214 



Mr. William Sutherland on the 



Clausius's equation of the virial is to be our guide in 

 studying dp/dT, 



where V is velocity and R is force between two molecules at 

 distance r apart. 



According to the law of the inverse fourth power, the 

 double sum of the internal virial reduces to an expression 

 varying inversely as the volume and independent of the tem- 

 perature, as I have shown before (Phil. Mag. July 1887). 



If we integrate Amagat's relation Bp/9T=/(u), we get 



and as in the perfect gaseous state j9v = RT, where v being the 

 volume of unit mass and T reckoned as temperature C. + 27o°, 

 R varies inversely as the molecular weight of the substance, 

 we will write our equation in the form 



pv=z~RTvf(y) +v(j>(v) } 



where we see that r<f>(v) stands for the internal virial-term. 

 If, then, according to the law of the inverse fourth power, the 

 internal virial varies inversely as v, then v 2 <p(v) ought to be 

 constant. Now Ramsay and Young have carefully tabulated 

 the values of R/(v) and (f>(v) for different values of y in the 

 case of ethyl oxide ; so it is easy to tabulate Ru/(v) and v 2 cj>(v), 

 as we proceed to do in the following Table, where v is the 

 volume of a gramme of ethyl oxide in cubic centimetres, and 

 the metre of mercury is the unit of pressure. These units 

 will be used throughout when we are dealing with experi- 

 mental results involving pressures \ but when necessary, for 

 theoretical convenience, we will convert to absolute units. 



Table I.— Ethyl Oxide. 



V. 



Kvf(v). 



v 2 <p{v). 



, 



WO). 



v 2 f(v). 



Perfect gas. 



■842 





3-3 



1758 



2413 



100 



•912 



5710 



3-0 



1-865 



2366 



50 



•973 



5190 



2-75 



2013 



2371 



20 



1-129 



4554 



2-5 



230 



2487 



15 



1201 



4302 



2-4 



2-42 



2519 



10 



1-327 



3908 



2-3 



2-56 



2550 



8 



1-409 



3661 



22 



2-73 



2589 



6 



1-525 



3308 



2-1 



2-95 



2646 



5 



1-595 



3047 



20 



3-19 



2691 



4 



1-654 



2656 



1-9 



3-54 



2771 



37 



1-682 



2534 









