304 Mr. J. Rose-Innes on the Practical Attainment of 
hydrogen or nitrogen thermometer, we shall thereby intro- 
duce an error involving squares o£ small quantities into the 
finally accepted values of the Joule-Thomson effect : such an 
error may be safety disregarded. For much the same 
reason it is permissible to employ approximate methods in 
evaluating the integral I. We can effect the evaluation most 
conveniently by a graphical method, — plotting a suitable 
curve and finding its area by means of a planimeter in the 
usual way. 
Having secured a sufficiently accurate value of \, we may 
proceed to calculate the absolute values of the Joule-Thomson 
effect from the experimental results of Joule and Kelvin. 
&t 
We will suppose that JK^- throughout the field of observa- 
tion may be fairly well reproduced by means of a series in 
descending powers of t, say 2 -£, where n is either positive 
or zero. The fundamental differential equation may then be 
written 
Divide by t 2 , 
* fdv\ v a„. 
t \dt) p t 2 *"* t n + 2 ' 
Integrate with respect to t along an isopiestic, and we 
obtain 
t (n + l)r+ J 
where P is a function of p only. Multiply by pt, and we 
have 
pv = pPt —p 2 
(n+l)P 
The product pP is a function of p only and may be 
denoted by f(p) : we thus have 
pv=f(p)t-p2 7 
(n + iyt*' 
1 yjr, an 
Denote pv by the single symbol y/r, and differentiate with 
respect to p>, keeping t constant, 
SK-'Cp)*-*^ 
