influence of Vibratory Motions. 5 
the square root of the charge, and consequently its tendency is 
opposed to that of the first influence. 
Lastly, there is a third influence opposed to the preceding 
one, and hence of the same kind as the first. As we have already 
remarked on concluding the second paragraph, the nascent divi- 
sions must be shorter the more feeble the charge ; but according 
to what has been above remarked, this shortening, by diminish- 
ing the excess in the length of each division beyond the timit 
of stability, ought to tend to augment the period of trans- 
formation. 
Consequently the 78th paragraph of the second series relative 
to the neutralization of the two opposite kinds of influences, and 
hence to the manifestation of Savart’s laws from moderate 
charges upwards, still holds true; it must be borne m mind, 
merely, that the influences to which it refers are not precisely 
those indicated in the 77th paragraph of the same series, but, as 
may be seen, are somewhat simpler. 
The second part of the 82nd paragraph (2nd series), however, 
in which we sought to establish @ priori the conditions under 
which Savart’s laws respecting the tones produced by jets are 
realized, cannot now be maintained ; for the considerations there 
presented are founded upon the first hypothesis. Reasoning 
according to the new hypothesis, we will remark, that as the 
charge increases, the jet issuing from a given orifice approximates 
more and more to what it would be were there no acceleration, 
and consequently the length of the nascent divisions converges 
towards what it would be in such a case; whence by virtue of 
the first part of the same paragraph 82, the laws of Savart will 
necessarily be satisfied from smaller, sufficiently strong charges 
upwards. This constitutes all that the new hypothesis can fur- 
nish respecting the conditions in question; it does not permit 
us to determine the smallest charge under which the same com- 
mence to be fulfilled, for it provides us with no accurate data for 
calculating the length of the nascent divisions. 
Lastly, it will also be necessary to rectify the commencement 
of paragraph 83 (second series), which establishes, by the first 
hypothesis, the approximate uniformity in the velocity with which 
the contractions are carried over the space corresponding to a 
nascent division. According to the new hypothesis, the trans- 
latory motion of these contractions coincides with that of the 
liquid itself, and consequently we may calculate with exactitude 
—for the charge and orifice employed by Savart—by how much 
the velocity has augmented at a distance from the contracted 
section equal to six times the diameter of the latter, 7. e. ata 
distance evidently greater than the length of a nascent division : 
the augmentation thus obtained scarcely exceeds a hundredth. 
