( 683 ) 



to be able to fix a meaning for some of the conditions which according 

 to this possibility are suggested by us, we must suppose that the material 

 can suffer stresses with imponderable as well as with ponderable 

 mechanism. Thus we may obtain actual values for 7^ as well as for v 

 at which we can keep the material homogeneous which in reality 

 would be impossible. No difficulty should arise if we in addition to 

 general assumptions suppose that the entropy can be kept constant. 

 We only extend to the imponderable mechanism what is generally 

 allowed for the ponderable, when one supposes the substance kept 

 homogeneous with constant volume in van der Waals labile conditions. 



We have thus in the following set ourselves to model the parts 

 of the GiBBs' surface Avhich are experimentally known, for substances 

 which exist in the solid state, to add to these portions the vapour 

 and liquid regions following van der Waals, and to combine the 

 region thus obtained with the solid ridge in such a manner that the 

 isotherms on the Gibbs' surface shall differ as little as possible from 

 the unchanged isotherm of van der Waals, and the course of the 

 isotherm in the ij v pi'ojection shall be as simple as j^ossible.Wehsive 

 e. g. excluded states on the surface where 2' =0 except at i^ = — oo 

 and have supposed that for every value of i] and v only one value 

 of 8 belongs. 



It is clear that the problem formulated thus does not extend further 

 than the search for a continuous function, which for a known range 

 coincides with the Gibbs' surface and satisfies a given — but phy- 

 sically we hope happilj- chosen — criterion of simplicity. The solution 

 obtained from this determination has a certain value and forms a 

 continuation of the investigation of Comm. Nos. 71 and 74 ^), the 

 development of the equation of state in series. 



There also the principal object was to produce a numerically correct 



combination of the experiments independent of the thermodynamic 



peculiarities of the substances treated. The solid state w^as at first not 



considered in order to avoid a too large field. With this limitation 



it appeared that the whole range of experiment for normal substances 



could be expressed by a series condensed to a polynomial in powers of 



1 ^ rdp 



— , so that we could find exact values for ;;, for -jj = I — dv, for 

 V J dt 



f = I j T 2^ J (and other quantities e. g. tp = — | pdv) for all 



states within the region considered, without tedious calculations. 



1) Kamerlingh Onnes. Ueber die Reihenentwickelung fur die Zustandsgleichung 

 der Gase und Fliissigkeiten, Livre jubil. Bosscha Archives Néerl. (II) T. VI p. 874 — 

 888, '01. Leiden Gomm. n^ 74. 



