influence of: Vibratory Motions. ~~ AAT 
which aré ideéntical-with each other at their respective origins, 
According to this, the quantities of motion will necessarily dis- 
tribute themselves amongst the detached masses proceeding from 
these three divisions in such a manner that the last, the first, 
and the intermediate one will leave the continuous part with 
velocities respectively superior, inferior, and equal to the normal 
velocity ; and as, in consequence of the perfect regularity of the 
vibrations, exactly the same things will take place in each of the 
groups of three divisions, there can only be three different velo- 
cities in the discontinuous part. Hence if the action of the 
vibrations does not entirely efface that which, before their influ- 
ence, the forces of figure exercised freely, the sheaf will resolve 
itself into three distinct jets; and if, on the contrary, the action 
of forces of figure is completely subordinated—which ought to 
occur more easily here than in the case of the octave below the 
principal note, in consequence of the still greater amplitude of the 
vibrations—there will, as we have shown above, be but one jet. 
As to the separation into two jets, which, according to the 
experiments, also occurs under the influence of the note under 
consideration, it may be thus accounted for. When the action 
of the vibrations preponderates, and thus only the divisions which 
it determines are generated at the contracted section, the latter 
have a great length, since each occupies the place of three of the 
divisions which the forces of figure would originate; but we 
know* that every liquid figure, one dimension of which is con- 
siderable with respect to the two others, tends to divide itself . 
into detached masses: we may assume, therefore, that new forces. 
of figure develope themselves in the divisions in question, pro- 
vided the acquired transversal velocities are not sufficiently great 
to oppose the same, and that these new forces divide each of the 
divisions into two new ones by forming a contraction in the 
middle; and hence, as each of the contractions thus produced is 
evidently in conflict, the reasoning employed with respect to the 
octave below the principal note shows that two jets ought to be 
obtained. ' 
We may here remark, that the abnormal forces of figure just 
considered cannot form more than one contraction in each large 
division ; for if they formed two, so as to divide each large di- 
vision into three small ones, the latter would have the same 
length 4s those of the jet when not submitted to the influence 
of the sonorous instrument ; but for this to be possible, it would 
be necessary that the new divisions should not experience more 
resistance to their formation than when every foreign action is 
absent ; for from what takes place in cylinders+, we may con- 
* Second Series, § 85. 
+ Ibid. $§ 58 and 59, . 
