162 The Quantum of Action. 



This can be transformed into 



a 



\pidq 1 = 16p 2 e 2 \ 



x 2 di 



(l + ^)(a + /3^ 2 ) 2 ' 

 o 



where ot=l + e 



and j3 = l — e. 



On evaluating the integral we get 



J 



p 1 dq 1 = 27rp 2 q_ ~j 

 Now, by hypothesis (3) 





\p i dq 1 =ph, 

 and 27rp 2 — <rh, 



where p and cr are positive integers. When these values 

 are substituted we have 



(p + <r)(l-e 2 )*=<r. 



The part which is common to all forms of the Quantum 

 Theory can be described very simply. When systems are 

 not exchanging energy, their equations of motion are 

 obtained by giving a stationary value to the integral 



J2L^, 



where L is the kinetic energy of the system, subject to the 

 condition of constant energy (Principle of Least Action). 

 The Quantum Theory lavs restrictions on the interchange 

 of energy between different systems. These restrictions 

 require that under certain circumstances the following 

 equation must hold 



^2Ldt = nh, 



where A is a universal constant, n is an integer, and the 

 integration is extended over the period of motion of the 

 system. 



Wheatstone Laboratory, King's College. 

 NoYember 1915, " 



