TKEMORS OVER THE SUEFACE OF AN ELASTIC SOLID. 



19 



The ratio of H' to K' is, of course, equal to that of H to K ; K' is, moreover, 

 identical with H, in conformity with the principle of reciprocity already referred to. 

 It appears, therefore, from the numerical values of H, K above given, that for X = oo 



and for X = 



H' = -03219, K' = -05921 ; 

 H' = -08516, K'= -12500. 



Again, in the case of the internal source (56) I find, for large positive values of x, 



u = - 8/cH'e- a ' / e'''> ( '->, t' = StVcK'e 'e^'' (84), 



and, for large negative values, 



u = 8K-H'e~ ai/ e 1/>( ' cx \ v = 8?'/cK'e~ a ' / e ?p(<+ " ) (85). 



The factor e~ aif indicates how the surface effect (at a sufficient distance) varies 

 with the depth of the source. 



8. If in any of the preceding cases we wish to examine more closely the nature and 

 magnitude of the residual disturbance, so far as it is manifested at the surface, it is 

 more convenient to use the system of contours shown in fig. 3. With this system we 



I i 



-K -h 



-h 



-6- 



Fig. 3. 



k K 







can so adjust matters that the radicals ^/(^ W] and ^/( 2 k") shall assume in all 

 parts of- the axis of f exactly the values a, ft with which we are concerned in formulae 

 such as (52). It is convenient, for brevity, to denote by a.', fi' the values assumed 

 by the same radicals on the two sides of the lines = h, and by a", i/ their 

 values on the two sides of the line g = k, these values being supposed determined 



D 2 



