734 



JOSEPH BARRELL 



shown, as illustrated in Fig. 15, that in passing uniformly and 

 horizontally through the crust on a line at right angles to the 

 direction of the ridges, the stress axes revolve with a uniform 

 angular velocity. In relation to depth, the maximum stress- 

 difference, as shown in Figs. 15 and 16, occurs at a depth equal to 



— of the wave-length and is then equal to 2 gwhe'"- or in gravitation 



units of force to o. jT^Gwh, in which h is the height from the mean 

 plane to the top or bottom of the undulations and w is the weight 

 of a unit volume. 



X + X 



j Surface of maximum slress 

 32 kilomet-er5 



^ ^— Depfh of i22Kilomerers 



h — Wave-lengt-h 200 kilomefers — J 



Fig. 15. — Diagram showing in vertical s ection uncompensated harmonic moun- 

 tains and valleys with relative magnitude and direction of stress-differences, which 

 they impose on the crust below. Mountain crests drawn as 5 km. above vaUey 

 bottoms. Wave-length 200 km. Stresses shown to a depth of 122 km. Maximum 

 stress for this wave-length is at 3 2 km. 



It is important to note that the value of this maximum depends 

 only on the height and density of the mountains and is independent 

 of the distance from crest to crest. The depth at which this maxi- 

 mum is reached depends, on the other hand, upon the wave-length 

 and not upon the height or density of the mountains. The effect 

 of a doubhng of the wave-length upon the vertical distribution 

 of the stress-differences is shown in Fig. 16. 



It is seen that the lateral pressure due to the elevations, instead 

 of being at the surface as it would be under hydrostatic conditions 

 or as in completely compensated mountains and valleys with the 

 special distribution of density assumed by Love,'' is at a depth of 

 about one-sixth of the wave-length. The maximum stress is, fur- 

 thermore, but 37 per cent of the full amount of the hydrostatic 



' Some Problems of Geodynamics (19 11), chaps, ii and iii. 



