THE 
LONDON, EDINBURGH ano DUBLIN 
PHILOSOPHICAL MAGAZINE 
AND 
JOURNAL OF SCIENCE. 
[FOURTH SERIES.} 
JANUARY 1861. 
I. On Ripples, and their relation to the Velocities of Currents. 
By T. Arcuer Hirst, Mathematical Master at University 
College School, London*. 
[With a Plate. | 
. eee oe we are all familiar with the ripples which 
solid bodies produce upon the surface of a stream in 
which they are partially immersed, their precise nature and their 
relation to the velocity of the current appear to have received 
but little investigation. The reason of this is no doubt to be 
sought in the well-known difficulties presented by the hydrody- 
namical problem whose solution is here, strictly speaking, in- 
volved. Upon this problem Newton, Laplace, Lagrange, Poisson, 
Cauchy, and others have expended the greatest analytical power 
and mathematical skill, and in every case the inherent difficulties 
of the subject have compelled them to introduce hypotheses and 
restrictions which more or less vitiate the results at which they 
at length arrived. The brothers Weber, again, by their elaborate 
researches, have shown that, in the experimental investigation 
of the problem in question, difficulties of equal magnitude are en- 
countered. 
But instead of considering the phenomena of ripples as a par- 
ticular case of this general and complicated hydrodynamical 
problem, the question arises, can we not in some more direct and 
simple manner arrive at the general relation which must exist 
between these beautifully symmetric ripples, and the velocities 
of the several parts of the current upon whose surface they are 
produced. Professor Tyndall, in his recent work ‘ On the Glaciers 
of the Alps’ (p. 398), has, in fact, prepared the way for us, in his 
chapter 29, “On the ripple theory of the veined structure of 
* Communicated by the Author. 
Phil. Mag. 8. 4. Vol. 21. No. 187. Jan. 1861. 5 
