i8 PHYSICAL PROPERTIES AND COMPOSITION 



paying no attention to molecular orientation. The equation 

 does not correspond quantitatively to the facts, but often 

 gives valuable indications, which may be extended into 

 empirical rules by experiment. 



Qualitative test of the characteristic equation. Beginning 

 with the qualitative test, it must be noted first that for 

 large values of F the original simple expression 



PV= ET 



is recovered, since b is small compared with F and -=~^ com- 

 pared with P. It may be added that this condition must 

 be satisfied by any characteristic equation ; so that the 



general formula 



PV-ET=F 



becomes necessary, F being a function which is zero for 



indefinitely great values of F. 



Representing the values of P and F in the above equation 



graphically for fixed temperatures, i. e. by drawing iso- 



thermals, P upwards, F to 

 the right, in Fig. i, for each 

 temperature there will be on 

 the right a part of a rect- 

 angular hyperbola. 



For further guidance let 

 us determine * the value of 



dP 



W 



at constant temperature, i. e. 



V dP 2 a ET 



Fig. i. dV~ V*^ (Vb)*' 



For large values of T this gives always a negative value 

 for -rf^ and consequently a curve like I. 



Further, for small values of F, since V b approaches zero 



Boltzmann, Vorlesungen uber Gastheorie, 1898. 



