WITHDRAWN FROM THE ACTION OF GRAVITY. 8317 
the discontinuous part, we perceive that each mass must attain its first pnase 
of greatest horizontal development a little before it completely detaches itself, 
and at the moment, no doubt, when it clings to that which follows it only by a 
thread. As to the system of films of which the expansions present the ap- 
pearance when the phenomena are not altogether regular, this, as Savart has 
stated, is evidently the result of the inexact superposition of several expansions 
individually produced by successive masses: these expansions are then seen 
simultaneously, and are observed as though through one another, from the effeet 
of the persistence of their impressions on the retina. 
§ 9. It is clear that the time comprised between two phases of the strongest 
horizontal contraction, or, in other words, that which each mass oceupies in 
accomplishing a complete oscillation of form, is independent of the velocity of 
translation; consequently, the interval which a mass traverses during the time 
in question is proportionably greater as the velocity of translation is more con- 
siderable; but this interval is evidently the distance which separates the centres 
of two nodes, or the length of an expansion;* this length must therefore in- 
crease with the discharge. 
The volume of the incipient divisions thus increasing with the discharge, 
and each of these divisions furnishing an isolated mass, the volume of these 
masses must equally increase with fies discharge; now the more volume these 
masses have, the greater must be their horizontal diameter in its successive 
maxima and minima; but these maxima and minima diameters are respectively 
the diameters of the expansions and nodes; hence the diameters of the expan- 
sions and those of the nodes must also augment with the discharge. Only this 
augmentation tends towards a limit of but little extent; for the greatest volume 
which the isolated masses can acquire is evidently that which they would assume 
were the movement of translation of the liquid uniform, that is to say, were it 
that of the spheres into which might be resolved an indefinite cylinder formed 
of the same liquid and having a diameter equal to that of the contracted see- 
tion, (2d series, § 74.) 
Now, if the quantity does not vary, but we use a larger orifice, the volume 
of the divisions of the vein, and consequently that of the isolated masses, will 
be more considerable ; but the greater these masses, the less rapid must be 
their oscillations of form, and therefore the more space must they traverse in 
their descent, during one of these oscillations ; hence the length of the expan- 
sions must increase with the diameter of the orifice. As to the respective 
diameters of the expansions and nodes, it is evident, from what has been re- 
marked above, that they will increase at the same time. We see, therefore, 
from the contents of this paragraph, that the facts of No. 5 of § 8 are neces- 
sary consequences of the theory; always, however, upon the supposition that 
the vibrations are of the same period with those of the sound proper to the 
vein. We pass now to the facts of Nos. 6 and 7. 
§ 10. When the vein is not under the influence of a sonorous instrument, 
but is received in a vessel placed upon the ground, the principal cause of the 
vibratory movements transmitted by the air and the supports to the vessel 
from which the discharge takes place is the impact of the isolated masses 
against the liquid into which they fall; we perceive then that, in these move- 
ments, vibrations must prevail of the same period with those which would 
result from the impact of the masses in question against a stretched membrane, 
aud consequently the action exerted upon the vein is explained by what has 
cen stated in the preceding paragraphs. But the vibrations thus produced 
not having a great intensity, the modifications of the vein cannot acquire all 
*Tt is thus that Savart seems to consider the expansions when occupied with their length, 
and we conform to his expressions in the following paragraph; but, in reality, it is obvious 
that the space in question is composed of an expausion and two half nodes. 
