( 126 ) 
rom the infinite series not only by approximate combination of the 
remainder to some terms, but also through suitable omission of inter- 
mediate terms. 
It must be borne in mind, that the co-efficients of each of the 
remaining terms will have to be also expressed by a contracted series in 
terms of the temperature and hence it is obvious that we must try in the 
first place to bring about an agreement with a number of terms as 
small as possible but equal for all temperatures. 
But for this it is not sufficient to pay attention to one substance 
only. The range of temperatures for which precise observations have 
been made in the case of single substances, is too limited for each 
of those substances to derive from them the way in which the co- 
efficients of the terms of an isothermal are dependent on the tem- 
perature. We are still far from having realised the idea which has 
occupied me for many years viz. that of the precise determination 
of the isothermals of hydrogen at temperatures going down to its 
boiling point and lower. To a certain extent it is possible to sub- 
stitute for the investigation of one single substance over the whole 
range of the equation of state, that of several others within diffe- 
rent limits, namely when we combine by means of the law of cor- 
responding states the portions of the ranges of reduced temperature 
and density given by each of the substances investigated. 
It is true that the various substances are not rigidly mechani- 
cally similar. Some time ago VAN DER WAALS has especially made 
clear how the different degrees of compressibility of the molecules 
(in connection with the number of degrees of freedom) will show 
themselves by a difference in the equations of state of various sub- 
stances. And instead of neglecting the deviations in order to arrive 
at the general equation of state we should be inclined to do the 
reverse and start from the complete equation of state of each sub- 
stance, in order to express the deviations from the law of the corre- 
sponding states as functions of reduced temperature and pressure, 
these deviations being small for substances belonging to one group, 
and somewhat larger for substances belonging to different groups *) 
consisting of mutually almost mechanically similar substances. But so 
Jong as the observations have not proceeded further the method described 
will be the only way to determine as function of the temperature 
the coefficients of the simple terms in an isothermal developed with 
regard to density, which I will call virial co-efficients, and to forma 
1) KAMERLINGH ONNES, Proceedings Royal Acad. of Science 1881, p. 11. 
