14t> On the Joule-Kelvin Inversion Temperature, 
These four equations of state give for the maximum value 
of the temperature of inversion 
6-75* c , 3-182^/l+-& 0-36^, and 4'24* c , 
respectively. For carbonic acid a and ^ are nearly equal 
in Clausius's equation, so that for this gas the limiting 
temperature of inversion is 4*5 t c . 
In conclusion, the subject of the above discussion has been 
the possibility of coincidence between Professor Olszewski's 
experiment and that of Dr. Joule and Lord Kelvin with the 
porous-plug, guided by van der Waals's equation of state. 
That this equation requires some modification, or at least 
entails a limitation in its applicability to all gases and in all 
conditions, is admitted ; and it may even be that the Olszewski 
experiment and the van der Waals's equation may each assist 
the other in the progress towards truth ; but, today, on the 
conditions assumed, there is apparent incompatibility between 
them. This does not at all affect the purpose, as I read it, of 
Professor Olszewski's experiment, nor its success, namely, the 
determination of a temperature suitable for moderate pres- 
sures, such that if expansion of a gas be made below that 
temperature, cooling will take place. Incidentally, the full 
meaning of the term " a Joule-Kelvin inversion-temperature '* 
has been developed ; and whatever form the fundamental 
equation of state may ultimately take, this meaning will 
probably not require alteration. Although the theory is 
simple, the calculations involved have been long and heavy, 
but it is hoped that, as nearly every one was repeated, no 
serious errors have crept in. 
Note. — The texts at one point iu the description of Professor 
Olszewski's experiment are confusing. The German text of the 
Krakau Bulletin (1901, p. 455) speaks of " die im Innern mit 
Samischleder ausgefiitterte Blechbuchse." The translation from 
this in ' Nature ' (lxv. p. 577, April 1902) is " a thin metal box 
which is lined with chamois leather." The translatioa in the Phil. 
Mag. iii. p. 537, May 1902) is " box . . . which is stuffed with 
chamois leather.'' The difference between stuffing and lining the 
box materially alters the question. A German friend, who is a 
well-known authority on the German language, tells me that 
ausgefiitterte means " lined, as a glove lines the hand." The 
detailed description of the experiment promised by Professor 
Olszewski will, however, clear up the matter. 
Peterhouse, Cambridge, 
October 1907. 
