126 Transactions of the Boyal Society of South A frica. 
The average value of ft is 0-002446. This gives a = 15-255 in the units 
employed. 
With a view to the applicability of the law of corresponding states to 
the modified equation, (6) may be written in the form — 
« = a,£/5T^(i-^) (7) 
where ^ is the reduced temperature, and /3T,. = 1-127. 
§ 3. The Modified Equation. 
Equation (2) now takes the form — 
.n-r'">-^)^^T 
If the law of corresponding states is to hold good, /3T;, should be the same 
for all substances. Whether this is the case or not has not yet been 
determined, but it seems probable that it will not be found strictly 
constant, but to vary more or less with the complexity of the molecule, 
just as in the case of the reduced diameter slope." In these circumstances 
we may, as a first approximation to a general equation, take /3T;. to be 
unity, and equation (8) then yields on reduction — 
7r + ^,£l-^)(3a>-l) = 8^ (9) 
In the sequel it is shown how much more closely this equation agrees 
with experiment than the original unmodified form. 
§ 4. The Modified Saturation Constants. 
A direct calculation of these constants is best made by a substitution 
method. If we write — 
3«.-l = n-/'| 
Z^^-l = r,P \ 
and substitute in (9) and in the Maxwell equation — 
J" Trdb) = TTgiu)^ — (11) 
we can eliminate tt and and obtain — 
^''^(/3 + l)£-/^ + (/3-lV^ (^^^ 
sinh 2/3- 2/3 
~/3cosh/3-sinh/3 ^ ^ 
* Cf. E. Mathias, H. Kamerwngh Onnes, and C. A, Ctiommelin : Comm. Leiden, 
Ko. 131a (1913). 
