2994 THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS 
less in proportion as the strength of the charge is greater; it is also evident 
that for it not to be very small, an extremely small value must be given to the 
charge; for when the charge is too small, either the flow does not take place, 
or it ensues drop by drop, in both which cases the nature of the phenomenon 
is changed, and cannot be referred to the transformation of a cylinder. We 
shall therefore suppose that the value of the charge is 4 centimetres, for instance, 
which is certainly a small value, and which is slightly greater than the least 
of the values employed by Savart in his experiments. We shall then have 
S—-2 
FH =0.0005 ; 
and transferring this value to the equation (1) we shall find 
L 
—==1-+0.0005, 
D ot 
or rather 
L—D=0.0005.D. 
Thus, according to this result, whatever the diameter of the orifice may be, 
with the feeble charge of 4 centimetres, the length of the continuous part of an 
imaginary vein of mercury only exceeds the distance D by a quantity equal 
to 6 ten-thousandths of the latter; so that, for instance, if the diameter of the 
orifice were such that the distance D were a metre, the length of the continu- 
ous part would only differ from it by half a millimetre; and in consequence 
of the very small value we have attributed to 0, even this probably exceeds 
the true difference. Lastly, if we pass from mereury to some other liquid, the 
difference between L and D, or rather the proportion of this difference to D, 
would necessarily vary in magnitude and direction with the nature of the 
liquid; but this proportion, as we have shown, is so small that we may safely 
admit that it will always be very small in regard to any other liquid. 
76. Let us now go within the limit commencing with which the real vein 
may be compared, in its continuous part, to the corresponding imaginary vein, 
(§§ 73 and 74;) in other words, let us suppose the charge to be so inconsidera- 
ble, or the diameter of the orifice to be so great, that the movement of trans- 
ference, in the extent of the continuous part of the real vein, is not perfectly 
uniform. he vein will also then tend to become thinner from above down- 
wards, and this diminution in thickness will become visible upon the limpid 
portion. The question of the laws which under these circumstances must 
regulate the length of the continuous part is very complicated; we shall, how- 
ever, attempt to elucidate it to a certain point. 
Let us consider a division of the vein at the instant at which its upper ex- 
tremity passes the contracted section. The two liquid sections between which 
the division in question is comprised separate from this position with different 
velocities ; for, in the short path which the inferior section has traversed, its 
velocity is even slightly augmented by the action of gravity. Now, it follows 
from this excess of velocity and the acceleration of the motion, that the two 
sections will continue to separate from each other more and more in proportion 
as they descend ; or, in other words, that the portion of the liquid included 
between them will gradually become elongated during its motion of transfer- 
ence. Consequently, if no other cause intervened, each of the divisions, con- 
veyed by the accelerated velocity of the liquid, would gradually increase in 
length up to the instant of the rupture of the line, and would preserve a con- 
stant volume during its descent. 
But there is a cause which acts in an opposite manner upon the. divisions. 
If we imagine the divisions of the continuous part to be suddenly effaced, the 
small portion of the vein thus modified which replaces, at this instant, any given 
division, will be smaller in proportion as the division in question is more distant 
