AND EXTENSION IN VELOCITY. 63 



Comparing (160) and (162) with (40), we get 



eV* = P = e l (166) 



or rj q + I P = ^. (167) 



That is : the product of the coefficients of probability of con- 

 figuration and of velocity is equal to the coefficient of proba- 

 bility of phase; the sum of the indices of probability of 

 configuration and of velocity is equal to the index of 

 probability of phase. 



It is evident that e 1 * and e 1 ? have the dimensions of the 

 reciprocals of extension-in-configuration and extension-in- 

 velocity respectively, i. e., the dimensions of t~ n e~* and e~, 

 where t represent any tune, and e any energy. If, therefore, 

 the unit of time is multiplied by c t , and the unit of energy by 

 c e , every rj q will be increased by the addition of 



n log c t + i?i log c. , (168) 



and every rj p by the addition of 



in logo.* (169) 



It should be observed that the quantities which have been 

 called extension-in-configuration and extension-in-velocity are 

 not, as the terms might seem to imply, purely geometrical or 

 kinematical conceptions. To express their nature more fully, 

 they might appropriately have been called, respectively, the 

 dynamical measure of the extension in configuration, and the 

 dynamical measure of the extension in velocity. They depend 

 upon the masses, although not upon the forces of the 

 system. In the simple case of material points, where each 

 point is limited to a given space, the extension-in-configuration 

 is the product of the volumes within which the several points 

 are confined (these may be the same or different), multiplied 

 by the square root of the cube of the product of the masses of 

 the several points. The extension-in-velocity for such systems 

 is most easily defined as the extension-in-configuration of 

 systems which have moved from the same configuration for 

 the unit of time with the given velocities. 

 * Compare (47) in Chapter I. 



