550 



Dr. C. Ohree : Applications of 



are coaxial right 



information when the walls of the flasl 

 circular cylinders, the common axis being vertical. Take 

 the origin at the lowest point of the axis, and employ 

 cylindrical coordinates r, (f>, z. For generality suppose that 

 gravity acts, while pressures II + Qz and II' 4- C : act re- 

 spectively on the outer surface r = a and the inner surface 

 r = a. These are typical of pressures exerted by surrounding 

 or contained liquids of uniform density. Employing a 

 method of solution given in the Camb. Phil. Trans, vol. xiv. 

 pp. 328 et seg., I find for the values of the stresses 



Q= _{IIa 2 -IIV 2 + (U'-U)(aa'/r) 2 + (CV-CV 2 )- 



+ (C'-C)z(aa'/r) 2 \l(a 2 -a' 2 ), 



^= -{Ua 2 -Il'a ,2 + {U-U / ){aa'/r) 2 + {Ca 2 -C'a l2 )z 



-f(C-(7>(aa7^) 2 }/(a 2 -a' 2 ) 5 



zz = — Z — gpl + g/pz, 



> (40) 



/■<f> = rz = (f)Z=:Q ; 



where Z is a uniformly distributed longitudinal stress sup- 

 posed to act at the height z — l. The corresponding values 

 of the displacements, u along r and w parallel to z, are 



:(rlE)[ V (Z+g P r,-(l-n)^ 



}- 



E(a 2 -a 2 ) 



nv 2 ^ ( n-noaV'/i 



2n(a 2 -a' 2 ) 

 2n(a 2 -a r2 ) 



V Ca 2 -CV 2 i {C-C')a 2 a' 2 zfr 



w 



iw cr — a 



Ca 2 -CW 2 

 2E(( 



, X .^ C 2 , 2> 



{(1 _, >? , +2 ^ + ^_ 



(a 2 -a' 2 ) 



logO/h), 



!>(4i) 



J 



where ^ is a constant, which can be determined so as to 

 make w vanish at any assigned value of r when z = (). 



The general form of the solution, when II and II', C and 

 CJ are unequal, implies that the external and internal liquids 

 are of unequal densities and do not communicate at all, or 

 only at a level where the pressures are equal. Thus, in 

 general, we must suppose that the cylinder is closed at the 

 lower end, or that it is carried liquid-tight on, or through, 



