractions, and being thus com- 
posed of an expansion and two semi-contractions, the duration 
of the passage of a division of the jet at the contracted section is 
necessarily equivalent to the sum of those of the passages of an 
expansion and a contraction ; and inasmuch as these two latter 
are equal, we arrive at this first conclusion: the duration of the 
passage either of a contraction or of an expansion at the con- 
tracted section is equal to half the time of passage of a division. 
But we know? that the number of vibrations per second corre- 
sponding to the note produced by the shock of the discontinuous 
part of the jet against a stretched membrane, is equal to double 
the number of isolated masses which impinge upon this membrane 
in the same interval of time; and, in virtue of our new hypo- 
thesis (§ 2), this Jatter number coincides with that of the divi- 
sions which pass the contracted section during the same time ; 
* Second Series, § 46. + Ibid, § 82. 
