530 Mr. E. Buckingham on the Thermodynamic 
Table II. Column 1 gives the initials of the observers to 
whom the observations on /u, are due ; column 2, the symbol 
•of the gas ; column 3, the reduced temperature of experi- 
Mr> 
ment ; column 4, the value of — — ./iC p deduced from the 
observed value of fju ; column 5, the number of separate 
experimental values of which /j, is the mean ; column 6, 
the average amount of impurity in the gas ; column 7, the 
value of y computed by equation (11) ; column 8, the 
differences y— 3/ calc . The values given by Kester are extra- 
polated to zero impurity from experiments with amounts of 
impurity up to 2'2 per cent. 
The points in Plate XV. represent the values given in 
columns 3 and 4 of Table II. They do all lie close to one 
smooth curve, including Olszewski's inversion-point *. The 
curve drawn is a satisfactory representation of the experi- 
mental results ; it is an equilateral hyperbola w r ith the 
equation 
^•^ = ^-10 (ID 
It will be found upon examination that the points which, 
from the number of separate experiments involved and the 
purity of the gas, appear a priori to deserve the most 
confidence, lie on the whole closest to the curve. 
Equation (11) is an empirical equation with three 
constants. It is therefore natural that it may be fitted 
to the observations somewhat more closely than one with 
only two constants : for example, the equation given by 
Eose-Innes f , 
/* = 4- B > ( 12 ) 
which follows 7 for low pressures, from van der Waals's 
equation of state, or the reduced equation 
M* = -^-B, (13) 
deduced by D. Berthelot J from his form of the equation of 
state. But aside from the fact that there is one more 
arbitrary constant available, equation (11) has an advantage 
over the two just mentioned, in that it does not make the 
curve asymptotic to the vertical axis. Inspection of 
* Compare A. W. Porter, Phil. Mag. [6] xi. p. 554 (1906). 
t Phil. Mag. [5] xlv. p. 227 (1898). 
% Trav. et Mem. Bur. Int. xiii. (1903). 
