TRANSACTIONS OF THE SECTIONS. 29 



he steam, if any remains, or in the water next to be introduced, introduce a par- 

 ticle of water. Instantly the ice begins to melt, and falls in temperature, at the 

 place of contact with water, to the temperature of water with ice for the applied 

 pressui'e ^j^ or p.^-{.8 ; that is, to the point V in the figure. But the surrounding bath 

 13 warmer than this, and so a decided difference of temperature is maintained, 

 involving a rapid conduction of heat from the warmer bath to the colder melting 

 ice and the cold water in contiguity to that ice. There can be no repose till all 

 the water-substance originally enclosed as steam with ice has become water ; be- 

 cause, while the steam can pass gently to ice under the pressure p^, on the sup- 

 position that some particle of ice is kept present, and will be forced down by the 

 infinitely small excess of pressure S, the ice must briskly rush to the state of water. 

 But we know we can have steam present in repose with water at the maintained 

 temperature t.^ if we make the pressure small enough. An infinitely small abate- 

 ment of pressure will not counteract or reverse the change which has been briskly 

 taking place ; and so the pressure must be made decidedly lower than either ^j^+S 

 or p., to allow of the water resting in equilibrium in contact with steam at the 

 temperatm'e t.^. 



That is to say, referring to fig. la, on any isothermal line, such as FG, the 

 point II, where it is cut by the steam-with-water line, must be nearer to the axis 

 X A than is the point G, where it is cut by the steam- with-ice line. 



This, then, closes the course of reasoning entered on hitherto in these pages, and 

 establishes (the author thinks with very little if any room left for doubt) that the two 

 curves do not cross as in fig. 1 b ; and that in meeting at the triple point, they do 

 not meet and pass tangentially without crossing, but that they must cross as in 



The conclusion here arrived at the author thinks may admit of e.xpenmental 

 verification ; and he thinks it opens a desirable field for further and more perfect 

 experimental researches than have hitherto been made on the coexisting pressures 

 and temperatures of steam and other gaseous substances, each in contact with its 

 own substance, either in the liquid or in the solid state, at temperatures ranging 

 above and below the triple point for each substance. Without its being necessary 

 to make experiments on substances in the conditions represented by the dotted ex- 

 tensions of the curves past the triple point, he thinks that very accurate experi- 

 ments might show, for steam, an obtuse re-entrant angle or corner at T, in the line 

 L T N, which appears not to be one cm've, but two distinct curves meeting in T, 

 and crossing each other at that point. 



Through an examination which the author has made of the experimentally 

 derived curve given by Regnault * for what is shown as L T X here in fig. 1 a, he 

 finds that the curve seems to show a slightly perceptible feature of the kind here 

 anticipated — a slight re-entrant angle, or at least a slightly flattened place, or 

 place of diminished curvature at the triple point ; but this feature does not appear 

 sufficiently marked to admit of its being relied upon as a decisive experimental 

 confirmation of the theoretical view here submitted. 



The author also submitted to the Meeting the following additional considera- 

 tions on the subject. 



It can easily be shown that the j^erpefual motion would be theoretically attainable 

 unless (1) the pressure of steam with ice for a temperature (!,, which is below the 

 triple point, were less than the pressure of steam with water for the same tempe- 

 rature t^ ; and also (2) unless the pressure of steam with water for a temperature 

 t.^, taken above the triple point, were less than the pressure of steam with ice for 

 the same temperature t^. 



To prove the first of these, we have to observe that at t^, which is below the 

 triple point, in pressing steam down into water, we give mechanical work to the 

 substance (call this (t). Then when we insert ice, there is a finite difference of 

 temperatures, with conduction of heat out to the bath ; now by making this heat 

 pass, not by conduction, but through a thermodynamic engine (an air-engine for 

 instance), we can obtain work, which let us call h. During this freezing, too, we 

 get back from the water-substance a little work, owing to the expansion of the 

 water in freezing under the presure p^ (call this c). Next allow the volume to 

 * Memoires de 1' Academic dea Sciences, 1847, plate viii. 



1872. 4 



