THE EQUILIBRIUM OF ELASTIC SOLIDS. 



61 



The equation of the equilibrium of a particle [see Equation (21)], becomes 



dp 



qp = r -r 

 dr 



" 



^ 



where q and p are the tangential and radial pressures, k is the weight in 

 pounds of a cubic inch of the substance, g is twice the height in inches that 

 a body falls in a second, t is the time of revolution of the cylinder in seconds. 



By substituting the value of q and -^ in Equations (19), (20), and neglect- 



ng o, 



which gives 



j^P. 

 m V* dr 



d"p 



r 



-4 + - 

 l 



3 



(57). 



If the radii of the surfaces of the hollow cylinder be ai and c 

 pressures acting on them h,, and A 2 , then the values of c t and c 2 are 



E\ 



m 



and the 



(58). 



When a, = 0, as in the case of a solid cylinder, c x = 0, and 



When A, = 0, and r = 



(60). 



When 5 exceeds the tenacity of the substance hi pounds per square inch, 

 the cylinder will give way ; and by making q equal to the number of pounds 

 which a square inch of the substance will support, the velocity may be found 

 at which the bursting of the cylinder will take place. 



