( 1105 ) 
lowest temperatures at least); and, therefore, the predominance of 
characteristics which are just the reverse of those in associative substances 
leads to the supposition that in our case a part of the attraction 
diminishes with the temperature. Even this idea is at first sight 
strange, for we are familiar with the idea of attraction increasing 
as temperature falls. According to BOLTZMANN's law this increase 
must take place in a perfectly definite mauner, even for a constant 
attraction between the molecules. When, therefore, we assume a 
decrease in the cohesion this must exist notwithstanding the cause 
for increase given by Bo.tzMann’s law. It would, perhaps, be due 
to the fact, that at lower temperatures the decrease in the attractive 
force originating in the helium atom would predominate. 
Let us work out a little further a modification that will affect 
the behaviour of the substance in such a way as to decrease the 
attraction, the a of vaN per Waars, with the temperature decreasing 
below a certain temperature. Its importance is far more radical than 
that which occasions an increase, for, while the latter changes the 
phenomenon more in degree, the former can occasion a fundamental 
alteration. 
A few simple illustrations may illustrate this point. For the sake 
of simplicity let us take the vaN Der WAALS equation of state. Putting 
a and 6 constant for higher temperatures so that Zp can be cal- 
culated, and putting also the attraction @=AT from 7'—0 to 
T = Tx and, therefore a= KTx at Tx, it follows then, in sucha 
simple manner that it is not necessary to write down the equations 
here, that all temperatures below the critical 7% show the eritical 
phenomena for v = 36, the critical pressure being for every tempe- 
eld Gn OF 
rature proportioval to the absolute temperature, viz. a ie With 
al De 
respect to the individual isotherms, the gas above 7% behaves as a 
VAN DER Waars substance, in correspondence with our assumption 
a=const., but, for every temperature 7’ below 7, the isotherms 
are determined by taking the isotherm of 7% and shortening its 
ordinate in the ratio of 7 to 7. 
Assuming now that a= KT holds only up to a certain tempera- 
ture 7, < 7, and that a= const. is the law from T > 7, onwards, 
then the isotherms from the critical temperature to 7’, ave determined 
from the equation of vaN per Waars, and from this equation, too, 
are determined the maximum vapour pressure, and liquid and vapour 
densities. Isotherms for lower temperatures are then determined from 
these by taking the ordinates for each volume from the isotherm 
for 7, and diminishing it in ratio of T'to 7. The densities of coc- 
