TRANSACTIONS OF THE SECTIONS. 27 



extracted, and then the counterpoise B must just balance th^ weight of the piston. 

 Let weights A, A be laid on the piston, which will give exactly the pressiire p, 

 to the fluid enclosed in the cavity of the cylinder ; and let this enclosed fluid be 

 supposed to bo water-substance taken at first in the state of steam with water, as 

 shown in the figure, where S is steam and W is water. 



Let the entire cylinder and its contents be maintained at the temperature t^ (a 

 temperature below that of the triple point) by immersion in a bath at that tempe- 

 rature, ^], as shown in the figure. 



Now apply an infinitely small extra weight on the piston, so that the internal 

 pressure becomes ;^i + S, where S is infinitely small. This causes the steam to go 

 perfectly gently down to water. 



Now insert a particle of ice. Brisk action or agitation instantly sets in. 

 Thus:— 



(1) The water with ice cannot repose without both coming to the temperature 

 which, for the pressure ^^i + S, or we may here as well say for the pressure ^jj, 

 belongs to water with ice ; that is to say, in reference to fig. 1 a, the water with 

 ice cannot repose without both coming to the temperature of the point U on the 

 water- with-ice line in that figure. 



(2) The water at this raised temperature, or at any of the intermediate tempe- 

 ratures between this and the temperatm-e i, of the sm-rounding bath, is in a state 

 tending to ebullition into steam, a state in which boiling will ensue if a beginning 

 be made at all, or if due facility to begin be afforded in any way. 



(3) Conduction of heat, or conduction with convection, is briskly going on, con- 

 veying heat out to the bath, since the temperature inside is at some parts warmer 

 than the bath, and is nowhere cooler. 



Now, either ebullition ensues, or it does not. 



First. Suppose it not to take place : — 



Parts of the water are warmed by the freezing-process. They briskly transmit 

 heat out to the bath, the freezing goes briskly on, and the same process of trans- 

 mission of heat from a higher to a lower temperature goes briskly forward. This 

 continues till all the enclosed fluid has become ice. 



Now it is obvious that if there is a brisk action, with rapid conduction of heat, 

 when steam, or water-substance partly steam and partly water, is allowed to pass 

 into the state of ice while the pressui'e is^s^ + S and the surrounding temperature is 

 <j, there could be no return or reversal to the old condition of steam, or of steam 

 with water, caused or allowed by merely an infinitely small abatement of pressure 

 from /^i-f-S to p^. To cause the ice to evaporate, or to get it to remain in equili- 

 brium with steam, which we know experimentally it can do at a low enough pres- 

 sure, a finite (not infinitely small) abatement of pressure is necessary. 



Thus has been proved what was wanted, provided we be right in supposing 

 ebullition not to talie place. 



But now : — 



Second. Suppose ebullition to ensue on the introduction of the ice — a com- 

 plicated interaction of water, steam, and ice, involving brisk agitation, must 

 set in. At any face of contact of water and ice, the temperature must be that 

 of the point U in fig. 1 « ; at any face of contact of steam and ice the tempe- 

 rature must become that which "belongs to the pressiu'e pj^ on the steam- with-ice 

 line, and which is shown at the point W in fig. 1 a on the supposition of the 

 curves crossing as represented in that figure ; and at any face of contact of steam 

 with water the temperature must be that of the point C. As yet we need not 

 assume that we know whether the point W for pressure p^ on the steam-with-ice 

 line is at a higher temperature than that of C, as is represented in fig. 1 a, or at 

 a lower temperature than that of C, as it would be if the curves crossed as in fig. 

 1 b ; but clearly we know that the temperature of LT is higher than that of C, 

 which is the same as that of the bath ; and we can also see that any steam in con- 

 tact with water and sm-rounded with the bath at temperature <j while the pressure 

 is Pj^ will be ready to condense to water, or will actually so condense if the pres- 

 sure be increased by the infinitely small augmentation 8, just as did the steam 

 originally supposed to occupy part of the cavity. Thus we must have an action 

 going briskly on, involving rapid conduction of heat, an action involving the 



