WITHDRAWN FROM THE ACTION OF GRAVITY. 295 
from the contracted section. Consequently we may consider each of the di- 
visions which at a determinate instant are arranged upon the entire length of the 
continuous part as arising respectively from the transformation of a different 
cylinder; and as the minute portion of the vein which replaces, in the above 
hypothesis, any given division would continue slightly diminishing in thickness 
from above downwards, we should exactly obtain the diameter of the corre- 
sponding cylinder by taking the mean diameter of this portion. Now, we know 
that for any liquid, the normal length of the divisions of a cylinder supposed 
to be formed in the air, and the entire convex surface of which is free, is in 
proportion to the diameter of this cylinder; consequently, if nothing opposed 
the action of the configuring forces upon the vein, the proportion of the length 
of a division to the above mean diameter corresponding to it would be the same 
for all the divisions; and as this mean diameter diminishes at each division 
from the top to the bottom of the continuous portion, it follows that the length 
of the divisions would continue to decrease in the same proportion. If, then, 
the cause with which we are engaged were alone in action, each division would 
gradually diminish in length and volume in proportion as it descended in the 
continuous portion. But then the divisions starting from the contracted section 
with the velocity of the liquid would necessarily follow in their movement of 
transference a different law. We shall show that this movement would be 
retarded, so that the liquid, which descends, on the contrary, with an accelerated 
velocity, must pass from one division to the other, and that the latter must 
simply constitute, upon the surface of the vein, a sort of undulation, which 
would be propagated according to a particular law. 
Let us assume the hypothesis of the entirely free action of the configuring 
forees, and let us commence with the moment at which the section of the sur- 
face of the vein which constitutes the neck of a constriction passes to the con- 
tracted section. After a brief interval, another superficial section, correspond- 
ing to the next neck, will pass in its turn, and these two sections will include 
a division between them. After another interval of time equal to the first, 
another division will have passed to the contracted section; but the first will 
even then be shortened, so that its lower neck, in this second interval of time, 
will have traversed a less space than the first. For the same reason, the space 
traversed in a third interval of time equal to the two others will be still smaller, 
and so on afterwards. The movement of transference of the necks, and there- 
fore that of the divisions which they include, two and two, will then consti- 
tute, as I have stated, a retarded movement. 
Now, the two causes which we have mentioned, and which act concurrently 
upon the divisions, will necessarily combine their effects. Consequently the 
velocity of transference of the divisions will be intermediate between the 
accelerated velocity of the liquid and the retarded velocity which would result 
from the second cause alone; in the second place, the divisions will gradually 
diminish in volume during their descent along the continuous portion, but 
according to a less rapid law than would be the case under the isolated action 
of this second cause ; lastly, the length of the divisions will follow a law inter- 
mediate between the gradual increase determined by the first cause and the 
decrease produced by the second. 
77. We shall now investigate the manner in which these modifications in the 
volume, length, and velocity of the divisions are capable of exerting an intlu- 
ence upon the laws regulating the length of the continuous portion of the vein. 
We must first draw attention to the fact that in our imaginary veins, where 
the movement of transference of the liquid is supposed to be uniform with all 
charges, the causes producing the above modifications do not exist; conse- 
quently the divisions must always descend with the same velocity as the liquid, 
without varying in either volume or length in the course of the continuous 
part. Moreover, we must recollect that after what has been detailed in §§ 72, 
