142 
Mr. J. D. Hamilton Dickson on the 
experiment, the constancy of: the potential function U -\-pv is 
accepted. The inversion-points concerned are (fig. 1) the 
points of intersection of the isopiestic ol = ^ q (approximating 
to the case of air) with isopiestics ranging from « = 05 to 
a = 4*0. These points lie near N*, within the sharp apex of 
the curvilinear triangle. A somewhat expanded portion of 
this part of fig. 1 is given in fig. 5, which shows the inter- 
sections of the isopiestics u = l, 2, 3 with a = ^ . These 
/*CTEAfT//lL 
four isopiestics touch the envelope at increasing distances 
from N (the point of contact of the zero-isopiestic, at the 
reduced temperature 27/4), and it is clear that the points of 
section of a= ^y by «=1, 2, 3 must be at successively lower 
points in the figure ; that is, at successively lower tempera- 
tures. In other words- as a increases in this neighbourhood, 
the lower pressure being always constant, the successive 
inversion-temperatures must fall. This verifies the result of 
the direct calculation earlier in the paper. In fact the locus 
of actualJoule-Kelvin inversion-points in this neighbourhood 
* These isopiestics intersect again within the inversion triangle near M, 
but the temperatures at M are only slightly above the boiling-point, and 
differ greatly from those in the Olszewski experiments. It may be noted 
that this is an inversion region deserving attention. All lower isopiestics, 
for which «< 1, ha\e three inversion-points for each inversion-temperature 
lying within certain limits, less than the critical temperature ; otherwise, 
for a given isopiestic, there is only one inversion-point for each inversion- 
temperature. It may, however, not be possible to obtain these experi- 
mentally, for other reasons. 
