Manchester Memoirs, Vol. Iv. (191 1), No. 30. n 



1 he stresses across the sections of the tube incHned y 

 to the vertical must support the weight of the included 

 portion of the tube. 



The formal solution will therefore be found from 



P=pd sin y +/^ cos 9 + S/, cos s% , 



Q^ir ~ + 2/ jysin 9 + (r ^ + 2/+^prjcos(^ + S^,cos.f0 , 



U= -pd cos y +2 u, sin sd , 



where / = 0, when r = a, and when r^d, and 



j pdr= - ^gfj(d'' - d') , 



a 



rp„ = rp + 2 j pdr + g(i{^ — d^) , 



and, in the series of complementary terms, 



s^, = r^+ 2^/j, 

 or 



I r^ +p, ) = r~ - (r - 2) ?^s. 

 \ (ir / cr 



The equations of condition in terms of displacements 

 are now, 



cr 



From these, again, the displacements might be elimi- 

 nated. But, if instead, we examine the solution of the 

 displacement equations, namely, 



/ \ CA CM 



(m + n)r- zn ~-^ ggrco^^i , 



cr CO 



I \ ^ A ^10 ■ ,. 



hn + n)-;— + 2/ir;r-= -gnrsmO, 

 cd cr 



