115 
1889-90.] Prof. Tail on Ripples in a Viscous Liquid. 
When fi and m are small, this is approximately 
R + 2 mm 2 = en 2 - igr 2 m . 
There is no other term in the first power of m, independent of g ; 
so that, to this degree of approximation (which is probably always 
sufficient), the dust layer has no effect except to increase R. When 
there is no viscosity this increases the ripple-length ( i.e ., diminishes r) 
for a given period of vibration. 
When terms of the first degree in the viscosity are taken account 
of, the effect on n (for a given value of r ) is merely to add to it 
the pure imaginary 
2/xr 2 t/(e — 2 mr ) , 
whose value increases alike with m and with r. 
Thus the period is not affected, but the surface layer aids viscosity 
in causing waves to subside as they advance. 
This investigation above may be easily extended to the case in 
which a thin liquid layer is poured on mercury to keep its surface 
untarnished. The only difficulty is with respect to the relative 
tangential motion at the common surface of the liquids. 
The Determination of Surface-Tension by the Measure- 
ment of Ripples. By C. Michie Smith. 
(Read March 17, 1890. ) 
Professor Tait has shown* that accurate determinations of surface- 
tensions would be obtained if we could measure the rate of propaga- 
tion of ripples set up by the vibration of a tuning-fork of known 
pitch. The relation between the rate of propagation ( v ) of the 
ripples and the surface-tension (T) is given by the formula 
gX 27 r T 
2tt X p 
where X is the ripple-length and p the density of the liquid. If for 
v we write X/t, where t is the vibration period of the fork, the 
equation can be written 
_XV _ gX 2 p 
2t rt 2 4t r 2 ' 
Proc. Roy. Soc. Edin., 1875, p. 485. 
