8 G^V^'TIIER, Conditions of Stresses in a Heavy Body. 



where 7i''=-''''^((?^ -/'''), and the .shell is an open shell bounded 

 3 



b)- the cone for which .i=«. 



The only relations of this character of which I am 

 aware are given in Rankine's Applied AleeJuDiies, but I am 

 not sufficiently versed in the subject to be sure that they 

 originate with his treatment. 



Rankine's proof offers no difficulty, except in the 

 assessment of his meaning of the phrase " intensity of 



pressure." If we assume that \Qrdr is the measure of 



the "intensity of the longitudinal pressure," \Rdr that of 



"the ring pressure,''and also assume that 6'=(), 5' = 0, 7'=0, 

 we arrive at Rankine's conclusions, which I gather from 

 various publications by Engineering Institutions in Eng- 

 land, Germany, and America, are used in the calculations 

 for the design of domes in concrete as well as for masonr}', 

 although Rankine only contemplated dry masonry con- 

 struction in his book. 



A general formal solution of the equations (i) may 

 now be obtained. 



Write 



I - .v'' 



/e-= [/x - I - A-)^- -gi, rx -'-il—^ — ^—^ + 1. . (3) 

 ex I - X- 



Then, by comparison with (2), we must have 

 ("rXdr^O, 



