lo R. F. GwYTIlER, Specification of the elements of stress. 



If the complete circumstances involve symmetry 

 about the cylindrical axis, the whole system is simplified 

 by the independence of all functions of the coordinate 6. 



Spherical Polar Coordinates. 



In a paper* read before the Society a year ago, I 

 proposed an alteration in the representation of the dis- 

 placements for such a system of coordinates, the proposed 

 form being 



//, sin 2', sin ^ zv. 



The elements of the strain consequently may be written 

 {^1 fi §,•: ^^> ^ sin 0, cs'mO}. 



and those of the stress 



{F, Q, R, S, rsinfJ, UsmO). 



I shall assume that this system is employed, and 

 shall write, as is usual, x in place of cos Q. 

 The equations of stress then become 



r' dr r ax (. J r af r 



r^ ctr r\dx i - x'-J r{i ■- x'-) a(]> r{i-x'-) nmH 



r'ar ' r{\-x-)dxV ' J r{\ - x') d<^ sin (J ' 



The Covipleinentary Function Solution. 



The expressions corresponding with those of (5) arc 

 long, but this is inevitable in view of the generality of 



* Manchester Memoirs, vol, iv. ( 1 91 1), No. 20. 



