WITHDRAWN PROM THE ACTION OF GRAVITY. 319 
massed on each other, and the nodes which separate the latter will seem to be 
elongated. And such, in reality, as we sce by No. 7 of § 3, is the state of the 
vein under the influence in question. 
The phenomena would be much more regular still if the vein were originally 
withdrawn from all extraneous influence, and Savart, in fact, speaks of the 
great regularity of the expansions which show themselves when such a vein is 
received on a stretched membrane, which then serves as a sonorcus instrument 
yielding an unison. 
§ 12. When the instrument, which is made to resound in the vicinity of the 
apparatus, yields a tone not in unison with that appropriate to the vein, the 
vibrations no longer succeeding one another at the same intervals occupied by 
the passage of the dilatations and constrictions due to the configurative forces, 
there can be no uninterrupted concurrence between the two species of action; 
but neither can these be incessantly in conflict, and it is obvious that from this 
alternation of accord and opposition must result effects of a very complicated 
kind. We will attempt, however, to discriminate to a certain point what then 
occurs in the vein. 
To simplify as far as possible, we will suppose extraneous action to be pre- 
viously annulled. During the succession of the phenomena let us seize, in 
thought, the instant when the middle of a constriction due to the configurative 
forces traverses the contracted section precisely in the middle of the duration 
of an ascending vibration; this vibration will then evidently®concur with the 
configurative forces to deepen the constriction. But if the sound of the in- 
strument is sharper than that of the vein, and the vibration has therefore less 
duration than the passage of the constriction, a part, more or less considerable, 
of the base of the latter will have been in conflict with the end of the de- 
scending vibration which has preceded, and an equivalent part of the summit 
will be equally in conflict with the commencement of the descending vibration 
which follows, since these descending vibrations tend to dilate the portions of 
the vein on which they act. If, on the contrary, the sound of the instrument 
is graver than that of the vein, it is clear that the concurrence will take place 
for the whole of the constriction, but that the commencement of the vibration 
will have been in conflict with the upper part of the preceding dilatation, and 
that the close of this vibration will be in conflict with the lower part of the 
succeeding dilatation. ‘ 
It is easy to perceive that after a certain number of vibrations an identical 
effect will be produced; that is, that the middle of an ascending vibration will 
coincide anew with the middle of the passage of a constriction, that the same 
thing will still recur after a number of vibrations equal to the preceding, and 
so on, periodically, at equal intervals. If, for instance, the duration of a vibra- 
tion be % of that of the passage of a constriction or a dilatation, the total dura- 
tion of six double vibrations, each composed of an ascending and a descending 
vibration, will be equivalent to the total duration of the passage of five con- 
strictions and five dilatations; now, it is easy to perceive that if we commence 
computing this duration at the instant of one of the above coincidences, it will 
also terminate at the instant of a like coincidence; m our example, therefore, 
the coincidences will be reproduced successively after intervals equal to the 
duration of six double vibrations. Let us now endeavor to: discover what 
passes during each of these intervals, or, in other words, between one coinci- 
dence and the following. 
With that view let us examine what takes place at the moment when the 
first half of one of these intervals terminates. In the example we have taken 
we shall evidently be then at the middle of an ascending vibration; but if we 
reflect that the interval commences at the passage of the inception of a division 
(§ 4) and exactly comprises the passage of five entire divisions, we shall reeog- 
nize that the end of its first half js the instant of the passage of the middle 
