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Physics. — Communication N°. 71 from the Physical Laboratory 
at Leiden by Prof. H. KAMERLINGH Onnes: “Expression of 
the equation of state of gases and liquids by means of series.” 
§ 1. I have followed in this communication a different method in 
considering the equation of state than has been done up to now. 
Various methods have been tried to empirically derive functions of 
v and ¢ for VAN DER WAALS’ a and 5 by means of kinetic or ther- 
modynamic considerations, but without obtaining a good agreement 
with the observations over the whole range of the equation of state. 
Neither was I successful in similar attempts which were repeatedly 
occasioned by my continued research on the corresponding states and 
other investigations resulting from them at the Leiden Jaboratory. 
Whenever I seemed to have found an empirical form, I discovered 
after having tested it more closely that it appeared useful only 
within a limited range to complete what had been found in a purely 
theoretical way by VAN DER WAALS and BOLTZMANN. Hence it 
appeared to me more and more desirable to combine systematically the 
entire experimental material on the isothermals of gases and liquids as 
independently as possible from theoretical considerations and to express 
them by series. The idea of making this attempt and executing the 
elaborate calculations required ripened gradually on talking the matter 
over with my friend Dr. E. F. van DE SANDE BAKHUIJZEN, and 
many thanks are due to him for his advice in arranging and exe- 
cuting all the stages of those calculations. 
§ 2. My calculations, in so far as they are given in this paper 
comprise AMAGAT’s observations!) relating to hydrogen, oxygen, 
nitrogen and carbon dioxide. 
Although I had in mind the development of the equation of state 
p=fT) in a convergent double infinite series in terms of the 
ti : 
molecular density — and the absolute temperature, it follows from 
v 
the nature of the subject that we can only obtain a representation 
by a polynomial of a limited number of terms, and we need not 
wonder that this polynomial does not even converge for all densities. 
Each co-efficient of such a polynomial can be determined for an 
individual isotherm only when the polynomial consists of a moderate 
number of terms. Only in this way we can obtain a good agreement 
at the first calculation. Therefore the polynomial must be derived 
1) Ann. de Ch. et de Phys. 6e Sér. t. XXIX, 1893. 
