30G Mr. J. Rose-Innes on the Practical Attainment of 
fulfil the last condition, we obtain the characteristic equation 
We shall next enquire what is the change in the coefficient 
of expansion corresponding to the above equation. We have 
= ±^>-X 
R*, 
Vi = 2, 
0+l)V 
p ^(n + l)W l 
Multiply the last equation by — , the last but one by 
t . v ° 
1 . and subtract, we obtain 
r o^o 
i'o *o r U + 1) V (»+l)*i\T" 
Similarly for pressure p' we should have 
vi _ t A _ 1 / h x a * v a * \ 
«b' t ~ vj \* * (n + 1) t« * (n + 1) iff ' 
These last two equations after a little reduction yield 
r_ _ / 1 1 \ h S x a n v ^»_ 1 
" * \v ' vj h -t \*(n+ 1) V l+1 (n + 1) *i" + 1 J ■ 
We see then that the series 2 — must be chosen so as to 
i n 
satisfy three conditions : — (i.) The observed Joule-Thomson 
effect at different temperatures must be proportional to the 
values of the expression X ~; (ii.) the value of ( -, — J must be 
represented by — 2- ^— - for some single isothermal ; 
r J (ri+i).? 1 ° 
(iii.) the observed change in the coefficient of expansion 
must agree with the calculated value. 
Variation of the above Method, 
In the investigation given above I have assumed that 
observations of the Joule-Thomson effect had been made at, 
& sufficient number of different temperatures to fix fairly 
