; 
WITHDRAWN FROM THE ACTION OF GRAVITY. 301 
Lastly, if, in the general expression of the relation of the extreme velocities 
found above, we replace / and 7 by the values 4.5 and 24 relative to the first 
vein of the table under consideration, we shall find for this relation the value 
2.5; which shows that with the charge 4.5, under which the vein is already 
placed in the effective conditions of Savart’s law, the velocity of transference 
of the liquid is still very notably accelerated. No doubt ean, therefore, remain 
of the legitimacy of the second conclusion of § 78. 
Let us now caleulate, for each of the four charges, the proportion of the 
lengths of the continuous parts corresponding respectively to the two orifices; 
we shall thus form the following table : 
Charges. Proportions. 
1 eRe alae aah te a5 Bic sae ac MEN ai Pe Poke ie Pn ca tt SR 4.46 
Ly iva: sacle adhe ttt meeting fen en goblets eM alte bli title ol ya ile 3.23 
BIL cake, Spt eyeblink tae ate Reman Me Beg aap Sy 2.46 
22 AS SSIS ES Ssh patie Nighi ed dg le i RII RS SL ph ale i 
This table shows, that for charges below 47 centimetres the relation between 
the respective lengths of the continuous portions of two veins of water escap- 
ing, one from an orifice 6 millimetres in diameter, and the other from an orifice 
of half this diameter, is far from being the same as those of the diameters; 
whence it follows that, under these charges, Savart’s second law is not satisfied. 
But it is evident, at the same time, that this relation converges towards that of 
the diameters in proportion as the charge is augmented, and that, under the 
charge of 47 centimetres, it nearly attains it; now, according to what we have 
seen above, under this same charge of 47 centimetres, the vein escaping from 
the larger of the two orifices very probably nearly attains the effective con- 
ditions of Savart’s first law. The conclusions of the preceding section appear 
then to agree, as those of § 78, with the results of observation. We shall now, 
however, see this agreement confirmed by the results obtained with veins of 
water when not withdrawn from extraneous influences. 
81. These extraneous influences, which consist of certain more or less regu- 
lar vibratory movements transmitted to the veins, do not appear to alter the 
laws under consideration, considered generally ; but they produce a curtailment 
of the continuous portions, and thus produce the same effect as a diminution 
of the diameters of the orifices, so that under their influence Savart’s laws be- 
gin to be realized with weaker charges. 
I have just stated that the complete laws which govern the continuous por- 
tion do not appear to be changed by the extraneous influences in question; 
this will be readily seen when, for each of the series made by Savart under the 
influence of these actions, in which series the orifices, the charges, and the 
liquid are the same as before, we construct a table of the proportions of the 
length of the continuous part and the square root of the charge. Notwithstand- 
ing the slight differences arising, on the one hand, from the irregularities inherent 
to the extraneous influences, and, on the other hand, from Savart always having 
given the lengths in whole numbers, we shall see that with an orifice of 6 mil- 
limetres the proportion still begins to diminish, and converge towards a certain 
limit; only here the limit is less, for the reason I have given above, and the 
limit appears to be attained under a less charge than 47 centimetres; 2d, that 
with an orifice of 3 millimetres the proportion is perfectly constant. 
Hence the series in question may also serve fcr the discussion of the laws 
which govern the length of the continuous part. I shall limit myself here to 
the production of two of these series; they consist of those which Savart 
adopted as his type, and from which he deduced his laws. The following are 
the tables centaining them : 
