Manchester Memoirs, Vol. hi. (1912), No. 10. 13 



r ar r- 



whence we must have from (13) 



^ d'-u 1 du I d'-u , dp' n, 

 ar- r ar r- dz' dr 



Using now the second set of conditions (14), we find 



dr- dr \ dr J ydf" r dr dz'- ] 



and 



d:;-{ dr ^ ' \ \dr 7~ Rdr' r dr dz') 



... , . , • ri^ 1 d'n I dti d'-ii 



givmg two equations connectmg F and -^-r, ~ - -^^ + -rv • 

 i= ^ ^ & dr- r dr dz' 



If each of these quantities is null, the stress is inde- 

 pendent of the elastic constants of the material. 



The general case where the stress is independent of 

 the elastic constants seems worthy of consideration. The 

 distribution of the stress would in this case be geometrical, 

 but the strain would depend on the elastic constants. 



