Properties of the Equation of State. 395 



value of U being equal to zero. Hence at the critical point 



TJ + u—u a =m a v(p — T^jn (9) 



The value of the expression (p — T-,£) at the critical 



point can be easily obtained from the facts. It is found to 

 be equal to 6'5 p c *. A knowledge of the value of this 

 expression increases the valne of equations (8) and (9) 

 considerably. 



The equations of condition at the critical point written 

 out more fully are thus 



°-j(S),? + jm?+?. • <"> 



n (Y<ra\ ST C(dh,\ §T cPZ M _. 



0= Ji3Sr;,l* + JW)«F + <i?' • (12) 



G5m °P=-Tv-ch> ^ 



and 6'5m a vp= U + w — u a (14) 



Possibly other conditions exist besides those given. 



A remark should be made here in connexion with the use 

 to which equations (7) have been put. The equation of state 

 is often written in the form p + P» = H, where P„ is the 

 intrinsic pressure and H a function of T and v expressing 

 the effect of the motion of translation of the molecules. 

 Attempts have been made to obtain the form of P ?l and H 

 by substituting for each an expression containing a number 

 of undetermined constants, and then to determine these con- 

 stants by means of equations (7). But this is not mathe- 

 matically sound, and may therefore lead to quite erroneous 

 results. It is evident that if we substitute for P n and H in 

 the equation the expressions (P n + <j>(v, T)) and (H + <£(?;, TV) 

 respectively, it reduces to its original form. It follows 

 therefore that the exact forms of P n and H consist of the 

 expressions obtained in the above way plus an undetermined 

 function (/> (v, T) . 



* Phil. Mag. Oct. 1911, p. 584. 



