310 THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS 
if the divisions descend with the accelerated velocity of the liquid, and if we 
suppose that there thence results no change in the duration of their transforma- 
tion, they will pass, during that duration, over a more considerable space, so 
that the continuous part will be longer than if the acceleration did not exist, 
and the excess, compared with the length which the continuous part would 
have in the case of the uniform movement, will be considerable under a weak 
or moderate discharge, while it will be inconsiderable under a very strong dis- 
charge—this latter rendering the movement of translation in the continuous 
part sensibly uniform. Accordingly, when we pass from the first of these two 
discharges to the second, the ratio of the leagths of the continuous parts which 
respectively correspond to them will be nearer to unity than it would be if the 
acceleration were null; that is to say, nearer to unity than that of the square 
roots of the discharges. ; 
But the divisions cannot descend with an accelerated movement without 
being at the same time elongated, (2d series, § 76,) aud thence proceed two 
causes of diminution in the duration of the transformation. We have seen 
(2d series, § 66) that the more the length of the divisions of a cylinder sur- 
passes the limit of stability, the greater is the rapidity of transformation ; and, 
on the other hand, the stretching out which the divisions of the vein thus 
undergo must attenuate the constrictions more than the dilatations, because 
the former, having already a tendency to grow deeper by the action of the 
configurative forces, oppose no resistance to the effects of the elongation, while 
the latter resist by virtue of the contrary tendency. This second influence, 
the diminution, namely, in the duration of the traasformation, a diminution 
which must be so much the more decided as the rapidity of translation less 
approximates to uniformity, or as the discharge is weaker, operates evidently 
to render the law more rapid than the proportionality to the square root of the 
discharge, and this influence is consequently opposed to the former. 
Finally, there is a third influence, the inverse of the preceding, and hence of 
the same character with the first: as was shown at the end of the 2d para- 
eraph, the incipient divisions must be proportionably shorter as the discharge 
is weaker; but, agreeably to what has been said above, this curtailment, by 
diminishing the excess of the length of each division beyond the limit of sta- 
bility, must tend to augment the duration of the transformation. Consequently 
the 78th paragraph of the 2d series, relating to the neutralization of the two 
opposite kinds of influences, and therefore to the manifestation of the laws of 
Savart, remains unchanged; only it must not be forgotten that the influences 
to which we now refer are not altogether those which were indicated in the 77th 
paragraph of that series, and it will be seen that, they are rather more simple. 
But the second part of the 82d paragraph of the 2d series, in which we sought 
to establish @ privri the conditions for realizing the laws advanced by Savart 
in regard to the sounds which veins render, cannot be maintained, for the con- 
siderations therein set forth rest on the first hypothesis. In reasoning accord- 
ing to the new one we will say: for a determinate orifice, in proportion as the 
discharge is increased, the constitution of the vein approximates more and 
more to what it would be if there were no acceleration, and consequently the 
length of its incipient divisions verges towards that which they would acquire 
in the same case; whence it follows, from the first part of the same paragraph 
82, that starting with a less discharge sufficiently strong, the laws of Savart 
will be necessarily satisfied. This is all that the new hypothesis can furnish 
us on the subject of the conditions in question; it does not enable us to deter- 
mine the least discharge under which these conditions begin to be fulfilled; for 
it does not give the precise elements for calculating the length of the incipient 
divisions. 
Lastly, the commencement of § 83 of the 2d series, which establishes, upon 
the other hypothesis, the approximate uniformity of the movement of transla- 
