EXPERIMENTAL KNOWLEDGE OF THE PEOPEETIES OF MATTER. 507 



bodies — not solid — are therefore conditions under which, in the above 

 sense, temperature, pressure, and volume correspond ; the boiling-points 

 at any pressure are not, therefore, points at which bodies are to be 

 expected to correspond in physical properties, and the principle of Kopp's 

 method and that of others for comparing bodies as to molecular volumes 

 or molecular heats is in this particular not strictly correct. 



On page 152 of Van der Waals' ' Continuity, &c.,' the following con- 

 clusion is stated : ' The coefficients of expansion of individual bodies 

 under corresponding conditions (of temperature, &c.) are inversely pro- 

 portional to the absolute critical temperatures of the bodies ' ; in which, 

 from the context, it is seen that by the coefficient of expansion of volume 



V at absolute temperature T is meant - — , in which — is the partial 



V dT dT 



differential coefficient, being rate of variation at temperature T with the 



temperature only and without altei-ation of pressure 



Hence for any pair of corresponding temperatures the values of 



- -5;^; ^^® *° ®^^^ other inversely as the absolute critical temperatures of 



the two bodies ; and therefore if Tj is this temperature for one of the 



bodies, - — x Ti=C, a quantity which is the same for each body. Now 



Mendelejeff's formula may be written l/v=l — 'k (T— 273) ; 



whence 1 '^=Jc; 



v^dT 



and lf^=lc/(l-Jc.T:^2r6); 



therefore - X ^ xT,=A-T,/(l-/.- . T-273) ; 



V dL 



therefore 1—Jc (T— 273)=Z;T, /C ; 



But C must be independent of the individual body, and dependent only 

 on the ratio T/T, ; and Jc is dependent not on T but on the body and 

 therefore on T,. These conditions are satisfied if 



l+273/.-=aiT, (a) 



so that -^=a— T/Ti, a being an absolute numerical constant. We thus 



have an equation connecting a, I; and T, which, when the value of a is 

 known, will give Mendelejefl's Jc in terms of the absolute critical tempera- 

 ture of the body. This equation (a) may be put in this form : — 



l/A;=aT,-273; 

 from which l/A--(T-273)=aTi— T ; 



so that l/v=k(il/k-t)=h(aTi-T). 



Hence the density of a given liquid is directly proportional to the result 

 of subtracting the absolute temperature from a times the absolute critical 

 temperature of the body. 



To determine the value of a we have then to find a number of bodies 



and 



