BRIDGMAN. — THERMODYNAMIC PROPERTIES OF LIQUIDS. 35 



and temperature had been linear was computed and plotted against 

 temperature. The slope of the difference curve was then found 

 graphically, and applied as a correction to the value found on the 

 assumption of a linear relation. The modification if Cj, at atmos- 

 pheric pressure is not known is obvious; a similar procedure, plotting 

 now the difference of heats against temperature gives the difference 

 of the specific heats at the pressure in question and atmospheric 

 pressure. In a few cases, where the liquid boiled at a low temperature 

 at atmospheric pressure so that it was not possible to prolong the 

 curves to the origin of pressure, the difference between the specific 

 heats at the pressure in question and 500 or 1000 kgm. has been given. 



It is now obvious why it was necessary to know the differences of 

 the mechanical work and the heat of compression at different tempera- 

 tures with a greater accuracy than could be found from the curves 

 obtained by a direct integration. 



The units in which the specific heats are given should perhaps be 

 mentioned because they are unusual. It is customary to give the 

 specific heat in gm. cal. per gm. of the liquid. But this method of 

 measuring specific heat makes no connection with the thermodynamic 

 formulas, in which the heat is measured in mechanical units corre- 

 sponding to the units of the other quantities. It w^as preferred here, 

 therefore, to give the heat in units which are more unusual, but which 

 are consistent with the other quantities, so that it is possible to substi- 

 tute any of the quantities directly in the formulas without the trou- 

 blesome work of changing the units. The unit of pressure is the kgm. 

 per sq. cm., and the unit of volume the c.c. Therefore the unit 

 of work which fits the formulas is the kgm. cm., and this is the 

 unit in which the results have been tabulated. It is to be noticed that 

 in making comparison with the usual values of the specific heats, it is 

 not only necessary to change the unit of work, but the unit of quantity 

 as well, because the amount of liquid to which this value of the specific 

 heat is referred is not the gm., as is usual, but is the amount of liquid 

 which at 0° C and atmospheric pressure occupies 1 c.c. In order to 

 convert the usual value of the specific heat into these units, it is 

 necessary to multiply by the density of the liquid at 0° and atmos- 

 pheric pressure, and by 42.66, the number of kgm. cm. in 1 gm. cal. 



As a check on the specific heat at constant pressure found in this 

 way, the same quantity was computed for the first three alcohols, that 

 is for methyl, ethyl, and propyl alcohol, by the alternative method 

 involving the second temperature derivative of the volume which was 

 used in the paper on water. The second derivatives were found 



