WITHDRAWN FROM THE ACTION OF GRAVITY. 335 
analogous to the phenomena which we have just been considering? in effect, 
for the simple grave fifth of the principal sound, by way of example, it will 
readily be seen that the length occupied by the sum of two of the divisions 
due to the vibrations alone would be equal to that occupied by the sum of three 
divisions due to the configurative forces, so that by imagining these two sums 
superposed and combined, there would be a concurrence in the two constric- 
tions of which the terminations of the system would constitute a part, and con- 
flict in the two intermediate constrictions pertaining to the second of the two 
sums under consideration; and since these two conflicts would be equal, we 
might expect, agreeably to our theory, to see the sheaf give place to three jets ; 
and we might also expect, for analogous reasons, the manifestation of three jets 
under the influence of the fourth sharp, and of two jets under that of the fifth 
sharp of the principal sound. , 
But, by our theory, the appearance of one, two, or three jets in place of the 
sheaf supposes, as we have seen to be the case, that the vibrations communi- 
cated to the liquid should regulate what passes in the vein, and this requires 
that they should have an energy of action capable of neutralizing the effect of 
the disturbing causes which tend to establish, in the successive constrictions as 
they arise, inequalities of length not symmetrically distributed; now, all things 
being otherwise equal, the action of the vibrations on the vein decreasing with 
the amplitude of these vibrations, we can conceive that above the grave octave 
ef the principal sound this action may simply be insufficient, and that if it had 
been possible to augment, by a more immediate transmission or by a better dis- 
position of the system of the orifice, the amplitude of the vibrations communi- 
cated, the three sounds indicated above would have ceased to show themselves 
inactive in regard to the sheaf. ‘This will become evident, if we observe that 
the vibrations act on veins projected obliquely in the same manner as on veins 
directed vertically from above downwards, and if we recall that, in the experi- 
ments of Savart mentioned in No. 14, § 3, and explained in §§ 21 and 22, ex- 
periments in which everything was so arranged as to give great intensity to 
the vibrations communicated, the mode of transformation imparted by these 
last was completely substituted for that of the contigurative forces, even as re- 
gards sounds extending to the fifth sharp of the principal sound. 
We have spoken of the possible influence of a change in the system of the 
orifice, and this because the orifice employed in my experiments was pierced in 
a very thin plate, (being but about half a millimetre in thickness,) and hence 
this plate vibrated, perhaps with difficulty, in unison with sounds not having a 
certain degree of gravity. 
§ 30. We have now, in order to finish the theoretical examination of the 
influence exerted by vibratory movements on liquid veins, only to show the 
connexion of the theory with the facts of No. 17, of § 3. 
Since the principal sound is also that (§§ 5, 12, and 26) for which the dura- 
tion of a vibration is equal to the duration of a constriction or a dilatation at the 
contracted section, and sincé, from experiment, the number of vibrations cor- 
responding to that sound proportionally diminishes as the direction in which 
the jet is thrown departs from the descending vertical, the same is necessarily 
the case with the number of incipient constrictions and dilatations, and conse- 
quently with the number of incipient divisions. But, as the velocity of dis- 
charge of the liquid is obviously independent of the direction of that discharge, 
the number of divisions which originate in a given time can only decrease 
notably by an augmentation in the length of these incipient divisions ; hence, 
with the same discharge and the same orifice, the incipient divisions continue 
to lengthen in proportion as the direction of the emission of the vein departs 
more from the descending vertical. Now, this result is directly deducible from 
the hypothesis of § 2. In effect, while a vein directed vertically from above 
