Dr. C. Cliree on Denudation and Deposition. -195 



p = 5"5. [The assumption of uniform density is merely for 

 simplicity ; one can easily allow for variation in the density 

 with the radial distance, but this does not affect the order of 

 magnitude of u.~\ 



From the above value of u, under the conditions supposed, 

 I find 



u= —(7/13) a approx. 



In other words the earth would possess an elastic displace- 

 ment of fully 2000 miles at the surface. My own view, 

 advocated some years ago in your pages *, with, I have reason 

 to think, pretty general approval from elasticiansf, is that 

 results deduced by treating the earth as an elastic solid of the 

 normal type cannot be taken seriously unless they make the 

 strains small quantities of the order allowed by the ordinary 

 mathematical and physical theories. 



The only satisfactory way, so far as I know, of deducing 

 results consistent with perfect elasticity is to treat the earth as 

 incompressible, or very nearly incompressible, throughout all 

 but the surface strata (Dr. Stoney's 'lithosphere'). If we 

 suppose the lithosphere homogeneous and perfectly elastic, its 

 thickness d being small compared to the earth's radius a, and 

 suppose the underlying material incompressible, the displace- 

 ment vf at the surface, due to uniform surface pressure p, is 

 approximately given by J 



tt'=-3p<Z/(3A + 4n), 



where k is the bulk-modulus, and n the rigidity, for the 



lithosphere. 



If u represent as before the surface displacement on Dr. 



Stoney's hypothesis of a uniform value k for the bulk-modulus, 



we have 



/ / ci a ofc 

 u ju=6 — 



a ok + An 



Supposing n=Sk/5, the relation given by uniconstant iso- 

 tropy, which is at least a fair approximation in ordinary 

 glass, we have 



u'ju = (5d/'3a) . 



This makes u'/u about 1/80 when the lithosphere is 30 miles 

 thick. 



I do not attach any importance to the numerical estimate 



* Phil. Mag. September 1891, pp. 233-252. 



f Of, Todhunter & Pearson's 'History, .of Elasticity/ vol. ii. part 2 

 arts. 1721-1723; and Love's 'Treatise on .. Elasticity' vol. i arts 

 127, 180, &c. 



X Deducible from results in Phil. Mag', vol. xxxviii. (1894) p. 175. 



