86 



Lord Rayleigh on 



[May 15, 



greatest. The smaller tlie causes by which, the original equilibrium is 

 upset, the more will the cylindrical mass tend to divide itself regularly 

 into portions whose length is equal to 4*5 times the diameter. But a 

 disturbance of less favourable wave-length may gain the preponder- 

 ance in case its magnitude be sufficient to produce disintegration in a 

 less time than that required by the other disturbances present. 



The application of these results to actual jets presents no great 

 difficulty. The disturbances, by which equilibrium is upset, are im- 

 pressed upon the fluid as it leaves the aperture, and the continuous 

 portion of the jet represents the distance travelled during the time 

 necessary to produce disintegration. Thus the length of the continuous 

 portion necessarily depends upon the character of the disturbances in 

 respect of amplitude and wave-length. It may be increased consider- 

 ably, as Savart showed, by a suitable isolation of the reservoir from 

 tremors, whether due to external sources or to the impact of the jet 

 itself in the vessel placed to receive it. Nevertheless it does not appear 

 to be possible to carry the prolongation very far. Whether the resi- 

 duary disturbances are of external origin, or are due to friction, or to 

 some peculiarity of the fluid motion within the reservoir, has not been 

 satisfactorily determined. On this point Plateau's explanations are not 

 very clear, and he sometimes expresses himself as if the time of dis- 

 integration depended only upon the capillary tension, without reference 

 to initial disturbances at all. 



Two laws were formulated by Savart with respect to the length of 

 the continuous portion of a jet, and have been to a certain extent 

 explained by Plateau. For a given fluid and a given orifice the length 

 is approximately proportional to the square root of the head. This 

 follows at once from theory, if it can be assumed that the disturbances 

 remain always of the same character, so that the time of disintegration 

 is constant.* When the head is given, Savart found the length to be 

 proportional to the diameter of the orifice. From (8) it appears that 

 the time in which a disturbance is multiplied in a given ratio varies, 

 not as d, but as di . Again, when the fluid is changed, the time varies 

 as pi T - 4. But it may be doubted, I think, whether the length of the 

 continuous portion obeys any very simple laws, even when external 

 disturbances are avoided as far as possible. 



When the circumstances of the experiment are such that the reser- 

 voir is influenced by the shocks due to the impact of the jet, the dis- 

 integration usually establishes itself with complete regularity, and is 

 attended by a musical note (Savart). The impact of the regular 

 series of drops which is at any moment striking the sink (or vessel 

 receiving the water), determines the rupture into similar drops of the 

 ]3ortion of the jet at the same moment passing the orifice. The pitch 



# For the sake of simplicity, I neglect the action of gravity upon the jet when 

 formed. The question has been further discussed by Plateau. 



