THE EQUILIBRIUM OF ELASTIC SOLIDS. 



dSx [ 1 1 \ , 1 



41 



dSx I 1 1 \ , 



3?" for Mi) (A 



dSy / 1 1 



-4 = fe ~ 3 



(13), 



c,v being the linear expansion for the temperature v. 



Having found the general equations of the equilibrium of elastic solids, I 

 proceed to work some examples of their application, which afford the means of 

 determining the coefficients /*, m, and <a, and of calculating the stiffness of 

 solid figures. I begin with those cases in which the elastic solid is a hollow 

 cylinder exposed to given forces on the two concentric cylindric surfaces, and 

 the two parallel terminating planes. / 



In these cases the co-ordinates x, y, z are replaced by the co-ordinates 

 x = x, measured along the axis of the cylinder. 

 y r, the radius of any point, or the distance from the axis. 

 z = rO, the arc of a circle measured from a fixed plane passing 

 through the axis. 



-j , p 1 = o, are the compression and pressure in the direction of the 

 axis at any point. 



y-75 



T 



radius. 



-j 



y 



~T = -T , p t =p, are the compression and pressure in the direction of the 



dSz 

 dz 



7C> f\ CS 



= , p t = q, are the compression and pressure in the direction of the 



tangent. 

 Equations (9) become, when expressed in terms of these co-ordinates- 



m 



m 



.(14). 



m d8x 



The length of the cylinder is b, and the two radii a, and a, in every case. 

 VOL. i. G 



