lO GWYTHER, Cflfiditions of Stj'esses in a Heavy Body. 



The equations of condition, of which the importance 

 is wished to be pointed out, may be written 



cr 



hx 



^^(r'^-v-uy2{i+.)C\ . .- . . (5) 



where it is more convenient to use the elastic constants cj 

 and a than ;// and ;/, and where 



(7= — , ,/= 2(1 +0-)//. 



2 W 



From these equaticMis we misjht eh'minate // and v, but 

 the results are very complex. 



We have already found the mathematical form which 

 7( and V possess if the equations are consistent, and these 

 values would exclude the gravitational portion of the 

 stress which is given by 

 .V - a 



Q'=gpf 



I - X- 



X - o 



■^= -spf-\^^ + 



Stress ill a Ions:;, Jicavy circnlar cyliiidrical tube, supported 

 horizontally. 



Take the interior and exterior radii as a and /;, and 

 assume the tube to be so long that the effects of the ends 

 may be neglected, the statical equations to be satisfied are 



r^~-\-P^^-Q =gii r cos ^ . 

 cr cH 



r'^+2C^+'^^-gprs\ne (6) 



dr cU 



