536 PROCEEDINGS OF THE AJIERICAN ACADEMY. 



that of the liquid with which it is in contact. This enables us to put 

 an upper limit of 10 per cent as the probable error introduced by 

 assuming all the change of volume along an equilibrium curve to be 

 brought about by changes of pressure. 



The complete values of the volume are shown in Table XXX., which 

 gives the approximate compressibility along these curves. For com- 

 parison, the approximate compressibility of the water at the corre- 

 sponding pressure and temperature is also given. In consequence of 

 the change of volume due to temperature, the quantity listed as com- 

 pressibility is too big on the ice I curve, and too small on the other 

 curves which rise to higher temperatures with higher pressures. The 

 compressibility of the ice is uniformly less than that of the water, as 

 one would expect, varying from 1/3 to 2/3. On all the curves except 

 the III-L curve, the compressibility shows a very marked decrease 

 with rise of pressure, the decrease being more rapid proportionally for 

 the liquid. The same decrease would probably also have been shown 

 on the III-L curve, if it had been possible to make the measurements 

 of the change of volume with greater accuracy. On the I-L curve, 

 the change for a range of pressure of only 2000 kgm. is abnormally 

 high. This might be accounted for by a negative temperature coeffi- 

 cient of expansion of ice at the lower end of the curve. The change of 

 volume measurements I-III have already suggested this as a possi- 

 bility. The change of compressibility with pressure is greatest at the 

 low pressures, being particularly great in the region of instability of 

 VI. In general, when one variety of ice replaces another, one would 

 expect the new form stable at the higher pressures to show the lower 

 compressibility, corresponding to the smaller volume ; but this is cer- 

 tainly not true in the case V-VI, and probably not true when III re- 

 places I. The compressibility of each modification seems to be a 

 property inherent in that modification, depending probably on the 

 symmetrical arrangement of molecules in the crystal, and not depend- 

 ing so directly on the volume. 



As verifying these values very roughly, the directly determined 

 difference of compressibility between L and VI has been shown in 

 Figure 35. The values are evidently not of any great regularity. The 

 only two points found below 15°, at 0°, are much too high. These would 

 give a value for the compressibility at 0° of .O53O as against .O56 from 

 the data above, .O56 being too small. But in the region where the points 

 are thicker, between 15° and 50°, the agreement is better, discrepan- 

 cies being of the order of O.O5I. These points run to higher pressures 

 than the actual determinations of the compressibility of water, and do 

 show strikingly the rapid decrease in the difference between the com- 



