Page:Philosophical magazine 21 series 4.djvu/15



I. ''On Ripples, and their relation to the Velocities of Currents. By, Mathematical Master at University College School, London''.

[With a Plate.]

1. LTHOUGH 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 hydrodynamical problem whose solution is here, strictly speaking, involved. 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 encountered. But instead of considering the phenomena of ripples as a particular 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 Phil Mag. S. 4. Vol. 21. No. 137. Jan. 1861.