132 Mr. J. D. Hamilton Dickson on the 
plus in his paper) and temperature for the ordinate, both 
in reduced coordinates. 
In discussing the problem we may proceed along two 
lines, and it will be instructive to follow both. We may 
eliminate r and r' from equation (8) by means of an 
equation (4) for each ; or, we may examine the properties 
of the isopiestics plotted to the reduced values of pv — 
and t as coordinates. There is important information to be 
got from both methods ; meanwhile, equations (13) and (14) 
show that the two methods are equivalent. 
The function U+p?J being of the nature of a potential, 
I shall, in what follows, use this name for it ; and in this 
connexion isopotential curves will also be employed. We 
have to find the equation connecting the inversion-temperature 
with the initial and final pressures. As the rest of the 
investigation deals only with this temperature, we may drop 
the suffix i, and understand that t refers only to it. 
The result of eliminating v and v' between the equations 
^.ift-SX 1 -?) < 8 > 
(y+^)^-6)=K«. (*') 
may be written in the simple form 
(P + 7r + i?' + w) 2 = 8?n/, .... (15) 
where 
p = hW + 'P), 7r =^ r = -p 8 = P -P ' 
and u = x 
V (16) 
J 
If the pressures differ only slightly, as in the Joule-Kelvin 
experiment, we may in the limit take them as equal, and 
consequently put 8 = 0, P =p, u = r, and equation (15) 
becomes 
(p + 7r + fr) 2 = Sirr (17) 
This equation agrees with equation (10) in Dewar's paper * 
* Proc. Roy. Soc. March 1904, vol. lxxiii. p. 260. 
