.160 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



several varieties of ice, a very rough experimental value for the com- 

 pressibility was given, as also a computation of the approximate 

 compressibility, neglecting the thermal dilatation of the ice, for which 

 no experimental value was found at that time. These measurements 

 here include a direct measurement of the thermal dilatation, and 

 two different determinations of the compressibility by two different 

 methods. The value for the dilatation may be combined with the 

 already determined values for the volume of the liquid and the change 

 of volume when ice VI separates out, to give a third independent 

 value for the compressibility. 



The determinations of the dilatation will first be described. This 

 was found in the same manner as the dilatation of the liquid, by chang- 

 ing the temperature at constant mean pressure, and measuring the 

 change of pressure brought about thereby. Three determinations of 

 this were made for the combination of ice and kerosene, and two for 

 the combination of kerosene and bessemer. The agreement of the 

 different determinations was within 2% of the mean. The dilatation 

 was found between 0° and 20° at a mean pressure of 10,000 kgm. The 

 correction introduced by the thermal dilatation of the bessemer 

 cylinder in the control experiment is fairly large here, being about 25% 

 of the entire effect. The value assumed for the cubic dilatation was 

 0.000036, which is the value for atmospheric pressure. The effect 

 of pressure is to decrease this number slightly, which would result 

 in a larger value for dilatation of the ice. The effect of pressure on 

 this quantity is, however, very small, and the error so introduced 

 is probably negligible. The mean dilatation found in this way for the 

 20° above 0° at 10.000 kgm. was 0.00241 cm.V gm., or 0.000120 

 cm.^/ gm. per degree. This is considerably less than the dilatation 

 of the liquid in this neighborhood, for which the value 0.00040 has 

 been found previously. 



This value for the dilatation may now be combined with the other 

 data for the liquid and the solid to give the compressibility of the 

 solid along the equilibrium curve. For this we have the following 

 data: vol. of 1 gm. of water at 0° and 6360 kgm., 0.8428 cm. 3, and at 

 20° and 9000 kgm. (these are the equilibrium pressures at these 

 temperatures) 0.8160 cm.^. For the change of volume when the 

 liquid freezes to the solid we have at 0°, 0.0916, and at 20°, 0.0751. 

 This gives for the volume of ice at the equilibrium pressures at 0° 

 and 20° the values 0.7512 and 0.7409 respectively. The decrease 

 of volume of the ice along the equilibrium curve is 0.0103. Part 

 of this is an increase due to rise of temperature, which according to 



