Stability of Superposed Streams of Viscous Liquids. 493 



The example of Zolss has been followed in taking the mean 

 of a + and a_ as a measure of the dissipation. 



The difference between the groups as regards declination 

 range is most substantial, but the difference between the 

 corresponding values of dissipation and of potential is too 

 small to possess any certain significance, and, as it so happens, 

 the smaller value of the dissipation appears in association with 

 the larger value of the declination range. 



As already explained, summaries of results obtained with 

 the Elster and Geitel apparatus have been published for a 

 number of stations abroad, and in most cases investigations 

 have been made as to the apparent association with different 

 meteorological conditions. For information on these points 

 the reader is referred to A. Gockel's " Die Luftelektrizitat " 

 and to Mache and v. Schweidler's " Atinospharische 

 Elektrizitat." 



XL IX. On the Stability of Superposed Streams of Viscous 

 Liquids. By W. J. HARRISON, B.A., Fellow of Clare 

 College, Cambridge*. 



§1. TX this paper it is shown that, if two streams of viscous 



r 



liquids are moving uniformly in laminar motion, 

 one of whic^i is superposed on the other, and both are of 

 great depth, the motion will be unstable under certain 

 circumstances for disturbances of the interface which are 

 of greater wave-length than some determinate limit f. It is 

 clear that if instability ensues in any particular case it will 

 be for great wave-lengths, comparatively speaking, and 

 not for small ones, since, in the latter case, the motion is 

 equivalent to two streams flowing with the same uniform 

 velocity, as far as the disturbance is concerned. Lord 

 Rayleigh has found a similar result when treating the 

 disturbances between two streams of a liquid moving in 

 opposite directions with uniform velocity, but separated by a 

 transition layer of liquid in which the velocity changes 

 uniformly. He says, " It appears, therefore, that so far 

 from instability increasing indefinitely with diminishing 

 wave-length, as when the transition is sudden, a diminution 

 of wave-length below a certain value entails an instability 



* Communicated by the Author. 



t It ought to be clearly stated that the stability here discussed is only 

 for the case of particular modes of disturbance, namely, those originating 

 from a disturbance of the interface. The arguments of Osborne Reynolds 

 would seem to show that the motion must be unstable for a general 

 disturbance, as there are no lateral boundaries to determine a limit to 

 the instability. 



