1886.] 



On the Equilibrium Theory of Tides. 



303 



April 1, 1886. 



Professor STOKES, D.C.L., President, in the Chair. 



Dr. John Francis Jnlius von Haast (elected 1867) was admitted 

 into the Society. 



The Presents received were laid on the table, and thanks ordered 

 for them. 



^ -- 



The following Papers were read : — 



I. " On the Correction to the Equilibrium Theory of Tides for 

 the Continents." I. By G. H. Darwin, LLD., F.R.S., 

 Fellow of Trinity College, and Plumian Professor in the 

 University of Cambridge. II. By H. H. Turner, B.A., 

 Fellow of Trinity College, Cambridge. Received March 12, 

 1886. 



I. 



In the equilibrinm theory of the tides, as worked out by Newton 

 and Bernouilli, it is assumed that the figure of the ocean is at eacn 

 instant one of equilibrium. 



But Sir William Thomson has pointed out that, when portions of 

 the globe are occupied by land, the law of rise and fall of water given 

 in the usual solution cannot be satisfied by a constant volume of 



In Part I of this paper Sir William Thomson's work is placed in a 

 new light, which renders the conclusions more easily intelligible, and 

 Part II contains the numerical calculations necessary to apply the 

 results to the case of the earth. 



If m, r, z be the moon's mass, radius vector, and zenith 

 distance ; g mean gravity ; p the earth's mean density ; a the 

 density of water ; a the earth's radius ; and Ij the height of tide ; 

 then, considering only the lunar influence, the solution of the 

 equilibrium theory for an ocean-covered globe is — 



water. 



\ 3m 1 

 a-2gr*(l-i«lp) 



(cos 2 z-£) 



(1) 



* Thomson and Tait's " Nat. Phil.," 1883, § 808. 

 VOL. XL. T 



