MODULUS OF ELASTICITY OF EOCKS. 



9 



y=J[(L.U. + R.U.)-(L.L. + R.L.)], 

 z = è[(R.L. + R.U.)-(L.L. + L.U.)], 

 where x = o + (c + d + I))y, 



J=-2dco, 



z = 2(c + d)6', 

 and d=a + ß 



CO — ß — a. 



Eliminating x, y, z, 6 and co from the above equations, we 

 have 



a = 5 



1 c + 2d 



d(c + d){(R-U-L-L-).(L.U.-R.L.)^}_ 

 In the example above cited, we have 



TABLE III. 



c = 12"4 cm. 



d = 241-5 cm. 



c+2d 



=2-503x10 



C+2J 

 d(c+dj 



= 1-0099x10 



M. 



R.U.-L.L. 



R.L.-L.U. 



ß 



900 

 1200 

 1500 



1-133 

 1-676 

 2 211 



-0-064 

 -0-088 

 -0-120 



11-46x10 rad. 



16-95 



22-36 



■093X10 rad. 



■1-31 



■1-76 



It is to be noticed that, in the above calculation, the tangent and 

 arc of an angle are taken to be equal to each other. The greatest 

 angle to be dealt with is of the order of 10~- radian : whence 

 the difference between the tangent and the arc is of the order 

 lO"'^, that is to say, it is of the order of 10~^ of their own 

 amounts, which is within the error of observation. 



