Manchester Memoirs, Vol. Iv. (191 1), No. *>fy. 3 



Limiting ourselves now to the case of equilibrium 

 under circumstances of symmetry about the vertical axis, 

 the equations reduce to 



(;// + /,) ^ + ^ _ (( I - a- )e.^) = ^ f) .V, 



cr r ex 



(;// + «)z— - 2/1 — (^B:i) =A'' (*''■> 



<>r ex 



The last equation becomes 



r S-T,(r7v) + ~(( I - x-)7i>) = 0, 

 cr' o.v- 



and need not be carried further. 



The solution of the first two equations is given b)' 



/ , \ \ , ^ f , oivr) 



(7'\ vr 



with 



u + ^-^'^ = :i(A,r'-^^:)K, 



or \ ' r''+y ' 



where V stands for a zonal harmonic. 



We can complete the solution by taking 



// = S//^,r^, and r' = Se'„F^,. 



In accordance with the notation introduced in the 

 displacements, it will be convenient to write the elements 

 of the stress P, Q, R, S, Tsinf), and ^/sin«, so that P, 

 Q, R, S, T, and U are functions of cos 9 or x. 



General Outlines of Argin/ieiit regarding' Stresses and 

 Elastic Stresses. 



If a heavy bod}-, say a cylinder, stands on a horizontal 

 plane in equilibrium, and is then held in the same orientation 

 by a grip on its upper surface, the supporting plane being 



