Law of Molecular Force. 121 



one type to be studied in the light of the equation of the 

 virial, was led by certain theoretical views to consider that 

 the term, independent of temperature, should have the form 



— — 2~^. But the equations constructed on this principle 



were found applicable within only a narrow range of tem- 

 perature and pressure. Now, before any definite conclusions 

 can be drawn from the forms of the terms in an empirical 

 equation, that equation must be proved to hold over a very 

 wide range of values of the variables in it. A brief comparison 

 which I will give below of the different types of equation that 

 have been constructed for gases, and of the different inter- 

 pretations that have been given to their forms, will show the 

 necessity for this condition of wide applicability in an equation. 



To find whether the virial of the molecular forces of a body 

 varies inversely as its volume, I resolved to seek for empirical 

 equations to represent the splendid series of experimental 

 results that Amagat has published for several gases (Ann. de 

 Chim. et de Phys. 5 serie, xxii.). In order to be able to 

 compare molecular potential energy and virial, I constructed 

 the characteristic equation for C0 2 first, because Thomson 

 and Joule's experiments on the expansion of C0 2 through 

 porous plugs, and Regnault's experiments on expansion of 

 C0 2 , give no data for rinding its molecular potential energy. 

 In view of the great importance of the deductions to be drawn 

 from the form of the equation, it seemed to me to be absolutely 

 necessary that it should represent not only the whole range of 

 Amagat's experiments, which extend from pressures of about 

 40 atmospheres to pressures of 400, and from a temperature 

 of 18° to 100° 0., but also such independent experimental 

 data as are available. The search proved to be a sufficiently 

 laborious one. 



The form of equation which Rankine adopted to represent 

 the result of Regnault's experiments on the compressibility 

 and dilatation of air and C0 2 may be taken as the point of 

 departure of certain more recent formulae. It was (Phil. 

 Trans. 1854, p. 336) :— 



^ = A ( 274 + ^(27^>^ 



where t represents temperature Centigrade. Thomson and 

 Joule, by the direct integration of the differential equation 

 expressing their approximate empirical law, that the fall of 

 temperature of a gas escaping through a plug from a region 

 of one pressure to a region of another is proportional directly 

 to the difference of pressure and inversely to the square of the 



