1 6 R. F. GWVTHE];, Specification of the eleuients of stress. 



Cvi.iNDRiCAi, Polar Coordinates. 



9. The dynamical stress equations are now 



?F P-Q T dU , cT 

 ir r r c'd cz 



nU 2U ,1 ?(2 95 • 



' r r r ( d cz 



rT , T I cS , cR ■■ . Q, 



;r— + - ^-::— + -~=pW .... (28). 



rr r r r^ cz 



1 am not able in this case to follow the simpler method 

 adopted for Cartesian coordinates, and I have to make 

 use of the solution of the statical equations corresponding 

 to (13) which I have given in Part I., and simplified in 

 Part II. of this series of papers.* 



The solutions take the form 



r- c'd" CZ' r or 



f f- (_ Z' 



„ _ r-'O., T r -0] 2 002 _ I c6i 



cr' r' cd' r cr r cr 



r ?ticz ' 



r rcz r cz r cz 



U= - - .— ^ + ~, .— (29). 



r ^ rr ti r~ c(j 



10. The elastic specification of stress is as usual 



given by 



„ / \/cu u 1 CV dw\ en 



-P ={m- n)[ .- +-4.-— + ^-+ 2U~ 



\cv r r cd cz / or 



*The simpler nielhod which I luive used for Cartesians has been so 

 employed as an introductory method. That used for Polars, cylindrical and 

 spherical, is tlie general meihod. 



