382 



ct/R, £qs. (1) and (2) may be reduced to 



^— H-|5-}-° O) 



and 



^Uo) = qM. 



3^-.-- .-■ (4) 



The general solution of iiq. (3) is very simply obtained by the 

 use of the Laplace transform and the Hankel transform with respect to 

 the variables ^Y^and x, respectively. Application of the Laplace trans- 

 form gives 



(5) 



where 



(6) 



Application of the Hankel transform to Eq. (5) gives 



(s^ + k2) H = G, (7) 



where 





(8) 



'o 'o 



and 



GrU)= 5j'5c>»; j;(kx:)xj?c. (9) 



65 



