and Mathematics to Seismology. 179 



§ 7. To form an idea of the relative importance of fa and 

 yfr 2 in the case of the earth, I have made the following selection 

 of hypothetical values for rj and n, the latter quantity being 

 measured in grammes weight per square centimetre : — 



(i.) 77 = -25, ?2 = 80 xlO 7 ; 



(ii.) "25, 35 x 10 7 ; 



(hi.) *5, 11 x 10 7 . 



According to the table in Lord Kelvin's Encyclopaedia 

 Article on Elasticity, (i.) may be regarded as representing 

 iron or steel, (ii ) as representing brass or slate of somewhat 

 low modulus, while (iii.) represents an incompressible material* 

 such as seems most compatible with the hypothesis of a homo- 

 geneous earth, naturally spherical but for rotation. According 

 to Lord Kelvin's table, the value of n in (iii.) is similar to 

 what one should expect in rock of somewhat low elasticity. 



If a be the earth's radius, p its mean density, 



g/y=4,irpa/3. 



Supposing p = 5*5, and a = 64 x 10 7 cms., we have approxi- 

 mately gpa = 35 x 10 8 grammes weight per square centimetre. 

 With the above figures, I find 



case (i.) fa/fa= 35/16= 2 roughly, 

 (ii.) 10/2= 5, 



(iii.) 350/33=11 roughly. 



The last result is likely, I think, to prove the nearest to 

 what ordinarily occurs in practice, so that the gravitational 

 effect may be expected to prove as a rule relatively small ; 

 still it ought not to be disregarded without due consideration 

 of the special circumstances. 



Pure Pressure Effects. 



§ 8. In all cases when the largest dimension of the loaded 

 area is small compared to its shortest distance from the point 

 of the surface where the slope is required, a good first approxi- 

 mation | to the surface vertical displacement — obvious on 

 inspection of (4) — is 



^ =(l-^)P/(27rnE), .... (11) 



where R denotes the distance from the centre of mass of the 

 total load P. 



* See Phil. Mag. Sept. 1891, p. 250, remembering E/»=2(l-fi ? ), 



t See Todhimter & Pearson's ' History,' vol. ii. pt. 2, art. 1498. 



