120 Mr. W. Sutherland on the 



is stipulated that <£(0) must be finite. On these assumptions 

 the virial of the molecular forces is found to be § of the 

 potential energy of the molecules — the same ratio as follows 

 from the law of the inverse fourth power without assump- 

 tion. 



Thus, then, if we proceed to deduce from experimental data 

 the value of the potential energy of the molecules of a body 

 and the value of the virial of the molecular forces, and prove 

 the latter to be J of the former, we shall have obtained weighty 

 confirmation of the Kinetic Theory of Matter and of the idea 

 of the action of molecules on one another as centres of force, 

 but we shall possess no absolute test between the law of the 

 inverse fourth power and any one of the unknown number of 

 unknown laws satisfying the conditions that they can be ex- 

 pressed by some function f(r), insensible for sensible values of r 

 but sensible for insensible values of r\ yet incapable of expres- 

 sion as a finite series of inverse powers of r ; and, further, that 



f(r) must be such that 1 r 3 f(r)dr and 1 r 2 1 f(r)dr are both 



Ja Ja Jr 



unaltered by variations in a, while a 6 \ f{r)dr is negligible in 

 comparison with I r 2 1 f(r)dr; but such an absolute test will 



Ja Jr 



hardly be required to distinguish between the nearness to the 

 truth of the simple and natural and of the elaborate and 

 artificial. 



In order to find whether the virial of the molecular forces 

 of a body does actually vary inversely as its volume, it is 

 necessary to construct empirical equations for the relations 

 between pressure, volume, and temperature found experi- 

 mentally for different fluids, and then to compare them with 

 Clausius's fundamental equation of the virial as applied to 

 the Kinetic Theory of Gases, 



%pv=i 2 mV 2 + i . i 22 m 2 r/W. 



The double sum in this equation as often written is multiplied 

 by only one factor J, the other being understood to be con- 

 tained in the meaning of the symbol of summation. 



If, then, the virial of the molecular forces of all bodies is 

 to vary inversely as the volume occupied by them, we must 

 always find in their characteristic equations for pv a term in- 

 dependent of the temperature and varying inversely as the 

 specific volume. Van der Waals, who endeavoured to apply 

 this idea of the construction of characteristic equations on the 



