and Mathematics to Seismology. 187 



plicated. Its general character will be sufficiently compre- 

 hended from the results in the case of symmetry, when 



#2= -3/1 = ^. 



Putting Xl = c, #2 = e + 2a, 



we then convert (14) into 



47rw /div\ x =y=° 

 p \a\c) 2=z 



= 2(l-») loo-^ + ^ + <? + *')( -& + yy+(c + 2q)«+j«) 

 & (-" + i/ft» + c> + ^)(6 + V& 2 + (c + 2a) 2 +^ 2 ) 



So long as zje is small the right-hand side of (29) can be 

 expanded in a rapidly converging series of the form 



A+B(«/ C )» + ..'., 



where A and B are independent of z. 



There is no tendency in B/A to become very large for 

 finite values of a/c and b/c. 



When we neglect B(z/c) 2 &c, we simply get the slope at 

 the surface. We thus see that at depths small compared to 

 the shortest distance of the loaded area the slope is nearly the 

 same as at the surface itself. 



The value of B is easily obtained in special cases. As an 

 example, take the sub- case of fig. 4, in which c/a and b/c are 

 both supposed small. We then get for the slope 



In (30) constant terms of the order (b/c)* are omitted, though 

 possibly more important than the variable term. 



Again, in the sub-case of fig. 5, when b/c and c/a are sup- 

 posed both small, we find 



In both these instances the slope increases with the depth. 

 The formulae hold only so long as z/c is small, so that the 

 phenomenon is rather of theoretical than practical importance. 

 Though somewhat opposed to a priori conceptions, this result 

 would not appear exceptional. Thus, take the case of an 



Q2 



