250 Proceedings of Royal Society of Edinburgh. [sess. 
this paper, that we may lawfully assume the existence of a liquid 
which, for some special (ordinary) temperature, shall give 
n = 2700 atm., e = 0*3. 
With these numbers the calculation is very much simplified. For 
such a liquid, if its volume were 1 at atmospheric pressure, would he 
reduced to 25/28 by 1500 atm., and to 16/19 by 3000 atm. The 
quadratic to which Van der Waals’ formula leads, is found to have 
imaginary roots ! 
The main cause of this totally-unexpected result” seems to be the 
factor 1 jv'^ in the term corresponding to K. Its effect is to make 
K increase at a rate quite inconsistent with the experimental data, 
at least if the rest of the equation is to retain its present form. 
This is easily seen by taking the following roughly approximate 
dp 
values of ^ for ether, at constant volume, which I obtained by 
a graphic process from Amagat’s Table 29. 
V 1 
•95 
•9 
•85 
(1) const. 10 
12 
14-5 
17 
p at 0° C. 1 
460 
1250 
2570. 
Since Van der Waals’ equation gives, for constant 
volume. 
we easily find the approximate values 
/8 = 0-63, R = 3'8; 
and the complete formula is something like 
+ - 0-63) = 1037 + 3-8<, 
where t is temperature centigrade. 
This cannot be very far wrong, so far at least as P and R 
are concerned, for it gives the following calculated values of 
^ (at the four selected volumes above) which are compared 
with the observed values 
Obs. 
Calc. 
10 
10-27 
12 
11-9 
14-5 
14-1 
17 
17-3. 
