•260 PROFESSOR TAIT ON THE 



Preliminary. 



In the preceding part of this paper I considered the consequences of a special assump- 

 tion as to the nature of the molecular force between two particles, the particles themselves 

 being still regarded as hard, smooth, spheres. My object was to obtain, by means of 

 rigorous calculation, yet in as simple a form as possible, a general notion of the effects 

 due to the molecular forces. My present objects are (1) to apply this general notion to 

 the formation and interpretation of the virial equation (in an approximate form), and (2) 

 to apply the results to the splendid researches of Andrews and their recent extension by 

 the truly magnificent measurements of Amagat. 



Passing over some papers of Hirn and others, in which the earliest attempts were 

 made (usually on totally erroneous grounds) to form the equation of the isothermals of 

 a gas in which molecular forces are prominent, we come to the Thesis of Van der 

 Waals,* who was the first to succeed in representing, by a simple formula, the main 

 characteristics of Andrews' results. His process is based upon the virial equation, and 

 his special object seems to have been an attempt to determine the value of the molecular 

 constant usually called " Laplace's K." Though the whole of this essay is extremely 

 ingenious, and remarkably suggestive, it contains (even in its leading ideas) much that is 

 very doubtful, and some things which are certainly incorrect. One of these was specially 

 alluded to by Clerk-Maxwell^ who, in reviewing the essay, said : — " Where he has 

 borrowed results from Clausius and others, he has applied them in a manner which 

 appears to me to be erroneous." It will conduce to clearness if I commence with an 

 examination of the equation which is the main feature of Van der Waals' Thesis, and 

 the modifications which it underwent in the hands of Clausius. 



XIX. — The Isothermal Equations of Van der Waals and Clausius. 



64. The virial equation (§ 30, above) is 



P(mw 2 ) = gpv + ^2(Rr) ; 



where, to save confusion, we employ u to denote the speed of the particle whose mass is 

 w. From this Van der Waals derives the following expression : — 



(p+£)(v-{3) = &(mu*); 



and he treats the right-hand member as a constant multiple of the absolute temperature. 

 (This last point is of extreme importance, but I shall discuss it farther on ; at present I 

 confine myself to the formation of the equation.) 



* Over de continuiteit van den gas- en vloeistoftoestand. Leiden, 1873. t Nature, Oct. 15, 1874. 



