due to Elasticity of the Earth's Surface. 411 



_ gwh 



a "^ t K 1+ i) r4,am i 



2v b 



dot. gwh/^ , :c\ .. . z 



(2)* 



The first of these gives the vertical displacement, the second 

 the horizontal, and the third the inclination to the horizon of 

 strata primitively plane. 

 At the surface, 



«=^cos|, y =0,j 



do. gicli . z [ ( 3 ) 



dz 2v b J 



Hence the maximum vertical displacement of the surface is 

 ±gichb/2v, and the maximum inclination of the surface to 

 the horizon, is 



± cosec V x gwh 1 2v seconds of arc. 



Before proceeding further, I shall prove a very remarkable 

 relation between the slope of the surface of an elastic horizontal 

 plane and the deflection of the plumb-line caused by the direct 

 attraction of the weight producing that slope. This relation 

 was pointed out to me by Sir William Thomson, when I told 

 him of the investigation on which I was engaged ; but I am 

 alone responsible for the proof as here given. He writes that 

 he finds that it is not confined simply to the case where the 

 solid is incompressible; but in this paper it will only be proved 

 for that case. 



Let there be positive and negative matter distributed over 

 the horizontal plane according to the law ic h cos (zj b): this 



* It is easy to verify that these values of « and y, together with the 

 value p=gwl\e— x l h cos zb for the hydrostatic pressure, satisfy all the con- 

 ditions of the problem, hy giving normal pressure ffw7i cos z b at the free 

 surface of the infinite plane, and satisfying the equations of internal equi- 

 librium throughout the solid. I take this opportunity of remarking that 

 the paper froni which this investigation is taken contains an error, inas- 

 much as the hydrostatic pressure is erroneously determined in section 1. 

 The term — "W* should be added to the pressure as determined in (8). 

 This adds TV to the normal stresses P, Q, R throughout the paper, but 

 leaves the difference of stresses (which was the thing to be determined) 

 unaffected. If the reader should compare the stresses as determined from 

 the values of «, y in the text above, and from the value of p given in this 

 note, with (38) of the paper referred, to, he is warned to remember the 

 missing term AV. 



2E2 



