Discontinuity in a Rotationally Elastic Medium. 609 



Now in order to use the dynamical equations, we must find 

 the influence of a first-order discontinuity upon the derivatives 

 of the second order*. We shall use the following notation : — 



To form the relations of identity as before, we proceed to 

 the second variation on S of the equation 



[?] = constant; 

 then we obtain 



&+g]*+g]*+K]*-* • (15) 



• • (16) 



together with 



/i=0 



.a£8»*=§ £ -sy+.§ t 



' o* oy os 



2!/" M_ _ 0/ M . , B/s» 



Consequently we have from (13), 



6-y*-o. 



when /i = 0- 



Hence for all values of 8#, Sy, &z we have a relation of the 



form 



% 2 = \f 2 ±2f 1 (A8j; + B8y + C8z). . . . (17) 



Now vary on S the equation 

 Then, since 



8 ta ra? & ' + a*5y y + a*ai &_ *S(5)' 



* Cf. Hadamard, loc. cit. p. 121. 

 Phil. Mag. S. 6. Vol. 10. No. 59. Nov. 1905. 2 T 



