WITHDRAWN FROM THE ACTION OF GRAVITY. 291 
converted, is that which we have designated by 0, and in which the liquid sec- 
tion traverses the distance D ; in our imaginary vein of mercury, the time 0 
will therefore be in proportion to the diameter of the contracted section. 
Now, we know that in a liquid vein, the diameter of the contracted section 
may be regarded as proportional to that of the orifice, when the latter exceeds 
6 millimetres, and that above this limit the proportionality does not alter very 
appreciably except when the diameter of the orifice becomes less than a milli- 
metre.* Moreover, as this alteration is attributed to the influence which the 
thickness of the edges of the orifice, although very slight, exerts, it is probable 
that it may be rendered still less by employing, as Savart has done, orifices ex- 
panded outwardly, and which may be shaped so that their edges may be very 
sharp. ‘Thus, with properly made orifices, we may undoubtedly admit, with- 
out appreciable error, that commencing with a diameter equal at most to a mil- 
limetre, the diameter of the contracted section is proportional to that of the 
orifice. 
Hence, as the length of the continuous part of our imaginary vein is in pro- 
portion to the diameter of the contracted section, it will also be in proportion to 
the diameter of the orifice, at least starting from a low value of the latter, which 
must not be much less than a millimetre. 
We have only considered the case of mercury; but the principle with which 
we set out, 2. ¢., the proportionality between the partial duration of the trans- 
formation of a cylinder and the diameter of the latter, very probably applies 
-also, as we are already aware, to all other very slightly viscid liquids; conse- 
quently, in the case of any of the latter liquids, it is very probable that the 
length of the continuous part of the imaginary vein will also be in proportion 
to the diameter of the orifice. The law may also be true in regard to all liquids; 
but it may be the case that this general application does not hold good. 
If we now pass from the imaginary to the true vein, we have only to sup- 
pose that the value of the constant charge is sufficiently considerable to allow 
of the condition assumed in the preceding section being satisfied throughout 
the entire extent which we assign to the variations in the diameter of the ori- 
fice; so that, for each of the values given to this diameter, the continuous part 
of the true vein is apparently of the same length as that of the corresponding 
imaginary vein. The law which regulates this length may then be regarded 
as the same in both kinds of veins. In aceccrdance with the two remarks ter- 
minating the preceding section, it is evident that if the common charge fulfils 
the condition in question with regard to the greater value assigned to the diame- 
ter of the orifice, it will, a fortiori, fulfil it with regard to all the others. 
We are, therefore, led to the following definitive conclusion : 
In the case of mercury, and very probably also in that of all other very 
slightly viscid liquids, such as water, if for the same charge increasing values 
are given to the diameter of the orifice, from a value slightly less than a milli- 
metre to some other determinate value, and if the common charge be sufi- 
ciently great, the length of the continuous part of the vein will be proportionate 
to the diameter of the orifice. 
This conclusion is, perhaps, true in the case of any liquid whatsoever; but 
the elements for deciding this question are wanting. 
Thus, with the restrictions contained in the above enunciation, the second 
law given by Savart results necessarily from the properties of liquid cylinders ; 
and it is also evident that if, in the case of a common inconsiderable charge, 
*Tn fact, the results obtained by Hachette show (Ann. de Chim. et de Phys., t. iii, p. 78): 
shat when the diameter of the orifice is equal to or greater than 10 millimetres, the mean 
proportion of the diameter of the contracted section to that of the orifice is 0.78; that in pass- 
ing from 10 millimetres to 1 millimetre, the proportion only increases 0.83; and lastly, when 
_ the diameter is equal to 0.55 millimetre, the proportion becomes 0.88. 
