304 THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS 
above condition was satisfied in the ‘experiments from which Savart deduced 
the two laws under consideration. 
In the series relating to the first of these laws, the diameter of the common 
orifice was 3 millimetres, and the smallest charge was 51 centimetres ; and in 
the series which refers to the second law, the value of the common charge was 
the same, 51 centimetres, and the diameter of the largest orifice was 6 milli- 
metres. For our condition to be fulfilled with regard to both series, it was 
therefore evidently sufficient that it was so in the vein which escaped under the 
charge of 51 centimetres, and from the orifice the diameter of which was 6 milli- 
metres. Now on multiplying this diameter by 0.8, we obtain for the approx- 
imative value of that of the contracted section of the vein in question 4.8 milli- 
metres, and 6 times the latter quantity gives us 28.8 millimetres, or nearly 
3 centimetres. Now if in the expression ee which gives the general value 
‘ 
of the relative proportions of the velocities of transference at a distance 7 from 
the contracted section and at this section, (§ 80,) we make A=51 and /—=3, we 
obtain for this proportion the value 1.03; whence it is evident, that from the 
contracted section to a distance equal to about 6 times the diameter of this 
section, the velocity of transference of the liquid of the vein in question only 
increased 3 centimetres more than its original value. 
83. Let us imagine a vein of water, and let us call a division considered im- 
mediately after its passage to the contracted section, 2. e., at the instant at which 
its upper extremity passes this section, the nascent division. It follows from 
what we have detailed in the preceding section, starting with a sufficient charge, 
that the proportion of the length of the nascent divisions of the vein in ques- 
tion to the diameter of the contracted section will assume a constant value, z.e., 
independent of the charge, and that this value will very probably differ but 
little from 4. 
Now the results obtained by Savart in the experiments relative to the laws 
which we have just discussed allow us, as we shall see presently, to verify the 
consequences of our principles. 
The two opposite causes which tend to modify the length of the divisions 
are also those which exert an influence upon the velocity of transference, or, 
more precisely, upon the velocity of the transference of the necks which termi- 
nate them, (§ 76.) Now, in the case under consideration, these same causes 
both remaining very small throughout the extent corresponding to a nascent 
division, their resulting action upon the velocity of transference of the necks 
will be insensible throughout this extent; consequently the velocity with 
which a neck descends may be regarded as exactly unitorm and equal to the - 
velocity of the flow, ¥2gh, from the contracted section to a distance equal to 
the length of a nascent division. 
If, then, for an orifice of a given diameter, 4 denotes the length of a nascent 
division, and ¢ the time oceupied by a neck to traverse it, we shall have 
A=t V2gh. 
Moreover, let x represent the number of divisions which pass to the contracted 
section in a second of time; as the time ¢ evidently measures the duration of 
the passage of one of them, we shall have, taking the second as the unit of 
, il! | Ee Se a 
time, (iz and therefore —- V2gh. Lastly, let k denote the diameter of 
the contracted section corresponding to the same orifice; to represent the pro- 
portion of the length of the nascent division to this diameter, we shall have 
the formula 
