466 O. Fisher — Rigidity not to be relied upon 



ities in physics, especially when backed by experienced geolo- 

 gists like Messrs. Clarence King and G. F. Becker : neverthe- 

 less I pray audi alteram partem. 



It will, I think, be at once admitted that these objections to 

 a yielding earth have been based upon the equilibrium theory 

 of the tides. It does not seem impossible that the equilibrium 

 theory may give a fairly good approximation to the truth in 

 the case of the bodity tides of the earth itself, although the 

 moment of inertia, and the forced period of oscillation differing 

 from the gravitational, must give rise to deviations from the 

 exact equilibrium value of the tidal distortion. But let us as- 

 sume that the bodily tide agrees with the equilibrium theory. 

 Then the pith of the objection to a yielding earth is well sum- 

 marized in Ld. Kelvin's words, " Had the solid part of the 

 earth so little rigidity as to allow it to yield in its own figure 

 very nearly as much as if it were fluid, there would be very 

 nearly nothing of what we call tides — that is to say rise and 

 fall of the sea relatively to the land, but sea and land together 

 would rise and fall a few feet every twelve lunar hours. This 

 would, as we shall see, be the case if the geological hypothesis 

 of a thin crust were true."" But this statement of the question 

 rests on the equilibrium theory of the tides, and takes no ac- 

 count of the horizontal motion of the water to which its 

 accumulation at high and diminution at low tide are due. As 

 Airy wrote, "the problem of the tides, it is evident, is essen- 

 tially one of the motion of fluids ;"f and again (one almost 

 hesitates to quote the words), " it must be allowed that it is 

 one of the most contemptible theories that was ever applied to 

 explain a collection of important physical facts. It is entirely 

 false in its principles, and entirely inapplicable in its results.";}: 



The hydrodynamical problem has never been treated fully 

 on account of its complexity, but for tides of short period the 

 canal theoiy is thought to give results most nearly in accord- 

 ance with nature. Jfow, the only investigation of the tide 

 upon a yielding earth according to the canal theory with which 

 I am acquainted is given by Professor Darwin§ but he has left 

 his result in general symbols without reducing it to a numer- 

 ical estimate. It is, however, perfectly easy on certain assump- 

 tions to supply this desideratum, all the quantities involved 

 having known astronomical values except two. These two are 

 the height of the bodily tide, and the amount of its lag. Let 

 us then suppose the earth's interior to consist of a liquid of 

 small viscoshVy, which is the case in which the ocean tide 

 ought to be most diminished. In that case the bodily tide 



* Thomson and Tait's Natural Philosophy, § 833. 



\ Encyclopaedia Metropolitana, '-Tides and Waves," § 14. 



% Ditto, § 64. § Phil. Trans. Part I, 1879. p. 23. 



