WITHDRAWN FROM THE ACTION OF GRAVITY. 309 
tionably less as the diameter of the cylinder is smaller, it would scem that the 
divisions of the vein must undergo, during their descent, 1 gradual diminution 
of volume in a certain ratio with the above attenuation. Now, notwithstanding 
the apparent legitimacy of the inference, this was nothing more than an hy- 
pothesis, and it was improperly presented as the expression of the reality. In 
effect, it led, in the first place, to a consequence difficult to be admitted, namely, 
(Ibid., §§ 76 and 77,) that the liquid descends more rapidly than the divisions, 
and that, moving thus in a sort of channel of dimensions alternately wider and 
narrower, its velocity would undergo a succession of periodical variations ; 
moreover, if the divisions lost something of their volume in the transit of the 
continuous part, it would follow that the volume of each isolated mass would 
be less than that of an incipient division, and as the same quantity of liquid 
must necessarily pass, within the same time, at all distances from the orifice, 
the number of masses which would strike per sécond upon a stretched mem- 
brane would be greater than that of the divisions which would commence per 
second at the contracted section, a result irreconcilable, as will presently 
appear, with our theory of the influence of vibratory movements on the vein. 
But another hypothesis may be formed equally probable, @ priori, which 
does not involve the difficulties just mentioned, and which, as we shail see, is 
sustained by the results of experiment. Instead of regarding each division as 
independent of those adjacent, and as thus freely and gradually diminishing in 
volume by reason of the progressive slendervess of the vein, so that all those 
which, at a given instant, are ranged along the continuous part shall have 
volumes decreasing from the upper to the lower, it may be assumed with equal 
probability that these divisions are reciprocally dependent (solidaires) as re- 
gards one another, and that, in virtue of this reciprocal dependence, (solidarité, ) 
they must all have an equal volume, but that, in consequence of the attenua- 
tion of the vein, this uniform volume is intermediate between those which 
would correspond separately to the two extééme divisions ; this volume would, 
therefore, be proportionably less as the vein tends more to grow slender, or, in 
other words, proportionably less as the discharge is weaker. In this way all 
complication disappears; the divisions descend with the proper velocity of the 
liquid without modifying their initial volume; the liquid does not pass from 
division to division, and hence its velocity of translation does not undergo 
periodical variations; finally, each division which leaves the contracted section 
furnishes only the material of a separate mass, and consequently the uumber 
of masses which strike, in a given time, upon a stretched membrane is always 
equal to that of the divisions which pass, in the same time, at the contracted 
section. Only, when we diminish or increase the discharge, the divisions 
acquire, from their origin, a less volume in the former case and a greater 
volume in the second, a volume which they will afterwards preserve through 
the whole passage of the continuous part. 
It is essential to remark here that these variations in the volume of the 
incipient divisions necessarily require corresponding variatious in their length, 
and that hence these divisions must be shorter or longer according as the dis- 
charge is weaker or stronger. 
§ 3 bis. We shall adopt, then, as more simple, and as harmonizing theory 
with facts, the new hypothesis just presented, and it will be necessary to cor- 
rect in this sense § 76 of the 2d series. This hypothesis leads us, like the 
first, to recognize two kinds of influences acting in opposite directions on the 
jaw which determines the length of the coutinuous part when we cause the 
discharge to vary; but here, again, we shall see that matters tend to simplifi- 
cation. 
First, let us remember that if the movement of translation were uniform, 
the proportionality to the square root of the discharge would still be satisfied, 
even beginning with very weak discharges, (2d series, §§ 72 and 75.) Now, 
