influence of Vibratory Motions. 451 
-tion due to gravity, on the other hand, a vertically ascending jet 
tends to become thicker in consequence of the retardation due 
‘to the same cause; and since, according to the hypothesis in 
question, and the therein assumed dependence between the divi- 
‘sions, the thinning of the vertically descending jet determines a 
diminution in the length of the nascent divisions, the thickening 
of the vertically ascending jet ought, for the same reason, to de- 
termine an increase in the length of the nascent divisions ; 
whence it follows, that as the direction of efflux passes gradually 
from the first to the second of these cases, the nascent divisions 
will become elongated by degrees. 
As may be seen from the No. under discussion, between 
the descending vertical and the horizontal direction of the jet 
the depression of its principal note is inconsiderable, but becomes 
greater between the latter and the vertically ascending direction, 
which necessitates the same relations between the elongations of 
the nascent divisions. This fact flows also from the hypothesis 
of paragraph 2; for the yertically ascending jet, in consequence 
of the gradual destruction of the velocity of the liquid, has a 
greater tendency to become thick (especially at its upper extre- 
mity), than has the vertically descending jet to become thin at 
an equal distance from the contracted section ; hence, in virtue 
of the same mutual dependence of the divisions, when the jet, - 
issuing first in a horizontal direction, is made to approach the 
ascending vertical, the successive increments in the length of the 
nascent divisions ought to be much greater than when the jet, 
starting from the vertically descending, gradually approaches the 
horizontal direction. 
Observed facts being thus connected in a necessary manner 
with the hypothesis of paragraph 2, serve reciprocally to confirm 
the latter; and it was to these facts that we alluded when, in 
paragraph 2, we intimated that the hypothesis in question was 
supported by experimental results. 
§ 31. In concluding the Second Series, we announced that in 
the present one, after having completed that which relates to jets 
of liquid, we should treat of the other figures of equilibrium 
besides the sphere and the cylinder; but, in order to avoid ex- 
tending our memoir too much, we have resolved to reserve this 
subject for future series*. 
* At the end of the above memoir the author adds a note, wherein he 
briefly describes the researches of Hagen, Billet-Sélis, Dejean and Magnus, 
which appeared during the interval between the publications of his own 
second and third series of Researches. His last memoir, however, “On 
the recent Theories,” &c., which appeared in the Philosophical Magazine 
for October 1856, renders the translation of this note here unnecessary.— 
TRANS. 
2G2 
