WITHDRAWN FROM THE ACTION OF GRAVITY. Sif 
tion of the necks (cercles de gorge) of the constrictions in the small extent 
which corresponds to an incipient division, must be also rectified. On the new 
hypothesis, the movement of translation of the cercles de gorge is the movement 
itself of the liquid, and we can calculate consequently with exactness, for the 
discharge and orifice employed by Savart, how much the velocity has increased 
at a distance from the contracted section six times the diameter of that see- 
tion, that is to say, evidently greater than the length of an incipient division, 
and the increase thus obtained scarcely exceeds a hundredth. The new hy- 
pothesis therefore establishes, as well as the first, the nearly exact uniformity 
of the movement of translation of the cercles de gorge in the small extent in 
question, and consequently all the rest of the paragraph is justified. 
§ 3. These rectifications having been made, we proceed directly to the sub- 
ject. We will first briefly recapitulate what, according to the researches of 
Savart, are the modifications which the vein experiences under the cireum- 
stances we are considering, that is, when it is under the influence of vibratory 
movements. The first fourteen of the following Nos. relate to veins descending 
vertically. 
1. The continuous part is shortened. 
2. The thickness of the limpid portion seems augmented. 
3. Each of the masses which are isolated at the lower extremity of the con- 
tinuous part is first flattened in the vertical direction, and consequently its 
horizontal diameter is greater than that of the sphere which it tends to consti- 
tute. 
4. The masses being thus abandoned to themselves under a flattened form, 
and tending to assume the spherical form, they afterwards exceed this latter 
through the effect of inertia, and are lengthened in the vertical direction, are 
then flattened anew, and again elongated, and so on in succession; so that their 
horizontal diameter, which was at first greater than that of a sphere of the same 
volume, becomes afterwards less than this latter, then again greater, &¢. These 
periodical variations of the horizontal diameter of the masses taking place 
while the latter are borne forward by their movement of translation, the im- 
pression left on the eye by the rapid passage of any one of these masses must 
be that of a figure presenting a regularly arranged series of maxima and minima 
of thickness, the former corresponding to the places by which the mass has 
passed at the moments of its greatest horizontal development, and the latter 
to the places by which it has passed at the moments of greatest horizontal con- 
traction ; and since the successive masses pass, either exactly or nearly so, by 
the same places in the same phases of their oscillations of form, the impression 
which they individually produce are more or less completely identified, and the 
discontinuous part of the vein presents in a permanent manner the differences 
of thickness in question; in other words, this discontinuous part appears to be 
composed of a regular series of elongated expansions and nodes occupying fixed 
positions. When the above superposition is imperfect, each expansion presents 
the appearance of an assemblage of films, of which each constitutes a species 
of cone having for its axis that of the vein. About the half of the first expan- 
sion is formed by the passage of the dilatations of the base of the continuous 
part, so that this continuous part terminates about the middle of the length of 
that expansion. 
5. The length and the diameter of the expansions are so much the more con- 
siderable as the discharge is stronger and the diameter of the orifice greater, 
and the same is the case as regards the diameter of the nodes. 
6. This assemblage of phenomena is manifested even when the vein is left 
to itself under the ordinary circumstances, that is, when vibratory movements 
are not designedly excited in the liquid of the vessel. ‘This results, on the one 
hand, from the circumstance that the impact of the discontinuous part upon the 
liquid in which it falls occasions vibrations which are transmitted to the vessel 
