( 234 ) 



(o be expected as a rule. Thus il appears from table II thai these 

 pressures become very high, it' the circumstances are not very 

 favourable. 



It would have a very favourable influence on the circumstances 

 of temperature and pressure at which limited miscibility in the gas 

 state might be observed, if it should pro\e that for mixtures of 

 helium with another gas a^u is smaller than is expressed by 



§ 9. Mr. van Laars remarks, (These Proc. May '07 p. 34—4(5) 

 which imply that we have set forth some of our results as new, 

 whereas they had been already derived and published by him 

 before, compel us to the following explanations in order to show the 

 incorrectness of these assertions. 



I. As to part of these observations, they are best refuted by shortly 

 repeating the train of thought followed by us. 



When we applied the equations laid down by van der Waals 

 with regard to the spinodal curve') in Cont. II, § 19 sqq., trans- 

 ferred to the ip-surface for the unity of weight, to the case that one 

 (if the components is a gas without cohesion 3 ) with molecules which 

 have extension, we arrived on the suppositions 4 ) mentioned in § '2 

 at a plait which starts from the side of the small volumes, comes 



') These Prcc. March '07 p. 796 note 1, and van der Waals These Proc. April '07 

 p. 831. 



2 ) The equation tor the spinpdal curve of the molecular i -surface (cf. Van Laab 



These Proc. May '07 p. 37 at the top) was a;iven by Van der Waals in Cont. II. p. 45, 



da i ll> il'ii 



equation (1) in a form which after substitution of — , — and -— passes imme- 



</,(■ ax ax 



diately into that used by van Laar. (See van Laar, These Proc. May '05 p. 33 



at the bottom). The equation given by us p. 788 referred to and was derived from 



the equation for the d-surface for the unity of weight (These Proc. Dec. '00 p. 510). 



For the rest we differ from the opinion repeatedly expressed by Van Laar (inter 



alia These Proc. May '05 p. 34), that it would be more difficult and more elaborate 



to derive the equation of the spinodal curve and also that of the plaitpoint curve 



from the J,-funclion than to do the same from the ^-function. 



3 ) This investigation was announced in Comm. No. 96Ö, Dec. '06 p. 505. 



0''b 



4 ) When we were not allowed to put 5-— =0 for and in the immediate 



O.v 



neighbourhood of v = b, as we did (cf. Van der Waals Cont. II p. 4'2), the spinodal 



curve will always be closed towards the t-ide v = b as Van der Waals observes 



I.e. and These Proc. April '07 p. 848. It is then to be expected, at least for 



d'b 

 small ^ — , that the plait in question makes its appearance for the first time at a 



maximum plaitpoint temperature, and for the rest extends to the large r's in the 

 same way as the plait described here. 



