442 M. J. Plateau on Jets of Liquid under the 
respective origins, and if from that time up to their respective 
ruptures they have suffered precisely the same modifications, 
though not altogether at the same moments, it is evident that 
after these two ruptures, that is to say, when the expansion 
becomes a detached mass, the sum of the quantities of motion 
imparted to this mass by the preceding contraction will have been 
absolutely compensated. by that of the quantities of motion in an 
opposite direction, imparted to it by the contraction which fol- 
lows, and hence that this same mass will leave the continuous 
part with the velocity which corresponds exactly to the general 
motion of translation. But it is also clear, that the compensation 
would no longer be complete if at their origin the two contrac- 
tions differed from each other ; if, for example, they were unequal 
in length. Since when the divisions, and hence also the con- 
tractions, are longer the time of transformation is shorter*, it 
follows that the longer of the two contractions m question will 
develope itself more rapidly than the other; and as, in conse- 
quence of its greater length, it encloses more liquid, it will 
transfer to the expansion more particles of liquid with greater 
velocities, and consequently a greater quantity of motion. If 
this same contraction, therefore, follows the expansion, the latter 
will leave the continuous part as a detached mass with an excess 
of velocity ; but if the contraction in question is that in front, 
the mass will depart from the continuous portion with a defect 
of velocity. Thus small differences in the lengths of the nascent 
contractions will occasion small inequalities in the velocities of 
the successively detached masses ; on this account the masses will 
necessarily describe parabolz of unequal amplitudes, and hence 
they will become dispersed in a vertical plane so as to form a 
sheaf. 
This explanation assumes that the disturbing causes produce 
no irregularities in the contractions in directions perpendicular 
to the axis of the jet; and, in fact, from the experiment of para- 
graph 23, we must conclude that the contractions and expan- 
sions tend, with great force, to symmetrize themselves with respect 
to the axis, and hence that irregularities in directions normal to 
the axis cannot long exist. 
According to this explanation, too, it is evident that there are 
two extreme limits for which the dispersion is zero, viz. when the 
jet descends and ascends vertically, for in these two cases all the 
detached masses describe one and the same rectilineal trajectory +; 
* Second Series, § 66. 
+ In a jet ascending vertically, the liquid, it is true, becomes dispersed 
when falling again; but it is scarcely necessary to remark, that the latter 
dispersion is due to a totally different cause, and has nothmg in common 
with the phenomena here considered. 
