WITHDRAWN FROM THE ACTION OF GRAVITY. 313 
sions and nodes such as, in the same. circumstances, are presented by that of 
vertically descending veins, (6,) and the vibrations of an instrument modify it 
in the same manner. If the vein be ejected obliquely from below upwards, 
the same phenomenaare still observed, so long as the angie which it forms with 
the horizon does not exceed 20° to 25°, 
16. But beyond that limit, and as far as 45° to 50°, the discontinuous part 
assumes other aspects: when the vein is not under the influence of the sound 
of an instrument, this discontinuous part appears spread out on one vertical 
plane into a sort of sheaf. Under the action of vibrations of a definite period, 
it may happen that the sheaf is resolved into two quite distinct jets, having 
each its expansions and nodes regularly formed; it may even be that, for 
another definite sound, the sheaf shall be replaced by three jets; finally, there 
is always a sound which reduces the entire vein to a single jet, presenting a 
system of expansions and nodes perfectly regular, and this sound is also that 
which produces the greatest shortening of the continuous part. 
17. For the same discharge and the same orifice, the number of vibrations 
corresponding to the sound which exerts the maximum of effect on the length 
of the continuous part and on the dimensions of the expansions of the vein, 
is so much less as the direction in which this last is ejected makes a greater 
angle with the descending vertical drawn from the orifice. The difference 
between the numbers of vibrations which correspond with the case in which 
the jet falls vertically and with that in which it is projected horizontally, is 
inconsiderable ; but it becomes very great between this last case and that in 
which the jet is an ascending vertical. 
§ 4. Let us proceed now to the explanation of these singular phenomena. 
What follows, as far as § 24, will relate to veins ejected in the descending ver- 
tical, and, up to that point, such veins must constantly be kept in view. 
Experiment has taught us (2d series, § 46) that, in the transformation of a 
liquid cylinder the length of a constriction is exactly, or at least almost exactly, 
equal to that of a dilatation, and we shall hereafter demonstrate that this 
equality is strictly exact*at the commencement of the phenomenon; now this 
result is evidently applicable to the incipient constrictions and dilatations of 
the vein, and it follows that the respective durations of the passage of one of 
these constrictions and of one of these dilatations at the contracted section are 
equal; on the other hand, a division of a cylinder or of a vein being com- 
prised between the centres of two neighboring constrictions, and hence being 
composed of a dilatation and two semi-constrictions, the duration of the 
passage of a division of the vein at the contracted section is necessarily 
equivalent to the sum of the durations required for the passage of a dilatation 
and a constriction; and since these two last are equal, we arrive at this first 
consequence, that the duration of the passage, whether of a constriction or a 
dilatation, at the contracted section, is equal to half that of the passage of a 
division. 
But the number of vibrations per second corresponding to the sound ren- 
dered by the impact of the discontinuous part of the vein upon a stretched 
membrane is, we have seen, (2d series, § 82,) double that of the isolated masses 
which, in the same interval of time, strike upon that membrane, and, in virtue 
of our new hypothesis, (§ 2,) this last number is always equal to that of the 
divisions which pass, within the same time, at the contracted section; hence 
the duration of each of the vibrations in question is, like the duration of the 
passage of a constriction or a dilatation, equal to half that of the passage of 
a division, and we thence deduce, finally, this fundamental conclusion: The 
duration of each of the vibrations corresponding to the sound proper to the vein 
as equal to that of the passage of a constriction or of a dilatation at the con- 
tracted section. 
