PROBABILITY OF PHASE. 19 



The values of the coefficient and index of probability of 

 phase, like that of the density-in-phase, are independent of the 

 system of coordinates which is employed to express the distri- 

 bution in phase of a given ensemble. 



In dimensions, the coefficient of probability is the reciprocal 

 of an extension-in-phase, that is, the reciprocal of the nth 

 power of the product of time and energy. The index of prob- 

 ability is therefore affected by an additive constant when we 

 change our units of time and energy. If the unit of time is 

 multiplied by c t and the unit of energy is multiplied by c e , all 

 indices of probability relating to systems of n degrees of 



freedom will be increased by the addition of 



"-- 

 n log c t + n log c . (47) 



