﻿382 Mr. H. S. Rowell on Energy Partition 



If we contract this again by multiplying by gP v , we get the 

 familiar identity 



<-H-?- ' (4) 



for since [gP v )p = 0, 

 similarly 



and *r 



<f (G r , ff ) = (/» G„„)„ = (G)„ =g 



since G is a scalar. 



Jersey, 



13th May, 1922. 



XXXVI. Energy Partition in the Double Pendulum. 

 By H. S. Rowell *. 



IN a letter to ' Nature ' (July 28, 1921) the present writer 

 gave a theorem on the double pendulum which is capable 

 of interesting extension. 



If the masses of the bobs are m and M and the respective 

 amplitudes are a and A with suffixes. to denote the normal 

 modes, then the theorem states that 



a Y a 2 M 



AjA 2 m ' 



If this equation is squared and both sides multiplied by 



m 2 /M 2 , we have 



ma^n 2 ma 2 2 n 2 2 _ 1 

 — 1» 



MAxVMA/tis 



where nj and n 2 are the radian frequencies of the two moles. 

 "This equation may be readily interpreted thus : — 



" The ratio of the kinetic energy of one bob to that of the 



* Communicated by the Author. 



