Corrections of the Nitrogen Scale. 527 
The absolute temperature by the constant-pressure scale 
satisfies the equation o£ definition 
J = f fp=*); (3) 
whence by eliminating v from equation (2) we have 
To *«>~«Je <? 2 W 
Let T , 6 , t' refer to the ice-point. T is then the 
reciprocal of a, the mean coefficient of expansion of the gas 
at the constant pressure it between the ice and steam points ; 
6 is the absolute thermodynamic temperature of the ice- 
point ; v is the specific volume at the ice-point under the 
pressure it. Equation (4) may be used to find the value T, 
on the absolute constant-pressure scale, of any temperature 
of which the value is 6 on the absolute thermodynamic scale. 
As a preliminary to this, the value of O must be found by 
successive approximations setting T = T + 100, # = # + 100, 
and, to start with, O = 273. 
To perform the necessary integration, the value of /iG p 
must be known as a function of 6. The value of 6 is very 
approximately 273 + £, where t is the centigrade temperature 
by any of the common scales. Hence, since the second 
member of (4) is merely a small correction-term, it is 
sufficient if we can express /xC p as a function of 273 + £, 
which will be denoted by r. In other words, if we can 
find the form of the equation /iC p =/(t), we may write 
fiC p =f(0) in integrating equation (4). 
2. Use of the Laic of Corresponding States. 
Our experimental knowledge of the value of \jl for any one 
gas is not sufficient to enable us to decide upon an equation 
fiC p =f(r) which shall inspire any confidence as a basis for 
extrapolation outside the small range of temperature within 
which the experiments have been made. We therefore have 
recourse to the law of corresponding states, and thus bring 
all the experiments on the various gases into one connected 
series. 
We have to consider experiments on carbonic acid, oxygen, 
air, nitrogen, and hydrogen. We assume that for these 
gases there exists a single reduced equation of state, 
'(*iD-» « 
where p e , v e , r c are the critical constants. This assumption 
2N2 
