WITHDRAWN FROM THE ACTION OF GRAVITY. 287 
the effects of the gradual transformation cannot begin to become obvious until 
a greater or less distance from the contracted section has been attained. Up 
to this distance the rapid passage of the dilatations and constrictions before the 
eye cannot give rise to any effect visible to the simple sight; so that this por- 
tion of the vein will appear in the form which it would affect if it had no ten- 
dency to become divided. Beyond this distance the dilatations will begin to 
acquire considerable development ; the vein will appear to continue enlarging 
until another distance has been attained beyond which the diameter will appear 
constant. Such is, in fact, as the observations of Savart have shown, the form 
presented to direct observation by a vein withdrawn from the influence of any 
disturbing cause. 
Lastly, we know that from the orifice to the point at which it appears to 
begin to enlarge, the vein is seen to be limpid, whilst further on it appears 
more or less turbid; and Savart has perfectly explained these two different 
aspects, as also some other curious appearances which the troubled part pre- 
sents, by attributing the limpidity of the upper portion to the slight develop- 
ment of dilatations and constrictions which are propagated in it; and the tur- 
bidity, as also the other appearances of the remainder of the vein, to the rapid 
passage before the eye, at first of the dilatations and constrictions which have 
become more marked, then, lower down, of the isolated spheres and the inter- 
posed spherules. We must refer for the details to the memoir quoted above. 
71. But we may go further: two consequences spring directly from our 
explanation of the constitution of the vein. In the first place, as the divisions 
become transformed during their descent, it is clear that the space traversed 
by a division during the time it is effecting a given part of its transformation 
will be as much greater as it descends more rapidly, or, in other words, as the 
charge, z. e., the height of the liquid in the vessel, is more considerable ; whence 
it follows clearly that, the orifice being the same, the length of the continuous 
part of the vein must increase with the charge. Now this has been confirmed 
by Savart’s observations. In the second place, since the transformation of a 
cylinder is slower in proportion to the size of its diameter, the time which a 
division of the vein will occupy in effecting any one and the same part of its 
transformation will be as much longer as the vein is thicker; whence it fol- 
lows, that if the rapidity of the flow does not change, the space which the 
division will traverse during this time will be as much greater as the diameter 
of the orifice is greater; consequently, for the same charge, the length of the 
continuous part must increase with the diameter of the orifice, and this is also 
verified by the observations detailed in the memoir quoted. 
With regard to the laws which regulate these variations in the length of the 
continuous part, Savart deduces from his observations, which were made by 
employing veins of water, that for the same orifice this length is nearly pro- 
portional to the square root of the charge, and that for the same charge it is 
nearly in proportion to the diameter of the orifice. 
_ Let us now examine whether these two laws also emanate from our explana- 
tion. 
72. Imagine for a moment that gravity ceases to act upon the liquid as soon 
as the latter passes the contracted section. Then, commencing at this section, 
the rapidity of translation will simply be that which is due to the charge, and 
the value of which, as we know, is V2gh, g denoting gravity and / the charge. 
This velocity will be uniform; consequently, if the vein had no tendency to 
divide, it would remain exactly cylindrical throughout any extent, (§69.) Now, 
all parts of the liquid being actuated by the same velocity of transference, this 
common movement cannot exert any influence upon the effect of the configur- 
ing actions; so that, for instance, the gradual modifications which each of the 
constrictions undergoes, and the time which it takes in their accomplishment, 
will be independent of the rapidity of transference. 
