108 MOLECULAR MOTION AND ITS ENERGY 47 



in which A, B, n are constants. Similarly Battelli 1 put 

 a = (A~ n - B% m }E(l + aS), 



so that he had one more constant at his command. G. 

 Jager, 2 on the contrary, added to a the factor 



@-y /e , 



where 7 is constant. 



These formulae exhibit much better agreement with ex- 

 periment than the simpler formula of van der Waals, as 

 is to be expected from the greater number of disposable 

 constants. Yet, as Korteweg 3 has remarked, the formula 

 of Clausius deviates from the observed behaviour of gases 

 in many other regards more largely than that of van der 

 Waals. For our theory the more complicated formulae 

 are less valuable than the original simpler one on account 

 of the difficulty of their interpretation. 



Amagat 4 has completed van der Waals 's equation 

 by giving it the form 



{p + Av~\v -s)}{v-b + B(v - b) n } = B(l + aty, 



which contains five constants, A, B, s, b, n. This formula 

 has proved itself good in a comparison with the observed 

 behaviour of hydrogen. 



Boltzmann and Mache 5 assume the formula 

 (p + flwr 1 ) (v - b) = E(v + 25) (1 + a&). 



48. The Cohesion of Gases 



If it can appear scarcely doubtful that the defects of the 

 theory, even after the corrections just applied, depend on 

 the cohesion having been insufficiently treated, there may 

 yet arise doubts as to the mode in which a strict theory 



1 Memorie di Torino [2] xliv. 1893, p. 27. 



2 Wiener Ber. ci. 1892, p. 1675. 



3 Wied. Ann. xii. 1881, p. 143. 



4 Comptes rendus, cxviii. 1894, p. 566. [He has also found (Comptes 

 rendns, cxxviii. 1899, p. 538) that the behaviour of C0 2 in a very wide range 

 of pressure and temperature is well represented by a formula of the type 



+ - {a + m(v - b) I 



kv n - a + V{(v - )8) 2 

 Wiener Sitzungsanzeiger, 1899, p. 87. 



