28 REPORT— 1872. 



continual courersion of -water-svibstance from tlie fluid state (gaseous or liquid) to 

 ice, aud wbicb goes on till no steam remains to condense to water at a face of con- 

 tact with water, and till no water remains to be frozen at a face of contact with 

 ice. As this process goes on with briskness or agitation, involving rapid conduc- 

 tion of heat, we can see that, as in the previously supposed case, the process is 

 in'eversible by an infinitely small abatement of pressure ; and we can see that to 

 get steam to remain in repose in contact with ice at the temperature t^ of the sur- 

 rounding bath, we must have the pressure abated by a finite amount, so as to be 

 decidedly less than the pressure p^ belonging to steam with water at the fixed 

 temperatm'e of the bath : that is to say, for a temperature below the triple 

 ^ioint the pressure of steam with ice is less than the pressure of steam with water. 



Hence, referring to fig. 1 a, we see that in the steam-with-ice curve the point 

 U, having the same temperature t^ as the point C of the steam-with-water curve 

 has, must, while situated in the isothermal line BD passing through C, be away 

 from C at the side where the pressure is less than at C ; or it must lie between 

 and the coordinate axis Y A produced past A. 



This may be regarded as very nearly establishing that the curves cross one 

 another, as drawn in fig. 1 a. It shows that they do not, as in fig. 1 6. Up to 

 the present stage, however, the reasoning does not excUide the suppositions : — 

 1st, that the curves might meet tangentially in the triple point T, and pass on 

 without crossing ; 2nd, that they might cross in the triple point, meeting each 

 other there tangentially j 3rd, that the steam-with-ice line might absolutely stop 

 short in the triple point. 



The first and second of these I'emaining suppositions, depending, as they do, on 

 supposed tangential meeting instead of meeting or crossing angularly, the author 

 thinks very unlikely. One reason is that the condensed water-substance in contact 

 •with the steam makes a perfectly sudden change in its character in changing from 

 water to ice or from ice to water ; and he therefore thinks that in the curve which 

 represents steam with water above the triple point, and steam with ice below it, 

 ■we should expect to find a sudden change of direction at the point where this great 

 physical change suddenly takes place. 



Another reason against the first of these suppositions ■wdU be given in what 

 follows almost immediately, bj- a proof that after meeting in the triple point in rising 

 from lower temperatures, they cannot go on further without crossing. The third 

 supposition, namely, that the steam-with-ice line might stop short in the triple 

 point, the author thinks A'ery imlikely to be the truth ; but he is not aware of any 

 experimental proof to oSqv against it. 



Now, that the cur\ es, after meeting in the triple point in rising from lower tem- 

 peratures, cannot go on further without crossing, will be proved if it be shown that 

 on the supposition of tlie steam-with-ice curve not stopping short on rising to the 

 triple point, it must, on passing that point, have its course on the side of the 

 steam-with-water curve remote fi'om the coordinate axis Y A ; or, in other words, 

 if it be shown that, for any temperature t-, above the triple point, the pressm-e of 

 steam ^^-ith water is less than the pressure of steam with ice. 



This can easily be done by a demonstration quite like the one already given for 

 a temperature below that of the triple point ; and a brief sketch of it will here 

 suffice. 



Let us imagine that we have a cavity of variable dimensions, such as a cylinder 

 with a piston which can be loaded so as to apply any desired pressure to fluid sub- 

 stance enclosed within. Let this vessel contain steam with ice at a temperature 

 <2, which is above tliat of the triple point; and let the cylinder be immersed in a 

 bath maintained constantly at the temperature t^. Let the pressure of the steam 

 with ice for this temperature be called/).,- 



Now increase the pressure by an infinitely small amount S, making it /Jo+S. 

 "While this is kept applied to the steam, the steam is by it kept going down to the 

 state of ice ; and thus we can conceive of the whole or any desired part being con- 

 verted quite gentlj' to ice*. Next, while maintaining the pressure /^ ox p.^-\-h in 



* The fact that the ice being rigid would oppose a mechanical obstruction to the com- 

 plete pressing of the steam down to ice by a piston, may be noticed in passing, but it does 

 not introduce any tlieorctical difliculty into tlie reasoning. 



