( 699 ) 



binodal curve is given by the line drawn in fig. 4 PI. IV. It is easy 



dp dp 



to see that now — <^ at the triple point 251^ and --^0 at lower 



dt dt 



temperatures. The transformation line has thus the course drawn in 

 fig. 5 PI. IV, which qualitatively is in complete agreement with 

 Tammann's determinations for this line. 



The transformation line from ice I to ice II is xerj similar to 

 that from ice I to ice III. Since the ice II ridge distinctly rises more 

 steeplj' than the ice III ridge the line of transformation from ice I 

 to ice II is more curved than that for ice I to ice III. The result 

 is that the line of transformation from ice I to ice II cuts, above 

 the absolute zero, the vapour pressure line of ice I, wiiich runs verv 

 close to the T-axis (see fig. 6 PI. IV). A triple point vapour 

 — ice I — ice II corresponds with this common point, this has not 

 been observed, but Tajdiann holds its existence as probable. Also the 

 transformation curve from ice I to ice III (PI IV fig. 5) when 

 produced cuts the T-axis. The common point then corresponds to a 

 negative temperature, and thus this triple point cannot be realised. 



The cur\e of transformation from ice II to ice III was not deter- 

 mined by Tammann, but its course can be seen on our model. 



From the model it follows that Tammann could obtain ice II by 

 cooling to — 80" C, w^hile less cooling would be sufficient for ice III. 



Owing to the form which we have chosen for the liquid ridge, 

 the expansion coefficient of water near 0° C. would be negative and 

 Avater would show a maximum density, while the expansion coeffi- 

 cient of ice would be positive, all in agreement with experiment. 

 The pressure lines for w^ater (see fig. 7 PI. IV) run in accordance 

 with this (at least near 0°) from larger to smaller value of v, and 

 simultaneously from lower to higher temperatures. The maxinuim 

 density of water, on our model, is shifted by increase of pressure 

 towards decreasing temperature, while at the same time it becomes 

 less marked and finally vanishes; also in agreement with experiment. ^) 



1) Amagat. Recherches sur les gaz. 



V. D. Waals. Arch. Néerl. Vol. XII. p. 457. 

 Grassi. Ann. d. chim. 3. 31, p. 437. 1851. 



