the Thermodynamic Scale of Temper at are. 305 
For several gases the quantity \j^\ is difficult to deter- 
mine experimentally at temperatures where the Joule- 
Thomson effect has been measured ; for such gases, however, 
it is always found possible to select some one isothermal as 
being fairly well determined ; the temperature of this iso- 
thermal is never far removed from ordinary atmospheric 
temperatures. The value of \j^) along the selected iso- 
thermal is found in all cases to be independent of the pres- 
sure to the degree of accuracy to which we are at present 
working. It follows that 
ip Jt (« + 1) t' 
must be constant along the selected isothermal ; hence f'(jp) 
will also be a constant along the same isothermal, say e. 
Further, the value of f{p) from its form must remain 
unaltered for any isopiestic change; hence it will remain 
equal to e for any condition of the gas which can be reached 
from the above-mentioned isothermal by means of an iso- 
piestic change. In other words, f'(p) must be equal to the 
constant e to our present degree of accuracy. 
Since t / y (j7j = 6, it follows that 
/O) = B+«P. 
where R is an arbitrary constant introduced by the integra- 
tion. Employing this value of j(p) we obtain 
yjr= Rt + ept—pX 
(n + 1) V 
If v is kept constant while p and t are both made to 
increase together, the term €pt will ultimately become more 
important than Rt. As it seems improbable that this can 
represent the true state of things at high temperatures We 
ought to try to make e vanish. We can secure this result 
if we can put 
/djr\ _ _ g a n 
\dp)t~ 0+l)*» 
along the isothermal we have selected for measuring the 
deviation from Boyle's law. Choosing the series X-^ so as to 
