Manchester Memoirs, Vol. h. ( 1 9 1 1 ), No. "It^. 



XX. The Conditions that the Stresses in a Heavy 

 Body should be purely Elastic Stresses. 



By R. F. GwvTHER, M.A. 



Read and received Marcli ftli, igii. 



Analytical Preface. 



To avoid breaking the continuity of the argument 

 in the main body of the paper, I prepare for a change 

 from the usual notation by introducing in this preface a 

 modification which I propose to introduce into the treat- 

 ment of the elastic equations for a spherical shell as 

 usually given in text-books. 



The Elastic Equations for a Spherical Shell. 



The displacements in the directions r, 6, are generally 

 written u, rj3 and rsin 67. I propose, in the first place, to 

 omit the factor r in the last two cases, and to introduce 

 the factor sin 8 in the second case. 



By this means sin 6 will also become an obvious factor 

 in other cases, and the remaining functions will be 

 functions of cos d. Following precedent, 1 shall write ;irfor 

 cos y, and for convenience I shall introduce a differential 

 coefficient with regard to x in the second of the dis- 

 placements. 



Shortly, I shall write the displacements as 



u, sin d :r-, Sin w. 

 ex 



May 22?id, igii. 



