EQUATION AND THE NATURE OP COHESION. 29 



e. Compulation of a from the equation of T&amsay and You////. 



The computations of a by the methods already noted may be 

 checked by computing a for a. few substances from the value 

 of the pressure of a liquid or gas when heated under constant 

 volume. Ramsay and Young j ) found that the pressure could then 

 be represented by the formula p = bT — a. This b and a are 

 not the constants of van der Waals' equation but a is in reality 

 ajV c 2 and b is dPjdT at the critical temperature. It will be 

 recalled that T c {dP)dT) e is equal to 1\ -f a/F c 2 . The value of 

 (dPjdT),, found in this way is about 10 — -20 °/ higher than that 

 of dPjdT calculated from Riot's formula for the vapor pressure 

 showing that the latter is incorrect. Van der Waals found for 



fT dP\ 



example that ( -77-77,) calculated from Burr's formula gave in the 



case of C'0 2 the value of 0.7. This is 1 2 °/ too low. It should 

 be 7.5. To return to Ramsay and Young's equation, the constant 

 a for pentane and isopentane, 2 ) when computed from the value 

 of b, was 162,890 mm. Hg. From this using the d c determina- 

 tions of Young we compute van der Waals' constant a for 

 isopentane to be 20.00 and for //-pentane to be 20.88 X 10 12 . 

 The mean value is 20.47 X 10 12 . This' as will be seen, is prac- 

 tically identical with the computation from the gravitation and 

 valences and is much higher than van Laar's value. For ether, the 

 value of Ramsay and Young's constant a was 174,810 mm. Hg. 

 With (/,, of ether 0.2025 this gives for a of van der Waals 

 the value of 18.52 X 10 12 . This is about 3% lower than most 

 of the values found for a of ether by other methods, but is far 

 nearer my values than van Laar's. For C0 2 Amagat 3 ) gives dPjdl 1 

 for V e as 1.72 atmospheres. From this with P c = 72.9 and d c = .404 

 we calculate a to be 4.11 X 10 12 which is about 4 °/ lower 

 than my value of 4.29, which is also the value originally assigned 

 to a of C0 2 by van der Waals. Rut 4.11 is 1 5 °/ higher than 

 van Laar's value of 3.50. In every case, therefore, the calculation 

 of a by this method bears out the calculations by the latent heat 

 and other methods already described, and they equally show that 



1 ) Ramsay and Young: Phil. Mag., .33, 435 (1887). 



2 ) Rose Innes and Young : Phil. Mag., 5th Ser., 47, 353 (1899). Young : Stoich- 

 iometry. Rose Innes: Phil. Mag., 44, 76 (1897). Phil. Mag., 45, 103 (1898). 



3 ) Amagat: Ann. de Chim. ct Phys., 6, 29 (1893). 



