326 THE ORIGIN OF LIFE 



This analogy may be applied to the case of an 

 electron which executes its rotations so rapidly 



Suppose a = distance between two consecutive particles and 

 T the tension of the string. Then we have for the wth particle 

 (see Preston's Theory of Light) 



m 



dt^ 



^ rp r Vn+i - yn l _ rp V Vn - 2/« " ^ l 



adapting the notation of Preston, Theory of Light, p. 49. 

 Let yn = A cos {wt — Ex) 



T 

 - mvfl cos (wi — Kx) = — |cos iyot - K{x + u))-2 cos {wt - En) 



+ cos {wt - E{n - u)) 



= - — cos {wt — En) cos Ea - cos {wt — En) 



- iT . , ^ . . ^Ea 

 = cos {wt - En) sm^ -^. 



Oj A 



Hence w^ = — sm^ — - . 

 nm, 2 



Now if V be the velocity of propagation of the wave, 



2iru 2' 



277 ^ It . rZal 2v . /Za\ 



-= = w = 2\ — . sin -5- = — sm I -7^ 1 

 T \ma L2J a \2/ 



when ■Uj = velocity of propagation in a wire of the same 

 density per unit length. 



„ ., ■n-a . /Ea\ 



Hence li = v = v-^— = sia ( -^ j, 



27r 

 we 



may write y = cos 27r f yj^ ~ 



ilTi' ^'^i°'^ means that - must be very small. 



— = sin 



A 



Also 





"■ (?) 



If X = a, then v = 0. 



V \ A. / sin ^ , „ iro 



-^— when ^ = X- 



