ON THE MEASUREMENT OF THE LUNAR DISTURBANCE OF GRAVITY. 107 



tain chains, and if tlie axis of x be drawn vertically downwards, then the 

 equation to the mountains and valleys is supposed to be 



x = — h cos 



6' 



so that the wave-length from crest to crest of the mountain ranges is 27r&. 



The solution may easily be found from the analysis of section 7 of the 

 paper referred to. It is as follows : — 



Let a, y be the displacements at the point x, z vertically downwards 

 and horizontally (a has here the opposite sign to the a of (44)). Let w be 

 the density of the rocks of which the mountains are composed ; g gravity ; 

 V modulus of rigidity, then 



1 , dW 

 2v dz 



-.rib 



where W= — gwh e cos 



h J 



(1) 



6J 



(2)' 



The first of these gives the vertical displacement, the second the hori- 

 zontal, and the third the inclination to the horizon of strata primitively 

 plane. 



At the surface 



qwh 7 s A I 



a = ^-— b cos -, 7 = 

 Zv 



da gwh 



(3) 



dz 



sm- 



Hence the maximum vertical displacement of the surface is + gwhl/2vy 

 and the maximum inclination of the surface to the horizon is 



Hh cosec 1" X givhl2v seconds of arc. 



' It is easy to verify that these values of o and y, together with the value 

 p = gwh e -^l'> cos zjb for the hydrostatic pressure, satisfy all the conditions of the 

 problem, by giving normal pressure gwh cos zjb at the free surface of the infinite plane, 

 and satisfying the equations of internal equilibrium throughout the solid. I take 

 this opportunity of remarking that the paper from which this investigation is taken 

 contains an error, inasmuch as the hydrostatic pressure is erroneously determined in 

 section 1. The term - W should be added to the pressure as determined in (3). 

 This adds W 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 o, y in the text 

 above, and from the value of jp given in this note, with (38) of the paper referred to, 

 he is warned to remember the missing term 11'. 



