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



haps will not care to undertake an examination of the reason- 

 ing employed in reaching it. 



Mi\ Fisher obtains this unlooked for result by discussion of 

 a formula of Prof. G. H. Darwin giving the height of the 

 oceanic tide relatively to the nucleus on the "canal theory" 

 for a yielding earth, whether the yielding is elastic or not. 

 For comparison Darwin also states the height of the relative 

 tide on the equilibrium theory for the same value of the 

 potential.* The formulas involve the lag of the tide, which 

 disappears when the case of a fluid earth or that of a rigid 

 earth is considered. 



Neglecting the lag, the formula for the " canal theory " 

 may be written 



«.-r = B( 1 -2A.ff) 



where r is the radius of the tidal water- surface, a n the radius 

 of the nucleus, R one-half the total amplitude of the tide on 

 a rigid earth, g the acceleration of gravity, A (which Darwin 

 denotes by E) the greatest semi-amplitude of the bodily tide 

 at the equator and r is three times the moon's mass into the 

 square of the earth's mean equatorial radius divided by twice 

 the cube of the moon's distance. 



The formula for the equilibrium theory under the same 

 conditions is 



R 



■(—•I) 



where the primed letters denote quantities corresponding to 

 the same letters unprimed in the other formula. 



From a comparison of the full formulas, equally applicable 

 to those given above, Darwin points out that where the one 

 formula gives high water the other gives low water. This is 

 also the main difference between the theories. + Either 

 formula gives the tide on a rigid nucleus when A is zero. For 

 a 'fluid homogeneous globe A is the same on either theory. 



Mr. Fisher draws his own conclusions from an evaluation 

 of 2A . 2<7/5r, which he computes at 2/5 nearly. He infers 

 that on the canal theory the tides cannot be less than 3/5 of 

 their height on a solid globe.J He might also by the same 



* Phil. Trans., vol. clxx. p. 26, .1879. 



\ Compare Darwin's article on tides, Enc. Brit., 9th edition, vol. xxiii, p. 354, 

 "tides inverted." The dynamical theory for an earth completely covered hy 

 the ocean would give tides of the same height as the equilibrium theory, if the 

 ocean were 3.000 fathoms deep at the equator and shoaled towards the poles. 

 In general its height depends on the distribution of depth. Ibid, section 15. 



% Proc. Cambridge Phil. Soc, vol. vii, 1892, p. 337. 



