262 Mr. C. Chree on Bars and Wires 



ever, if desired, be easily considered separately, 

 when r = b, P = 0, i. e. 



(m-n)B + 2mA-^A' = 0, ... (7) 

 when r = a, Pj=0, i. e. 



(m 1 -w 1 )B + 2m 1 A 1 --^A I / = 0; . (8) 

 and when r = a 1} 

 ( m _ w )B + 2mA-^A' = (m 1 -<)B + 2m 1 A 1 -^ 1 A 1 / . (9) 



At this last surface also the radial displacements in the two 

 media must be equal ; therefore 



A ttl +— =A 1 a ] +^- / (10) 



From (10), 



V-A^a^A-Ax); 



while from (7), (8), and (9), 



Thus, if for shortness, 



n 1 b 2 Xa 2 -u 1 2 )+na 2 (a 1 2 -b 2 )=^ ) . . (11) 

 we get 



A/= na?a\a 2 -b 2 ) A^A-A^J * * ^ 

 If, again, for shortness, 



i+S^>^ 2 - ai2 ) +M (<- 62 )}=i> • < 13 ) 



we get by substituting the values (12) in (7) and (8), dividing 

 these equations by 2m and 2m x respectively, and subtracting, 



A-A 1 =B(<r 1 -<r)^, .... (14) 



where 



_ m — n _ mi — n^ 



Thus from (7) and (8), finally, we obtain 



A=-B{<7 + (<r 1 -*)^a 1 2 (a 2 -a % 2 )& 2 \, 



A 1= -B {<r x - fa-*) ^afla^^Aj } 



