134 
Mr. J. D. Hamilton Dickson on tJie 
magnitude to a lower pressure of any magnitude subject to 
certain conditions, namely, it must enter and leave the 
neighbourhood of the plug at the same temperature ; some 
considerable time must elapse between the starting of the 
experiment and the commencement of observations so that 
the flow of gas may be steady both as regards pressure and 
temperature ; the gas must leave the plug with kinetic energy 
differing so little from that with which it approaches the plug 
that this difference may be neglected ; then, the temperature 
in question is an inversion-temperature for the gas concerned 
and the pressures employed. 
For the discussion of the general question it is convenient 
to express equation (19) in reduced coordinates. Let a, a' 
be reduced pressures, and put 
a + a! a. — a! a 
a = 
r = 
(21) 
54 21 
the equation then becomes homogeneous and of the fourth 
power in a/b*. On dividing this factor out, it takes the form 
9/3 4 -fl6(l+3o-)/3 :; -2{4(l + a)(5-llc7)4-3e 2 }/3 2 
-16{4(l4-<7) 2 (l-<7)-(5-o-)e 2 }/3 
+ 16(l + o-) l -8{2r3-cr) 2 -(l + o-) 2 }e 2 + e 4 = 0, . {22) 
whence the reduced temperature corresponding to any pair 
of pressures a, a / is 27 /3. 
8 
As numerical examples of equation (22), I have taken the 
case of a gas with a critical pressure of 40 atmospheres, and 
have supposed expansions, on the Joule-Kelvin process of 
experiment, to take place from 160, 120, 80 and 40 atmo- 
spheres in each case to one atmosphere. Thus the values of 
a are 4, 3, 2, 1 respectively, and that of a is ~ . Linde and 
Berthelot quote 39 atmospheres as the critical pressure of air, 
so that the following results will approximate to those for 
air, on the suppositions made. 
The four equations are: — 
for a=4, a'=4 
9£ 4 + 19-575/3 3 -36-06£ 2 -66-66/3 + 18*56 = 0; 
for a = 3, a' = ^, 
9/3 4 +18-685/3 3 -37-10/3 2 -66-37i/3+ 18*31 = : 
for*=2, a'=^, 
9/3 4 + 17-795/3 :! -3^10/3 2 - 65S6J3 4-17-82=0; 
for * = l } a'=~, 
9/^+16-908/3 2 -39-0;H/3 2 -65-06/3 +17-07=0. 
Y . - (23) 
