4 M. J. Plateau on Jets of Liquid under the 
volume of the divisions necessitate corresponding variations in 
their length, so that they are longer or shorter according as the 
charge is more or less strong. 
§ 2a. Since the new hypothesis just presented is simpler, and 
since it accords theory with experiment, we shall in future adopt 
it, so that the 76th paragraph of the second series will require 
rectifying accordingly. 
This hypothesis too, like the former one, leads us to the recog- 
nition of two kinds of influences acting oppositely upon the law 
which governs the length of the continuous part of the jet when 
the charge is made to vary; here again, however, greater sim- 
plicity is attaimable. 
In the first place, we must remember that if the translatory 
movement were uniform, the proportionality to the square root 
of the charge would always be satisfied, even down to very feeble 
charges*. But if the divisions descend with the accelerated 
velocity of the liquid, and if we assume that no change results 
therefrom in the duration of their transformation, they will de- 
scribe a greater space during this transformation, so that the 
continuous part will be longer than if the acceleration did not 
exist; and the excess, compared with the length of the conti- 
nuous part in the case of uniform motion, will be considerable 
under a feeble charge, whilst it will be inconsiderable under 
very strong ones, for the latter render the translatory motion in 
the continuous part sensibly uniform. On passing, therefore, 
from the first to the second of these charges, the ratio of the 
lengths of the continuous parts which respectively correspond to 
them will be nearer unity than-if the acceleration were zero, 
that is to say, nearer unity than the ratio of the square roots of 
the charges. 
But the divisions cannot descend with accelerated velocity 
without becoming simultaneously elongated+, and hence arise 
two causes of diminution in the period of transformation. We 
know, in fact}, that the more the length of the divisions of a 
cylinder surpasses the limit of stability, the greater the rapidity 
of transformation, and, on the other hand, that the elongation 
which the jet thus experiences must diminish the thickness of 
its contractions more than that of its expansions; for on the 
former the effect of elongation is assisted, whilst on the latter 
it is opposed by the forces of figure. This second influence, 
that is to say, the diminution of the period of transformation— 
which diminution is greater the more the velocity of translation 
diverges from uniformity, or the feebler the charge—evidently 
tends to render the law more rapid than the proportionality to 
* Second Series, §§ 72 and 75. 
+ Ibid. § 76, t Ibid. § 66, 
