Discontinuity in a Rotationally Elastic Medium. 611 



Now for the particular medium in question we have the 

 equations : — 



[SHIMS] =»• 



i-ygi+r ^ii-f d 2 n-o 



Lc^ 2 J LdxdyJ Idriz] ' 



and three similar equations. 



Also there are three dynamical equations o£ the type 



La^J Ldfj L^ 2 J c s La* 2 J- 



Supply in these the values from (20) and use for shortness 

 the vector notation : — 



A=(A, A', A") and similarly for B, C, D ; 



also V(E.N) H ==2(E.|^)i. 



Then we obtain the following equations : — 



R.N=0, 

 V(R.N) E +(A, B, C).N=-(A + B' + C")N, 



B.|?+D.N=-(A + B' + C")|£ 



From these equations, representing eight scalar equations, 

 we can deduce the following scalar equation : 



N .V(K. N ) R -^ E .|f)= : (A + B' + C"){N. N 4(|j 2 } ; 



and this equation can be written in the ordinary notation 

 under the form 



+ (SB«)'H- <m 



Equation (21) is satisfied for all values of the arbitrary 

 parameters by 



(SHg)M!9*-MtD"-°- 



