Elastic Equilibrium of Semi-Infinite Solid. 3^ 



north or south. ^^ Various explanations of this anomaly have been 

 proposed, among them one, suggested by Prof. A. E.H. Love,^^ 

 is that a possible cause may perhaps be found in the efïect of the 

 tide wave in the North Atlantic. Recently Prof. A.A. Michelson^^ 

 has found a similar result in his arduous task of measuring the 

 lunar perturbation of a very long water-level at Chicago. Prof. 

 Sir J. Larmor kindly suggested to me a query whether the excess- 

 pressure of the tide in the North Atlantic would affect much the 

 measurement of the water-level at Chicago, owing to the depression 

 of the solid earth that it would produce. A calculation is under- 

 taken in order to ascertain to wdiat extent the consideration of the 

 tilting of the ground is important for the explanation of this 

 geodynamical discrepancy; we may in a first estimation neglect 

 the curvature of the earth. ^^ 



II. Solution of Equation of Equilibrium, 



§5. The equation of equilibrium of an isotropic elastic body 

 free from the action of a body force is 



curl curl «. = ^ grad A, {\) 



where u denotes the displacement, / and !^ Lame's constants which 

 specify the elastic nature of the body concerned,' and A is the 

 amount of dilatation defined by the equation 



J = èiwn. (2) 



Our first object is to find the solution of the equation of 

 equilibrium, which is appropriate for the discussion of the problem 

 concerning a semi-infinite elastic body. 



Since div. curl of any vector quantity vanishes, if we perform 

 the operation div on both sides of equation (1) we have simply 



div grad J = 0, (3) 



1) A similar result has been found by A. Orloff at Dorpat and T. Shida at Kyoto. 



2) Some Problems of Geodynamics, Cambridge, (1911) p. 8S. 



3) The Astrophysical Journal, vol. 39 (1914) p. 105-. 



4) The geodynamical application will appear shortly in the Trans. Roy. Soc. London. 



