BRIDGMAN. — THERMODYNAMIC PROPERTIES OF WATER. 337 



these five points at e\ cry eonstant pressure, and the intermediate 

 vahies so chosen as to given smooth values for the second (Hfferences 

 over the entire tenijxM'ature range. The vahies for the points helow 

 zero, whicli are also <;i\en in the table, were taken diri'ctly i'rom the 

 previous work, the values for the dilatation found there being kept 

 without modification, l)ut the present value for the compressibility 

 at 0° being used. The difi'erences so introduced may be seen by com- 

 parison of the two tables to be only slight. 



The table gives the volume to only fom* significant figures, since 

 this is as many as the variations in the values of the compressibility 

 would entitle one to, but in nudving the calculations of the thermal 

 expansion it was necessary to keep three significant figures for the 

 expansion, which would mean five figures in the table. 



The thermal dilatation per degree rise of temperature was deter- 

 mined from the \alues used in the construction of the table for the 

 difi'erences of volume at 5° inter\als by dividing by 5, and using the 

 result as the thermal expansion at the mean temperature. The values 

 of the total change of volume for five degree intervals had been 

 smoothed so as to give smooth second flifferences, so that the dilata- 

 tion as found in this way was smooth also with respect to the second 

 difi'erences, and could be used directly to give the second tempera- 

 ture derivative of the volume at constant pressure. 



The difference of thermal dilatation at different temperatures can 

 evidently be combined with the known compressibility at 40° to 

 give the compressibility as a function of the temperature. 



These several quantities so determined; the compressibility, the 

 thermal expansion, and the second temperature derivative of the 

 volume, in their dependence on temperature and pressure, are the 

 basis of most of the calculations of the quantities of thermodynamic 

 interest to be given presently. The accuracy of most of these quan- 

 tites is not so high but that they can be shown as well in figures as in 

 tables, and this manner of presenting them has been chosen as giving 

 the most ready general survey of the facts. 



The tables and figures follow. The results are given simply for 

 themselves, without much comment, except to call attention to the 

 unexpected features, or those properties which seem to be peculiarly 

 characteristic of high pressures. It would not be safe to generalize 

 from the behavior of this one liquid, al)normal at low pressures, to 

 the general behavior to be expected for any liquid for high pressures 

 and the bearing on a possible theory of liquids. Such a general 

 treatment must be reserved for another paper, when the data for 

 more liquids are in hand. 



