1. The problem of wave-motion in a fluid of variable density 
was attacked in 1883 by Lorp RavLEIGH!, with a view to studying the 
stability conditions which, according to HELMHOLTz’s suggestion, govern 
the formation of cirrus clouds. Lord RAYLEIGH considers two otherwise 
unlimited fluids of different densities, separated by a horizontal stratum 
whose density, according to a special law of transition, gradually 
changes from one value to the other. From a more general point of 
view, the theory of waves in heterogeneous liquids has been dealt with 
by BunNsipE? and LovE?, 
Lord RAYLEIGHS problem may be described as dealing with the 
propagation of waves on a diffused boundary, and is one which, freed 
from restrictions as to special laws of density-variation ete., is of like 
importance to hydrography and meteorology. The following note gives 
a general result which is quantitatively interpreted with the practically 
well-founded restriction that the waves considered have a small wave- 
length compared with the thickness of the layer of density transition. 
The result is presented in the form of a correction to be applied to 
Stokes’ well-known formula for the velocity of propagation of waves 
on à non-diffused boundary. 
We may diseuss also a more general problem, including the 
above as a special ease, by considering two uniform liquids animated 
by different horizontal velocities. Friction and diffusion combined will 
cause the fluids to mix with each other at the surface of separation, 
and a layer is soon formed in which there is a gradual transition of 
‘| »Investigation of the Character of the Equilibrium of an incompressible Heavy Fluid 
of Variable Density». Proc. Lond. Math. Soc. t. XIV (1883). 
2 Proc. Lond. Math. Soc. t. XX (1889). 
> Proc. Lond. Math. Soc. t. XXII (1891). For special recourse to the related pro- 
blem in the theory of »Temperature Seiches», see also WrppEnBunN, Edinburgh Trans: (1912). 
Nova Acta Reg. Soc. Sc. Ups., Ser. 4, Vol. 4, N. 2. Impr. ?/e 1915. 1 
