110 
Proceedings of Boyal Society of Edinburgh. [sess. 
Note on Ripples in a Viscous Liquid. By Prof. Tait. 
(Read March 3, 1890.) 
The following investigation was made in consequence of certain 
peculiarities in the earlier results of some recent measurements of 
ripples by Prof. Michie Smith, in my Laboratory, which will, I hope, 
soon be communicated to the Society. These seemed to suggest 
that viscosity might have some influence on the results, as might 
also the film of oxide, &c., which soon gathers on a free surface of 
mercury. I therefore took account of the density, as well as of 
possible rigidity, of this surface layer, in addition to the surface 
tension which was the object of Prof. Smith’s work. The later 
part of the paper, where Cartesian coordinates are employed, runs 
somewhat on the lines of an analogous investigation in Basset’s 
Hydrodynamics. My original object, however, was different from 
his, as I sought the effects of viscosity on waves steadily maintained 
by means of a tuning-fork used as a current interruptor ; not on 
waves once started and then left to themselves. Besides obtaining 
his boundary conditions in a singular manner, I think that in his 
§ 521 Mr Basset has made an erroneous investigation of the effects 
of very great viscosity. 
The stress-function in a viscous liquid may be obtained {Phil. 
Mag ., Jan. 1890) from that in an elastic solid, by substituting 
velocity for displacement ; in the form 
cf)0) = — + VStotf-) — (c — |/*)(oSV cr ~ • • (1) 
where, in order to include the part of the pressure which is not due 
to motion, we must write p instead of the quantity 
Here er is the vector velocity of an element at p, and p. is the co- 
efficient of viscosity. 
Hence, supposing the volume of the element to be unity, we have 
for the equation of motion 
is-gj- = - V(eP) + ff<\Mvds 
= - v(» + eP) - mv§- + jvs v-). 
