234 Mr. William Sutherland on the 



with B = 56*5, /3 = 1'53. For the elements we had v c =3k/2, 

 for ordinary compounds v c =7k/6 ; so that to make ethylene 

 intermediate v c is taken as 5k/ '4, all these being of the general 

 form (l + 2ra)/2w, with ri=l, 2, 3. 



With the values of the constants B and /3 given above as 

 derived from Auiagat's results at high pressures, we can 

 determine the density of liquid ethylene ; at —21° under 

 saturation-pressure the density is '414, identical with the 

 experimental value of Cailletet and Mathias (Compt. Rend. 

 cii.). 



It will be as well at this stage to extract clear from among 

 the argumentative detail the most important results so far 

 obtained. 



First, in the elements the internal virial varies inversely as 

 the volume over the whole experimental range. 



Second, in compounds there is mathematical discontinuity 

 in the value of the internal virial at volume k ; from volume k 

 downwards the internal virial varies inversely as the volume : 

 from the volume k upwards it tends towards variation inversely 

 as the volume as the limiting law, the limiting constant being 

 double that which holds below the volume k ; between the two 

 limiting cases the internal virial of compounds varies inversely 

 as (v + k). 



Third, a fact of the highest importance in connexion with 

 the kinetic-energy or temperature term in the equation arrests 

 our attention, namely, that the coefficient of T in it, or the 

 apparent rate of variation of the translatory kinetic energy 

 with temperature at constant volume, attains near the critical 

 volume double its value in the gaseous state, and below the 

 critical region increases rapidly with diminishing volume (see 

 column Hvf(v) in Table I.), becoming at ordinary liquid 

 Volumes as much as ten times as large (see coefficient of T in 

 infracritical equation). Now the specific heat of liquids at 

 constant volume, which is the rate of variation of the total 

 energy with temperature, is rarely much more than twice that 

 for their vapours. Hence we must seriously consider the 

 interpretation to be put on the different terms of our equations. 



5. A short digression on the general interpretation of Clausius's 

 Equation of the Virial, — Returning to Clausius's theorem of 

 the virial, 



we see that strictly the kinetic-energy term includes not only 

 the energy of the motion of the molecules as wholes, but also 

 that of the motion of their parts, and at the same time the 





