72 AVERAGE VALUES IN A CANONICAL 



of these anomalies is of course zero. The natural measure of 

 such anomalies is the square root of their average square. Now 



(.-3" = ?_, ( 2 04) 



identically. Accordingly 



(205) 

 In like manner, 



(206) 



Hence 



G-l) 2 = G fl - I,) 2 + (e p -e p ) 2 . (208) 



Equation (206) shows that the value of de g /d can never be 

 negative, and that the value of d 2 ty g /d 2 or drj q /d can never 

 be positive.* 



To get an idea of the order of magnitude of these quantities, 

 we may use the average kinetic energy as a term of comparison, 

 this quantity being independent of the arbitrary constant in- 

 volved in the definition of the potential energy. Since 



* In the case discussed in the note on page 54, in which the potential 

 energy is a quadratic function of the q's, and Ag independent of the <?'s, we 

 should get for the potential energy 



and for the total energy 



We may also write in this case, 



(fq a) 2 n 

 (e-e ) 2 ~n' 



