Rotatory Inertia on the Vibrations of Bars. 55 



■•■ t -* ea +"-'-*"'-]:-?j>s "+*>*kM<- 



or, putting x = k% 



where f = — and dashes now refer to f. 

 Now „ = %fp<t>P- 



V 



.'. Considering only the integral in 



p,q *- ° ' 



by equation (47). 



Now, -J- v"v' — v'"v vanishes identically if each end 



k L J 



be clamped or pivoted. 



If both ends be free it is — \ v'"v . -=— 



L Jo 2/e 



= -2- r I = t J/^1/«m • 



.*. In any case Y reduces to 



