296 THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS 
74 and 75, Savart’s laws are already satisfied with regard to these veins com- 
mencing with very feeble charges; the first law in the case of any liquid 
whatever, and the second in the case of mereury, very probably also in that 
of any other very slightly viscid liquid, and perhaps even in that of all liquids. 
Let us now recur to the true vein of the preceding section, and let us begin 
by examining the influence exerted by the diminution of the volumé of its 
divisions. Since a cylinder, supposed to exist under the conditions of our laws 
and formed of a given liquid, becomes transformed with rapidity proportionate 
to the smallness of its diameter, it necessarily follows that as the volume of its 
divisions is smaller, the gradual diminution in the volume of the divisions of 
the vein tends to render the velocity of their transformation more accelerated 
than it would be in the imaginary vein of the same liquid if it flowed under 
the same charge, and from an orifice of the same diameter. Under the isolated 
influence of this modification of the volume, the time which the portion of the 
phenomenon corresponding to the course of the continuous portion requires 
would therefore be shorter; consequently the length of this portion would be 
less than in the imaginary vein. Now if the charge under consideration were 
replaced by a charge very nearly sufficient to annihilate the acceleration of the 
movement of transference of the liquid in the continuous part, this portion of 
the vein would then be equal in length to that of the corresponding imaginary 
vein, (§73;) therefore in passing from the first charge to the second, the con- 
tinuous part of the true vein would augment more than that of the imaginary 
vein, 2. e., would consequently augment in greater proportion than that of the 
square roots of the two charges. Thus the gradual diminution in the volume 
ot the divisions tends to render the law regulating the length of the contmuous 
part of the vein, when the charge is made to vary, more rapid than that of 
Savart. 
Let us pass on to what relates to the length of the divisions. As the accelera- 
tion of the velocity of the transference of the liquid forms an obstacle to the 
iree shortening of the divisions, the latter must be gradually extended in the 
direction of their length, in proportion as they descend upon the continuous 
part. Now this gives rise to an influence exerted in the same direction as the 
preceding ; for in consequence of their less thickness, the constricted portions 
will yield more readily to this traction than the dilated portions,.which will 
necessarily increase the rapidity with which the former become diminished in 
thickness, and will therefore tend to produce, in each of them, the formation 
and rupture of the line sooner than in the corresponding imaginary vein, But 
the difference of the laws which the divisions and the liquid follow in their 
respective movements of transference, engenders an influence which acts ina 
contrary direction to the two preceding. In virtue of the excess which the 
velocity of the liquid acquires above that of the divisions, the liquid passes, as 
we have seen, from one division to the other, so that any one portion traverses 
successively, sometimes the narrower canal of a constriction, sometimes the 
larger space of a dilatation. But ‘as the liquid thus moyes in a conduit the 
dimensions of which are alternately smaller and larger, its velocity must be 
greater in the constricted parts, and less in the dilated parts, than if the divi- 
sions did not exist; whence this singular consequence results, that the velocity 
of transference of the liquid, instead of being uniformly accelerated, is sub- 
jected, in the course of the continuous part, to a series of particular variations 
which render it alternately greater and less than that which a solid body fall- 
ing from a point situated at the elevation of the liquid in the vessel would have. 
Moreover, the liquid molecules, instead of moving in the direction of lines pre- 
senting a very slight curvature, and always in the same direction, as they would 
do if the divisions were absent, will necessarily describe sinuous lines .in their 
passages from division to division. Now, the configuring forees emanating from 
. . . =] * . . 
the superficial layer of the vein, and which produce the divisions, cannot force 
