Pressure. TABLE IV. VOLUME OF WATER AS A FUNCTION OF PRESSURE AND TEMPERATURE. kgm. -20°, -15°, -10°, -5°, 0°, 5o, 10°, 15°, 20°, 25°, 30°, 35°, 40°, 45°, 50°, 55° 60°, 65°, 70°, 75°, 80°. cm. 0 500 1000 1500 .8766 .9896 .9732 .9585 .9457 .9337 9226 .9123 .9028 .8940 .8858 1.0017 1.0006 1.0000 0.9999 1.0001 1.0007 1.0016 1.0028 0.0041 1.0057 1.0076 1.0096 1.0118 1.0143 1.0168 1.0195 1.0224 1.0255 1.0287 3500 4000 4500 In presenting the results, the quantities have been arranged in order of simplicity of the thermodynamic formulae, which is also the order of directness with which they are derived from the experimental data. Volume, cm.3 per gm. 0 1 2 3 4 Pressure, kgm. / cm.2 x 10 5 6 7 8 9 10 11 12 FIGURE 3. Isothermal lines for water, showing volume against pressure. In Table IV are given the values of the volume for intervals of pressure of 500 kgm., and intervals of temperature of 5°. The table does not require comment. It was computed in the way already described. The values of the volume at intervals of temperature of 20° are shown as a function of the pressure in Fig. 3. The figure does not show the results as accurately as the table, but enables one to form a clearer mental picture of the nature of the results. The curves, on the scale of the figure, do not show any abnormalities to the eye, except in the neighborhood of the origin, where the well known negative expansion at 0° results in the curves drawing together. There are various abnormalities besides those in the neighborhood of 0°, however, as will be shown by the other figures. With regard to the compressibility there seems to be some variance of usage, so that it will be well to call attention to the fact that the quantity used throughout this paper in the sense of compressibility is FIGURE 4 The isothermal compressibility of water, (ap), against the derivative av др др Sometimes the expression v pressure. is used in the same sense. Figure 4 shows the compressibility, that is, the analytic expression (3); as a function of the pressure at 0°, 20°, and 80°. It would have made the figure too crowded to have tried to show the values for 40° and 60° also. The complete values for the five standard temperatures are shown in Table V separately, however. The figure shows the well known abnormality in the compressibility at the low pressures, namely a higher compressibility at the lower than at the higher temperatures. This abnormality disappears above 50°, and from here on the compressibility increases with rising temperature. The figure shows that at 80° the initial compressibility is higher than at 20°, although it has not yet risen to the value at 0°. In addition to the abnormality at low pressures, the curve shows also a slight abnormality at the higher pressures in the neighborhood of 6500 kgm. Here the compressibility at 20° rises and at the melting point of ice VI, it has become higher than the compressibility at 80°. The thermal dilatation shows abnormality in the same locality; it would seem to be connected in some way with the appearance of the new variety of ice, but the exact connection cannot at present be stated. The large change in the value of the compressibility brought about by pressure should be noticed, amounting at 12,000 kgm. to a decrease of five fold. Furthermore the rapid flattening of the curve at the higher pressures also should be commented on. The curve gives the appearance, for the pressure ranges used here, of becoming asymptotic to some value greater than zero. Of course this cannot really be the case for infinite pressures, for otherwise we should have the volume completely disappearing for some finite value of the pressure, but it may indicate the entrance of another effect at the higher pressures, which may persist in comparative constancy for a greater range of pressure than will ever be open to direct experiment, such an effect as the compressibility of the atom, for example. This possibility has been already mentioned and made plausible from the data of the preceding paper. If instead of the compressibility as defined above, the quantity 1 (მო which in this paper will be called the relative compressibility, is plotted, a curve of the same general character as that shown will be obtained. v The compressibility may also be plotted against a different argument than the pressure. For many purposes the pressure is perhaps not the most significant independent variable that might be chosen. This is because the external pressure is not a measure of what is happening inside of the liquid. We conceive a liquid as composed of molecules in a state of constant motion and of collision with each other, acted on also by attractive forces between each other. The effect of these attractive forces is to produce at the interior points a pressure which may be much higher than the external pressure. The external pressure is equal to the interior pressure diminished by the amount of the attractive pressure drawing the molecules to the interior at the exterior surface, where the attraction is an unbalanced action in one direction. The amount of the unbalanced pressure at the outside depends in a complicated way on the law of attraction between the molecules, on their mean distance apart in this surface layer, and on the distribution of velocities in this layer. The external pressure required to hold the liquid in equilibrium is, therefore, largely a surface phenomonon, and is connected in a complicated way with the state of affairs at inside points. A more significant independent variable, therefore, would be one involving only the condition of the |