THE EQUILIBRIUM OF ELASTIC SOLIDS. 45 



by the product of the number of pounds in the weight into the number of inches 

 in the lever; 6 is the distance of two points on the cylinder whose angular 

 motion is measured by means of indices, or more accurately by small mirrors 

 attached to the cylinder ; n is the difference of the angle of rotation of the two 

 indices in degrees. 



This is the most accurate method for the determination of m independently 

 of p, and it seems to answer best with thick cylinders which cannot be used 

 with the balance of torsion, as the oscillations are too short, and produce a 

 vibration of the whole apparatus. 



CASE III. 



/ 



A hollow cylinder exposed to normal pressures only. When the pressures 

 parallel to the axis, radius, and tangent are substituted for p lt p 2 , and p t , 

 Equations (10) become 



9/i 3m/ ' m 



(20). 



d(rd) " r \9/* Sm^ 

 By multiplying Equation (20) by r, differentiating with respect to r, and 



75 



comparing this value of j with that of Equation (19), 



p-q_f 1 _LW^> , dp + ^2\_I^2 

 rm " \9/x 3m/ \dr dr dr) m dr ' 



The equation of the equilibrium of an element of the solid is obtained by 

 considering the forces which act on it in the direction of the radius. By 

 equating the forces which press it outwards with those pressing it inwards, we 

 find the equation of the equilibrium of the element, 



p_ ..(21). 



dr 



