BRIDGMAN. — WATER UNDER PRESSURE. 493 



four times that found here. Tammann states concerning his own data 

 that his temperature coefficient is in all probability too high. His value 

 at —33.5° for the supposed change I-II, but really for I-III, is 0.193 

 cm./gm. This agrees exactly with the value found here at the same tem- 

 perature for the known change I-III, giving another bit of evidence from 

 Tammann' s own data that above— 35° II changes spontaneously to III. 

 Tammann's value for the change I-III at —45° is 0.192, giving a tem- 

 perature coefficient of the opposite sign from that found here. The 

 actual values for the I-III change agree much better with the values 

 found here than for the I-II change. The present values for I-III are 

 0.1904 at —32.5° and 0.2005 at —45°. 



The data taken from these two curves needed in the calculation of 

 AZTand A^are shown in Table XV. and Figure 15. I gives out heat 

 on passing to II and absorbs work. The work is greater than the heat, 

 so that the internal energy increases on passing from I to II. 



The Curve II-III. 



This has been already stated to have been the curve overlooked by 

 Tammann, but demanded thermodynamically. The discovery of it 

 places beyond question the essential difference between the two varie- 

 ties of ice II and III. The change of volume on this curve is very 

 slight, so that it is easy to overlook it altogether, as did Tammann. A 

 special method had to be used here in determining these equilibrium 

 points. It is the reverse of the usual method. The usual method 

 consists in changing the piston displacement and so the pressure at 

 constant temperature. Change of phase is indicated by change of 

 displacement with constant pressure. In the modification of the 

 method used here, the displacement is kept constant and the tempera- 

 ture changed. The resulting change of pressure is plotted as a func- 

 tion of the temperature. Change of phase, accompanied by a slight 

 change of volume, is indicated by a discontinuity in the direction of 

 the temperature-pressure line. 



At any given temperature during this change of phase there is only 

 one corresponding pressure, the equilibrium pressure, unlike the for- 

 mer method, where the piston displacement may have any value within 

 a considerable range corresponding to the same pressure and tempera- 

 ture. The change of volume is so slight that the interval of discon- 

 tinuity in the direction of the temperature-pressure line extended over 

 only 1° and 100 kgm. The method was made practicable by two 

 things, the smallness of the containing cylinder, resulting in a very 

 rapid attainment of temperature equilibrium, and the fact already 



