184 THERMODYNAMIC ANALOGIES. 



be convenient for physical purposes. But when these units 

 have been chosen, the numerical values of , de/dlogV, 

 de/d<j>, 7), log FJ <, are entirely determined,* and in order to 

 compare them with temperature and entropy, the numerical 

 values of which depend upon an arbitrary unit, we must mul- 

 tiply all values of , de/dlogV, de',d^ by a constant (7T), 

 and divide all values of 77, log FJ and <f> by the same constant. 

 This constant is the same for all bodies, and depends only on 

 the units of temperature and energy which we employ. For 

 ordinary units it is of the same order of magnitude as the 

 numbers of atoms in ordinary bodies. 



We are not able to determine the numerical value of K> 

 as it depends on the number of molecules in the bodies with 

 which we experiment. To fix our ideas, however, we may 

 seek an expression for this value, based upon very probable 

 assumptions, which will show how we would naturally pro- 

 ceed to its evaluation, if our powers of observation were fine 

 enough to take cognizance of individual molecules. 



If the unit of mass of a monatomic gas contains v atoms, 

 and it may be treated as a system of 3 v degrees of free- 

 dom, which seems to be the case, we have for canonical 

 distribution 



If we write T for temperature, and c v for the specific heat- of 

 the gas for constant volume (or rather the limit toward 

 which this specific heat tends, as rarefaction is indefinitely 

 increased), we have 



since we may regard the energy as entirely kinetic. We may 

 set the e p of this equation equal to the e p of the preceding, 



* The unit of time only affects the last three quantities, and these only 

 by an additive constant, which disappears (with the additive constant of 

 entropy), when differences of entropy are compared with their statistical 

 analogues. See page 19. 



