﻿688 Dr. J. R. Wilton on Ripples. 



mineral (206'06 found ; 206*2 theoretical value). As more- 

 evidence accumulates, the ratios for other geological periods 

 will be similarly tested. At present it would seem that the 

 age of the older intrusive rocks of Ceylon, as deduced from 

 Pb/U ratios in thorianite and thorite, is probably too high. 

 These ratios are nearly always greater than 0*2, giving an 

 age exceeding 1600 million years. Zircon from the same 

 pegmatites, however, gives a ratio of 0*164 (1370 million 

 years), which seems to be more probable, in the light of 

 atomic weight estimations. Zircon is much less likely to 

 contain original lead than thorite or thorianite, and apart 

 from the difficulty of estimating the very small quantities of 

 lead which have accumulated, zircon represents one of the- 

 most valuable minerals for age determinations. 



Finally, in addition to our previous acknowledgments 

 to Professors Strutt and Mache, we wish to express our 

 thanks to Professor Stefan Meyer, for his kindly interest 

 and encouragement during the progress of this work. 



LXXIL On Ripples. By J. R. Wilton, M.A., D.Sc, 

 Assistant Lecturer in Mathematics at tlie University of 

 Sheffield *. 



IN carrying the approximation to the form of a wave to 

 such an extent as is done in my paper on " On Deep 

 Water Waves" (Phil. Mag. Feb. 1914, pp. 385-394), which 

 will here be referred to as " Waves," it is important to make 

 certain that the sense of accuracy thus obtained is not 

 illusory. The present paper therefore takes up the con- 

 sideration of the corrections which have to be applied. Wo 

 shall, however, still suppose that the wave (or ripple) is 

 formed under ideal conditions, — that there is no wind, no 

 secondary disturbance of any kind, — that the " ocean " is 

 " deep " (a depth of ten centimetres will be ample for the 

 ripples we shall actually consider) and of unlimited extent. 

 With this understanding there are three things for which 

 we have to make allowance, namely : — 



(1) Surface Tension, 



(2) The formation of waves in the air, 



(3) Viscosity. 



Now the first order approximation to the velocity when 

 (1) and (2) are taken into account is known to be given by 



, 2 _ 9± P-P' , 



T 



2ir p-j-p' ' X p + p" 

 * Communicated by the Author. 



