1894.] of the interior of the earth. 135 



that connection that my mistake occurred. Desiring to ascertain 

 the amount of diminution of the tide in an equatorial canal, 

 I chose for the tidal deformation of a liquid globe an inapplicable 

 value, viz. If feet from highest to lowest. I took this estimate 

 out of Thomson and Tait's Nat. Fhil} but, as Mr Becker of the 

 U.S.A. geological survey has pointed out, I unfortunately over- 

 looked the condition on which it had been obtained, which was 

 that there should be no mutual attraction among the particles 

 of the liquid^ interior. The use of this number led to the 

 incorrect result, that the diminution of the ocean tide would be but 

 small, and I concluded that more importance had been attached 

 to this point than it possessed. 



I have lately calculated what would be the tidal deformation 

 of a liquid earth owing to the attraction of the moon, supposing 

 Laplace's law of density to obtain. The method followed was 

 simply to substitute the moon's potential in place of that of the 

 centrifugal force in the usual calculation of the earth's figure 

 by means of Laplace's functions. The result that I obtained was 

 a deformation of 3'45 feet, or 6'90 feet from highest to lowest. 

 Whether this is to be found in text books I do not know. 



The first three pages of the paper referred to consequently 

 lose their force. But if the tidal objection can momentarily be 

 waived, I think the remaining portion of the paper contains 

 among other things a forcible argument in favour of liquidity, 

 owing to the accumulation of the heat generated in the central 

 parts by tidal friction during the lengthening of the lunar day in 

 the lapse of ages^. 



This being so I am encouraged to make another attempt to 

 find a way of escape from the tidal argument for rigidity. 



The potential at a distance r from the centre of a liquid 

 sphere deformed by the moon's attraction may be expressed by 

 the formula 



ga 

 r 



+ ga€(i,-fM') + TQ-f,% 



where a is the earth's mean radius (i.e. of the undeformed sphere), 

 e the ellipticity caused by the moon's attraction (a negative 

 quantity), and /uu is the cosine of the angle between r and the line 

 joining the centres of the earth and moon, and 



_ 3 



moon s mass 



^ (distance)* 



~ ^ jyi^ ' 



1 2nd Ed. § 804. 2 Ibid. § 799. 



3 There is an obvious erratum at p. 340 regarding the lunar day. For " The 

 present " read " Suppose the". 



