140 
Mr. J. D. Hamilton Dickson on the 
by means of the inversion-isothermals, — curves of constant 
inversion-temperature drawn with potential and pressure 
as coordinates. These are given in fig. 3, and have been 
drawn from readings taken directly from fig. 2. If we 
want to arrange for 1*4 times the critical temperature 
as an inversion temperature, we may expand the gas from 
about 25 times the critical pressure down to a vacuum ; or 
from about 19^ down to about 1£ times the critical pressure ; 
or from 13J to 2J ; or from 10 to 3f ; or, finally, a Joule- 
Kelvin experiment may be made for this temperature as an 
inversion-temperature if we expand the gas from a little 
above to a little below 5f times the critical pressure. Joule- 
Kelvin experiments with small differences between the two 
pressures are represented by points on the parabolic arc 
FG-H...KJ, whose equation is 
9(3a?-2) 2 =16(9-a) (35) 
The area of inversion is here again a curvilinear quadri- 
lateral. It is bounded by the axis of #, and the isopotential 
x= — *6, by the zero-isothermal, and by a parabolic arc, part 
of which is the curve ST whose equation is 
27^ 2 +l« = 108 (36) 
These inversion-isothermals will afford the means of clearly 
testing the reduction of Olszewski's observations made 
recently by Porter. The basis of his calculation is that 
from Olszewski's experiments the inversion-temperature is * 
"about 5*8 times the critical temperature/' Putting # = 5*8 
in equation (25), the quadratic for a is 
4« 2 + (27^-108A' + 77-6) a -(729 t t' 3 -523-8^ 2 -2152-96) = 0, 
.... (37) 
from which the following Table has been calculated. 
X. 
a x . 
a,. 
1-70785 
3-5119 
1-7105 
5-28 
1-76 
1-715 
641 
0-64 
1-7185 
7-065 

1-725 
803 
-0-93 
1-750 
1069 
-351 
1-8 
14-33 
-7-00 
1-9 
1968 
-1215 
20 
2406 
-16-46 
* Loc. cit. p. 503. 
