( 1013 ) 
individual results, which cannot be satisfactorily represented by a 
special equation of state, with results obtained for other substances, 
and, particularly, with results obtained for those substances which 
have served for the calculation of equation VII.1. When deviations 
of some particular substance from the imaginary substance in the 
same reduced state have been calculated, then, the far more concise 
deviations from VII. 1. may replace the actual results of the experi- 
ments themselves.Such deviations were determined for each of the 
substances used in the synthesis of equation VII. 1. with respect to 
whose reduced surfaces of state that of VIi.1. plays the part of a 
quasi-enveloping surface. The critical temperatures of the substances 
can greatly influence the differences existing between the separate 
surfaces; the peculiarities of the molecules, however, can influence 
them, too, in another way. 
The object we had in view in our research upon the isotherms 
of monatomic substances was to obtain, in the same manner as that 
in which equation VII. 1. was obtained, a mean reduced equation 
of state in the synthesis of which observations on monatomic substances 
should exclusively be used. Unless in the structure of the various 
atoms of the monatomic substances further peculiarities are discovered 
which influence the equation of state, then, the only influence 
exerted upon the form of the reduced surface is that of the critical 
temperature. This influence will manifest itself in the deviations 
of the special equations from the mean equation undisturbed by 
other possible factors. And it is to be expected that the special 
surfaces of state for the various monatomic substances should 
sysiematically differ from the enveloping surface and from each 
other in such a manner that a gradual transformation would change 
the xenon') surface into those for krypton, argon, and neon, to 
finally assume a limiting shape in the case of helium). From the 
sequel, in which is given a first, but very small, step in the desired 
direction, it is evident that the mean reduced equation of state for 
monatomic substances which we desire to obtain, and which we 
shall indicate by VUImon., will exhibit important characteristic differences 
from the general mean equation VII. L. 
1) We shall, for the present, leave out of consideration substances of higher 
critical temperature. 
*) It was remarked in 1881 that a separate equation of state would have to be 
applied to each group of substances having similar molecules. (H. KameRLiNGH ONNes. 
Verh. Kon. Akad. 1881, Arch. neérl. 30, p. 101). The group of monatomic 
substances has been made a subject of special study from this point of view by 
H. Harper, see Ann. d. Phys. (4). 13. 340. 1904. 
