Manchester Memoirs, V^ol. xlvi. (1902), No. 1. n 



(14) tv= -b{^^'I^Ax--J'^{a^-b)x'(\og^y^ 



b b r a'^ — b^ r- f r i\ 



- 2ja + b){y,x'' + 2y,a-) + ^^{a + b)Ae''\og~^ - —^ ^T^^^g- - - ) 



A„ (a + b)-,, r 2(0" - b'') r- 



-(a + b) - ;-- - -L\\oq,~ - — -7, bD. 



^ '2 a ' ^ri a '^2 



A, Z>, /3|, /Sa, yi, yo, being determined by the external 

 conditions. 



External Conditions. 



(I.) There must be no shearing force or axial stress over 

 either plane face, i.e., s and q must both be zero at ,r= ±£, 

 this is satisfied by (12). 



(II.) At the cylindrical face r=ri it was found im- 

 possible to make/ vanish independently of .i-. The course 

 adopted, therefore, was to make 





(i.) I pd\: = o, i.e., total radial pressure vanishes. 



(ii.) I pxdx = o, i.e., total moment equal zero. 



The value of p at the outer edge therefore varies from 

 positive to negative, is always small, and has no resultant 

 force or moment over the section by this assumption. 



III. At the inner face 



(i.) p> = o when r = o x = f.- 



+^ 

 (ii.) pdx = -"^ T, 



in being a factor depending on the slope of the inner 

 surface. Assuming the inner face conical, then with the 

 previous definition of e and/" 



m = -r^ ~r approximately. 



