G. F. Becker — Fisher's New Hypothesis. 139 



process have concluded that the tides would show a corres- 

 ponding amplitude on the equilibrium theory, as appears from 

 the formulas stated above. 



Mr. Fisher's computation is incorrect because he takes for 

 A the value which it would have for a fluid globe, homo- 

 geneous or not, were there no mutual attraction between the 

 fluid particles. It was for the purpose of dealing with the 

 effect of this mutual attraction that the method of u spherical 

 harmonics" was evolved. The effect in the case of a fluid 

 globe of uniform density throughout on the equilibrium theory, 

 is well known to be an increase in the ellipticity in the ratio 

 1 to 1-3/5. The ellipticity, e, of the equilibrium lunar tide, 

 in a fluid earth, with this distribution of density, composed of 

 mutually attracting particles is 



_ 5 3 a 3 M 

 6 ~ ~2 ' ~2 ' D^E' 



where (as in Thomson and Tait, Nat. Phil.) a is the earth's 

 mean equatorial radius, D the moon's distance, E the earth's 

 mass, and M the moon's mass.* 



Since the ellipticity is small, it is easy to see that 2A=$<? 

 and therefore also, since for this case ~E/a?=g, substitution for 

 A and r of the values assigned to them above gives 



2g 5 3 a 4 M 2 E 2 D 3 



' br " 2 2 D 3 E 5 ' a- ' 3 Ma 



2 ) 



and here the second member reduces to unity by cancellation. 

 In general, therefore, or irrespective of the fluidity of the 

 earth, the quantity 2 A . 2^/5r is simply the ratio of the 

 greatest bodily equatorial tide in any special case to the equi- 

 librium tide on a fluid earth. Thus for a fluid earth the canal 

 theory and the equilibrium theory give the same result, viz : 

 no relative tide, or 



1 — 2A . 2g/5r = 0. 



On any theory yet propounded for the tides, the existence 

 of semi-diurnal tides indicates an earth presenting great resist- 

 ance to deformation. This resistance, so far as the tides are 

 concerned, may be due either to rigidity or to the viscosity 

 of an ultraviscous fluid, some 20,000 times as viscous as 

 hard brittle pitch at 34° F. In the same paper by Darwin 

 quoted above, he comes to the conclusion " that no very con- 

 siderable portion of the interior of the earth can even dis- 

 tantly approach the fluid state." 



Washington, D. C, June, 1893. 



* Compare Nat. Phil., section 819. 



