306 THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS 
the case of any other liquid, the nufaber of vibrations corresponding to a given 
charge and orifice, the value of ; referring to this liquid is also obtained by 
means of the formula (a.) If we confine ourselves to liquids, the viscosity 
of which is very slight, the values would very probably be found to differ but 
little from the preceding; and it may consequently be considered that, with 
the same charge and the same orifice, the sounds produced by the veins formed 
respectively of these various liquids are very nearly of the same pitch; but 
the case would undoubtedly be different, at least in general, if we passed to 
liquids of considerable viscosity. 
Savart says that the nature of the liquid appears to exert no influence upon 
the number of vibrations corresponding to a given charge and orifice; but he 
does not point out what the liquids were which he compared in this respect ; 
from what we have stated, it may be presumed that these liquids were some of 
those the viscosity of which is very slight. 
84. Since the partial duration of the transformation of a cylinder may evi- 
dently be taken into account, as we have already remarked, by considering 
only one of the constrictions of the figure, or simply the neck ‘of the latter, 
and, on the other hand, as this duration varies, for the same diameter, with the 
nature of the liquid, it follows that in the vein the time comprised between the 
instant at which the superficial section, which constitutes the neck of a con- 
striction, passes to the contracted section, and the instant of the rupture of the 
lixe into which this constriction is gouverted, will also vary, all other things 
being equal, with the nature of the liquid. Now, it necessarily follows from 
this, that for the same charge and the same orifice the length of the continuous 
part of the vein will vary according to the nature of the liquid; and this con- 
clusion is also in conformity with the results of experiment. In fact, as is well 
known, Savart has measured the continuous portion of four veins flowing un- 
der identical circumstances, and formed respectively of sulphuric ether, alco- 
hol, water, and-a solution of caustic ammonia, and he found the following 
lengths: 
1 DH os gee tees ears eerie SNe Pe los SOR el es Se ee as ay 90 
PAN CONG ngern cero cS ok ae See eee Oe eee eee eee 85 
WW ater ii cpcte (ole! o ter bre Guebes o eroas She rete tare TeLe Re Peeters eater eaten 70 
SAOMINOMTAS SSS wees Saw austin ee open ee eere tee attee eon eee 46 
85. Hitherto we have only entered upon the consideration of veins projected 
vertically from above downwards. Let us now consider veins projected in other 
than vertical directions. ‘These are incurved by the action of gravity, and can- 
not, therefore, be any further compared to cylinders; but we must remark, that 
the phenomenon of the conversion into isolated spheres is not the result of a 
property belonging exclusively to the cylindrical form; it appears that this 
phenomenon must be produced in the case of every liquid figure, one dimen- 
sion of which is considerable with regard to the two others; we have, in faet, 
seen the liquid ring formed in the experiment described in § 19 become con- 
verted into a series of small isolated masses, which would constitute so many 
spheres if their form were not slightly modified by the action of the metallic 
wire which traverses them. We can understand, then, that in curved veins 
divisions passing gradually to the state of isolated spheres ought also to be 
produced; consequently, the constitution of veins projected either horizontally 
or obliquely must be analogous to that of veins projected vertically from above 
downwards, which conclusion agrees, in fact, with Savart’s observations. 
This analogy of constitution must evidently extend to the ascending por- 
tion of the veins projected vertically from below upwards; only in the case of 
ne oe veins the phenomena are disturbed by the liquid which is thrown 
@ back. 
