. [ m ] 



XLIV. Denudation and Deposition. 

 To the Editors of the PhilosopJiical Magazine. 

 Gentlemen, 



DR. G. Johnstone Stoney's paper on this subject in 

 your April number will, I think, somewhat startle 

 practical men, whether geologists or engineers. If I lightly 

 understand him, he concludes that to increase the radius of 

 the earth one has only to remove its surface-layers, and con- 

 versely. The problem which Dr. Stoney considers on p. 373 

 is simply that of an elastic solid sphere of uniform bulk- 

 modulus (resistance to compression) acted on by a uniform 

 surface pressure. If p be the pressure, a the radius, and 

 k the bulk-modulus, the surface displacement, as is well- 

 known, is 



u= —pa/3k ; 

 and if one puts 



a= 64 x 10 7 centim., 



*= 423 x10V, 



i. 6\, if one supposes a to He the earth's radius, g ' gravity ' at 

 its surface,^* the pressure due to a layer 1 centim. deep of water, 

 and k the largest value quoted for the bulk-modulus of glass 

 in Lord Kelvin's Encyclopaedia article — one gets in agree- 

 ment with Dr. Stoney 



u= — 0'5 centim. approx. 



If, however, Dr. Stoney treats the earth as perfectly elastic 

 throughout for pressure introduced by the action of its 

 gravitation on fresh surface material, it is difficult to see how 

 he can avoid treating it as also perfectly elastic so far as con- 

 cerns the gravitational forces between the already existing 

 material. It may be legitimate enough to hold that the deep- 

 seated material has had its elasticity, so to speak, " killed " 

 under the enormous pressure to which it is exposed ; but 

 this view does not appear consistent with treating this identical 

 material as responding like glass to a slight increment of 

 exactly the same type of pressure stress. To see the nature 

 of the results to which we are led by the hypothesis that the 

 earth as a whole behaves like glass, let us glance for a moment 

 at the expression for the surface displacement due to the 

 mutual gravitation of a homogeneous elastic sphere, viz., 



u= — gpa 2 /U)kj 



when we ascribe to a and k the values quoted above, and put 



