Results of the Contraction of a Solid Globe. 15 



must be diminished by the areal contraction, or by 



2e^dt±7rz*dz. 

 at 



Hence the contribution to the surface-elevations in the 

 time dt from this shell will be 



±TTr*^ z dtdz = (±Trz' z -£Trz*)dz-Ze C ^ t dt±iTz*dz. 



... ^» = ^_i?_ 2 ^. 



dtdz -dt dt dt 



Substituting for z" 2 , and neglecting terms in e 2 , 



*&&=**'—*>£ +2eZ ) Zo a¥ dz - 2eZ dt- 

 Since z=r — x } 



dz = —dx ; 

 therefore 



I dz=— \ dx= \ dx. 



Jz J z J X 



The equation then becomes 



We are concerned only with values of x down to the level 

 of no strain, where x is about 2 miles ; so that the largest 



value of — is about 4^00? anc ^ terms in - may be neglected. 



Now 



v = const. + 



b 



Cx _!L 2 



v4/rtJo 

 where a 2 =4#£. 



We have seen that when a, or -v/4/ef, is taken for the 

 unit, 



therefore restoring a, 



,3 





« §0 — #0) §(*•— #0) 



In the present problem the order of increasing magnitude 

 is x, x 0} a, and these all vanish when t = 0. The above 



