440 M. J. Plateau on Jets of Liquid under the 
and stopping about midway between the two; by this means the 
oil was accumulated in greater quantity towards the other disc, 
in such a manner, however, that during the whole time the figure 
never ceased to regulate itself with respect to its axis; that is to 
say, it always remained a figure of revolution, and thus presented 
an expansion and a contraction similar to those which result from 
a spontaneous alteration. Now as long as the diameter of the 
greatest circular section of the expansion did not exceed about 
41 millims., the mass, when left to itself, gradually reassumed 
the cylindrical form; but when the diameter in question attained 
41 millims., the mass, when left free, continued spontaneously 
to deform itself, and concluded by becoming disunited. 
In this experiment the artificial deformation necessary to de- 
termine the spontaneous continuation of the phenomenon was 
considerable; for, according to approximative measurements, when 
the diameter of the greatest circular section of the expansion was 
4] millims., that of the least circular section of the contraction 
was only 15 millims., so that the latter was scarcely a third of 
the former: we must not forget, however, that the ratio between 
the length and the diameter of the cylinder was below that which 
in the jet of water corresponded to the fifth above its principal 
note*. Moreover, there are two other reasons why the passage 
of the note of the jet toa fifth above ought to be brought about 
by vibrations which directly would produce a much smaller de- 
formation. For, in the first place, after the immediate action of 
the vibrations, the deformation ought to increase in virtue of the 
velocities acquired (§ 6); and, in the second place, since the 
divisions, and consequently the expansions and contractions, 
become elongated during their descent (§ 2a), the sum of the 
lengths of an expansion and a contraction, which was at first less 
than the limit of stability, soon approaches that limit; so that 
the progress of the transformation, according to the abnormal 
mode originally imparted, becomes more easy. 
§ 24, Thus theory accounts for all the phenomena resulting 
from the action of vibrations upon jets descending vertically, at 
least for all those described by Savart in a precise manner ; let 
us now pass to jets issuing in other directions. 
In the first place, simce in these jets there is also a gradual 
transformation into detached masses, foreign notes ought neces- 
sarily to exercise upon them an influence analogous to that. which 
they exercise upon jets falling vertically ; No. 15 of paragraph 3, 
therefore, requires no explanation. 
§ 25. With respect to No. 16 it is otherwise. If all the divi- 
sions on attaining successively the extremity of the continuous 
* An error in the construction of the small apparatus caused the ratio 
to be 2°8 instead of 2°92. 
