influence of Vibratory Motions. 449 
too, as under that of the double fifth, if the vibrations are prepon- 
derant, but not sufficiently so to oppose an ulterior development 
of the forces of figure, each large division will only be subdivided 
into two, so that the discontinuous part of the jet will present 
two jets only. 
It will also be admitted, that notes in the neighbourhood of 
the octave below the principal note will cause the mode of trans- 
formation corresponding to the latter note to prevail, and thus 
the sheaf will never be changed otherwise than into two jets.° 
Lastly, it will likewise be admitted, that, for notes not too far 
distant from the second octave below the principal note, the vi- 
brations will always have sufficient amplitude, and consequently 
sufficient action, to overcome the ordinary forces of figure, and 
that at the same time the divisions which they originate will 
always be sufficiently long to necessitate a subsequent subdivision 
of each of them at most into three parts, and possibly only into 
two, provided the vibrations offer a greater resistance; hence 
there will be either three or two jets. 
As to the systems of ventral segments and nodes, which are 
observed in all the jets, they are evidently occasioned by the 
acquired transversal velocities which proceed from the action of 
the vibrations. 
§ 29. It may be asked why, above the principal note and be- 
tween this and the octave below, there are no notes except those 
in the neighbourhood of the two latter, which, in the experi- 
ments described in paragraph 27, occasioned phenomena analo- 
gous to those just studied; in fact, in the case of the fifth below 
the principal note, it will easily be found that the length occu- 
pied by a group of two divisions due to the vibrations alone is 
equal to that occupied by a group of three of the divisions due 
to the forces of figure; so that if we imagine these two groups 
to be superposed and combined, there will be concurrence in the 
two contractions which form the terminations of the system, and 
conflict in the two intermediate contractions belonging to the 
second of the groups above considered ; and as the two conflicts 
would be equal, one would expect, according to our theory, to 
see the sheaf resolve itself into three jets ; lastly, and for analo- 
gous reasons, one might also expect three jets to manifest them- 
selves under the influence of the fourth, and two under that of 
the fifth above the principal note. 
But in our theory, as we have seen, the manifestation of one, 
two, or three jets in place of the sheaf assumes that the vibra- 
tions communicated to the liquid regularize what takes place in 
the jet; and for this it is necessary that these vibrations should 
have an energy of action capable of neutralizing the disturbing 
causes which tend to establish, in the successive nascent contrac- 
Phil, Mag, 8, 4, Vol, 14, No. 95, Dec. 1857. 26 
