﻿THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[SIXTH SERIES.] 



JUNE 1915. 



LXXVIII. On a Tidal Problem. 

 By Prof. H. Lamb and Miss L. Swain *. 



THE object of this note is to illustrate the theory of the 

 tides in a very simple case, viz., that of an equatorial 

 canal of finite length, the tide-generating body (say the 

 moon) being supposed to revolve uniformly in the plane of 

 the equator. Simple as the question is, the results are hardly 

 intelligible without detailed numerical or graphical inter- 

 pretation. Moreover, the problem is at present almost the 

 only one which can be used to exemplify a point of some 

 importance in tidal theory. 



On Laplace's dynamical theory, as on the equilibrium 

 theory, there is necessarily exact agreement (or exact oppo- 

 sition) of phase between the tidal elevation and the forces 

 which generate it, in the case of an ocean covering the globe 

 or bounded by parallels of latitude, the depth being supposed 

 either uniform or a function of latitude only. The con- 

 spicuous and varied differences of phase which are observed 

 were accounted for in a general way by Newton f, as due to 

 the inertia of the water combined with the irregular con- 

 figuration of the actual oceans. On the other hand, Airy, in 

 his * Tides and Waves' (1845), attached great importance to 

 the action of friction, and appears to have regarded the 

 phase-differences in question as attributable mainly to this 

 cause. This view seems to have met with wide acceptance, 



* Communicated by tit e Authors. 

 + Principia, lil>. i., prop. xxiv. 



Phil. Mag. S. 6. Vol. 29. No. 174. June 1915. 3 B 



