influence of Vibratory Motions. 3 
withstanding its apparent legitimacy, this was but a hypothesis, 
and we were wrong in presenting it as the expression of a fact. 
For, in the first place, we were thus led to a conclusion difficult 
to admit, that is to say*, that the liquid descends more rapidly 
than the divisions, and that, moving thus in a kind of canal 
whose dimensions are alternately broader and narrower, its velo- 
city suffers a series of periodic variations: again, if the divisions 
lost volume in the course of the continuous part, it would follow 
that the volume of each detached mass would be less than that of 
a primitive division; and as at all distances from the orifice the 
same quantity of liquid necessarily passes during the same time, 
the number of masses which would strike a stretched membrane 
during a second would be greater than the number of divisions 
generated in the same time at the contracted section,—a result 
evidently irreconcileable with our theory of the influence of vi- 
brations upon the jet. 
But there is another hypothesis, equally probable @ priori, 
which does not involve the difficulties just alluded to, and which 
moreover is, as we shall see, supported by experiment. Instead 
of regarding each division as independent of its adjoining ones, 
and thus as diminishing freely and gradually in volume on account 
of the attenuation of the jet, so that the volumes of all those 
which at a given moment are situated on the continuous part of 
the jet diminish from the highest to the lowest, it is just as per- 
missible to assume that these divisions are dependent one upon 
the other, and that, in virtue of this dependence, they all have 
the same volume, but that in consequence of the attenuation of 
the jet this uniform volume is intermediate between those which 
would correspond, individually, to the two extreme divisions. This 
intermediate volume will consequently be less the more the jet 
tends to become attenuated, in other words, the more feeble the 
charge. All complication thus disappears: the divisions descend 
with the same velocity as the liquid without altering their initial 
volume ; the liquid does not pass from division to division, and 
hence the velocity of its translation suffers no periodic variations; 
lastly, each division which leaves the contracted section only fur- 
nishes matter sufficient for one detached mass, and consequently 
the number of masses which in a given time strike a stretched 
membrane, is always equal to the number of divisions which pass 
the contracted section during the same time. It is only when 
the charge is diminished or increased that the divisions will 
assume, from the moment of their generation, a less or a greater 
volume, which they will afterwards retain throughout the course 
of the continuous part. 
It is essential to remark here, that these variations in the 
* Second Series, §§ 76 and 77. 
B2 
