Manchester Memoirs, Vol. Ivi. (19 12), No. 10. 9 



Cylindrical polar coordinates. 

 The stress equations in this case are 



r dr r di) dz r 



r dr r dU dz 



'-'{Tr)^^-fy^ =Z . . . . (9). 



r dr r do dz 



With the guidance given by having obtained the 

 complementary /miction solution in cartesians, it is not 

 difficult to determine the corresponding solution in this 

 case, namely — 



p _l_ d-Q., _ 2 d-^^ d'-Q^ I (l^z _ 2 <^l^i 

 r'^ di)'- r dddz dz" r dr r dz ^ 



Q" = —ri ~ 2 — — + — r J 

 dr- drdz dz' 



„ _ d'Q, _ 2 d-^s , I ^^'01 , 2 de. _ I dQ, _ 2 d^z 

 dr"'- r drdd r" dd'- r dr r dr r'^ d6 



^ ^ _ d-^^ I d"% d-% _ I d-Oi _ T fl^i _ I d^i'i 2 d%, ^Pi 

 dr- r drdi) drdz r dQdz r dr t"^ dH r dz r"^ 



T =~ ^^^ - ^ ^^"'^- ^ ^li^ - ^-e.^ i_ d^j 1 ^61 _ I dO^ 

 ' ~ ~r drdd r" dd- r dddz drdz 7' lid ~r~dz r~dz ' 



U„- - + --—./- 1+ i- i . . . (10). 



drdz r dddz dz" r drdd r" dd r dz 



In accordance with the relation noticed in cartesians 

 between (5) and (6), we may similarly deduce from (10) 

 the relations connecting the elements of the strain. 



It seems unnecessary to reproduce either this system 

 of equations, or the system of equations corresponding 

 with (7) or (8). 



