192 HENEY A. EOWLAND 



= J a\4lk (Lfji + L>jf* + etc.) 



&,) a' 2 + k,][M;j. + M'/S + etc.]} 

 or for very small values of // we can write in terms of </> 

 - 2al<>> \lc,L + ((&! - &,) ' 2 + & 2 ) M\. 



If I is the moment of inertia of the bar and t is the time of a single 

 vibration, we may write 



=/-#. 



If we hang up the bar so that a' we have 



and if we hang it up so that a' = %TT we have again 



2a" 

 whence 



7T 2 / 1 



where 



x - ^ - u t A n F + (II ^: /y + v- ^ A) ^- -v/ *,** + -VV/ 



For a cleavage bar of calc spar we must use the general equation. 

 For equilibrium we have 



h {Aa* + Ba' 3 - Caa'\ + k, { A (1 a 2 ) + B (1 - a' 2 ) + Caa' \ = 0, 



which gives us the ratio of Jc 1 to Tc 2 . For this experiment it is best to 

 hang up the bar so that the axis is in the horizontal plane and we 

 should then have 



a 2 = I a' 2 . 



For obtaining another relation it is best to suspend the bar with ' = 

 and we then have the position of stable equilibrium at the point 6 \K 

 which gives 



T?I 



t* 



whence 



