262 Miss Lorna M. Swain on the Period of 



P.E. due to bending 



72EI g /l 11 , 3/ 2 l/ 3 \ 

 ~ W+W V (,5 + 2c T 7? + 8? )' 

 P.E. due to the tension 



^.# 



= 8 /Oft ,V ^T(. l - 3 -3^ + 3.0 (J (1 - .!•') - iKiz^l)^, 

 , , , /61 341 l/c \ 



We have made two assumptions in calculating the kinetic 

 and potential energies. In the first place we have neglected 

 rotatory inertia and in the second we have followed Glebsch 

 in calculating the potential energy due to bending ; this is 

 justifiable in most practical cases*. 



Assuming periodic motion of period 2tt/p, we finally 

 obtain the equation for the period 



72 



lc_ 3 lc 2 3c 1 

 5/ 3 + 2P H " 7l + 8 



(l + c/7) 3 



fl22 682 1 • 

 + L45 3151 + c/Z. 



52 292 1 



where 



<7EI 



45 315 1 + c/l 



x _i P a o a > 2 l 4 : .a—P ^oP 2 ! 4 



gEI ' 



* Clebsch, Theorte der Elasticitat fester Korper, p. 253. Rayleigh, 

 ' Theory of Sound,' vol. i. § 188. Bnc. der Math. Wissenschaften, vol. iv. 4 

 p. 251. 



The neglect of one term in the potential energy due to the tension and 

 the retention of another is legitimate, since it will be found that the 

 ratio of these terms depends on the ratio of a radius of gyration of a sec- 

 tion to the length of the rod, which must be small, when the approximate 

 theory for thin rods is used. 



