1892.] liquid condition of the Earth's interior. 337 



We must now estimate the numerical value of ■= ■ — . 



5 r 



From the definition of t already given we have 



4 gE 4 2 (distance) 3 1 earth's mass r 



5 t 5 3 moon's mass a' 2 a 2 



_ _8_ earth fd\ 3 E 

 15 moon \a/ « ' 



= 15 0-01228 ( 60 ' 2634 )' 90902404 ' 



= 045474.fi"; 



a foot being the unit. 



If the interior is considered liquid, the bodily tide may be 

 taken equal to the equilibrium tide, which would be about If feet 

 from highest to lowest - !", and E would be half that, so that 



!#£ = 0-39789. 



O T 



The lag of such a tide would be small. Darwin seems to con- 

 sider 14' as an admissible value for 2e in that case, and cos e would 



be 0-99996C8. Hence cos e would be greater than - — , and we 



& o T 



may assume 



sin e 



4<r/E 

 cos e — - - — 



O T 



= tan D, 



and by substitution and reduction we obtain for the height of the 

 measurable tide 



- E |l - 2 cos £ x | ^ + (| ^)*l* cos {2 (</> - cot) - D), 



or, cos e being very nearly unity, 



-hU ~\^\ cos {2(0- cot)- B], 



= -Hx 0-60211 cos (2 (<f> - art) - £>}. 



Hence the tide would be fths of what it would be on a rigid 

 earth. 



It is evident that tan D is small. Hence low water will occur 

 a little west of the moon. 



* " The Moon " by Proctor, Tab. iv. p. 313. 

 t Thomson and Tait, § 804, 2nd Ed. 



