Elastic Equilibrium of Semi-Infinite Solid. 5 



where Jm (r) is the Bessel coefficient of order m, and Cm is a 

 constant of integration. Thus we obtain 



§7. To find n corresponding to 



assume that 



11, = Urdosmd, 



Ug = Ü g sin VI d, 



U,, C/q, U„ being functions of r and z. Then equations (6) trans- 

 form into 



^ilL + l. M^ + ^:il^-J!l+lü,-^ü, = -'^^ kC,,e-r„»r), (8) 

 or" 1 àr dz r r !^ 



^!^ + l l^ + ^^._i!^f7,=A+i^A-C..-^-^/„,(ÄT) (10) 



in which Jm (.*•) means dJm {jx)\dx as usual. 



The last equation suggests that TJ^ has the form VJmQcr), 

 where F is a function of z only and satisfies the equation 



d'V 



.],^V=^^l-C„,e-'--' 



The solution of this equation is 



Dm being an arbitrary constant. Thus 



w, = -(^-^C,„^-D,„)^-^V,„(At)cosw^. (11) 



To find TJr, and C/q, write 



