( 120 ) 



preceding it follows that Korteaveg's eighth case: 



TxiA<iTk , i-jpi^vk en 1 — 1 <0 



is in general not possible. 



A direct proof of this circumstance may easily be given. Because 

 ???„, must be negative, I put ,i = p^^ « — r^ ; T:cpi<^Tk requires that 



(,? — poi«)^ = ^Pii" — ^'^- Hence we may put: « = t, and 



'-'4 V\l O 4PHP3O 



SO that all the terms of r,^,i ai-e positive. Hence we see that, if 

 T,-^,i <iTk and f'-M < 0, o^,/ < a i« ^i' impossibility. 



18. The numerical ralue of the reduced dlferentinl quotients. 



To find this numerical \aluo 1 have lirst tried to derive it directly 

 from the observations by means of graphical representations; but as 

 I did not succeed in tinding more or less reliable values for the 

 higher differential quotients (i%i, \\g, v\o etc.) I was obliged to use 

 tbrnudae which satisfactorily represented the observations. Undoubtedly 

 Kamkrlingh Onxes' ^) developments in series are best fitted for this 

 purpose, although just in the neighbourhood of the critical point, 

 where in our case they have to be applied, they deviate rather nnicii 

 from the observations ^). Therefore the values of tlie derixatives obtained 

 in that way, especially those of the higher orders, can only be con- 

 sidered as approximate. 



By means of the temperature co-eflicients of reduced virial co- 

 efficients marked by V. s. 1 ») deri\ ed from Amagat's observations, 

 I find for those virial co-efficients ('31^, S^, etc.) and their first deriv- 

 atives according to the temperature {^\\, ^\ etc.) at the critical 

 point (t = 1), 



1) Proc. Royal Acad. 29 June 1901, Gomm. N'. 71, and Arch. Need. (2). 6, 874, 



1901, Gomm. N'. 74. 



") Gomp. Arch. Nécrl. loc. cit. p. 887. Pieviously I have given parabolic for- 

 mulae (Proc. Royal Acad., 31 March 1900, Gomm. N". 55 and Arch. Néerl. (2), 6, 

 650, 1901) which very well represent the observations just in the neighbourhood 

 of the critical point. These formulae, however, do not harmonize witli our con&i- 

 deralions, because they do not yield finite values for higher derivatives. 



3j Gomm. N". 74, p. 12. 



