318 THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS 
the development of which they are susceptible ; besides, these vibrations being 
but little regular, and being accompanied by slight and still more irregular 
vibrations which proceed from external noises, the phenomena cannot fail to 
be impressed by these irregularities, and it is under these circumstances, in 
effect, that Savart describes the appearance of films in the interior of the ex- 
pansions. Sih 
Savart has approximately measured, under the circumstances in question, in 
veins of water ejected by two different orifices and with different discharges, 
the lengths and diameters of the expansions as well as the diameters of the 
nodes. We deem it not superfluous to reproduce here the results of those 
measurements, in which the centimetre is assumed as unity: 
‘ 
Orifice of six millimetres diameter. 
Discharges. | Lengths of thecon-| Lengths of the | Diameters of the | Diameters of the 
tinuous part. expansions. expansions. nodes. 
4.5 40 25 | 0.9 0.70 
12 59 30 1.0 0.75 
27 82 39 i4 0. 80 
47 112 60 1.2 0. 90 
Orifice of three millimetres diameter. 
Discharges. | Lengths of thecon-| Lengths of the | Diameters of the | Diameters of the 
tinuous part. expansions, expansions. nodes. 
4.5 16 7.8 0. 50 0. 28 
> 12 20 9 0.52 0. 32 
27 41 13 0.55 0. 36 
47 5d 16 0. 60 0, 40 
We will here remark that the length of an expansion being the space tra- 
versed by a mass during the continuance of one oscillation of form, and that 
continuance being constant in the same vein, the expansions pertaining to this 
latter must, because of the acceleration of the descent, increase in length, 
beginning with the first. It is strange, therefore, that Savart, who, in another 
part of his memoir, speaks of this increase in reference to a particular experi- 
ment, should have given, in the above tables, the lengths in question as abso- 
lute; we must presume that they relate to the first expansion of each vein. 
In fact, the experiment in which Savart observed the increase of length of the 
expansions would render the effect more apparent, because the first expansion 
occurred very near the orifice. 
§ 11. lf, while the vein falls freely in the liquid of the vessel which receives 
it, we cause an instrument which yields a unison. as has been supposed in 
the preceding instances, to sound in proximity with the apparatus, then, under 
the action of these more intense and perfectly regular vibrations, the modifica- 
tions of the vein will be necessarily more distinct; that is, the limpid portion 
will appear a little thicker, the continuous part will undergo a new shortening, 
the expansions will be enlarged and the nodes reduced. Moreover, the expan- 
sions individually formed by each of the masses will be superposed in a more 
exact manner, and hence will less overreach one another towards their extremi- 
ties, so that the expansions which result from them collectively will be more 
