78 PROCEEDINGS OF THE AMERICAN ACADEMY. 



tone and ethyl iodide. The rule, therefore, that dilatation decreases 

 with rising pressure has many exceptions. 



As regards the behavior of dilatation with respect to temperature, it 

 is a striking fact that at the higher pressures the dilatation is usually 

 greatest at the lower temperatures, instead of at the higher tempera- 

 tures, as at atmospheric pressure. Every one of the diagrams shows 

 this. What is more, the reversal of the effect in almost all cases 

 takes place sharply at a definite pressure, the same for all tempera- 

 tures; or in other words, the curves for the four temperatures, 20°, 

 40°, 60°, and 80° all cross at approximately the same point. This is 

 exhibited still more strikingly in the curves for the average Cj, of the 

 twelve liquids (Figure 99). We have the thermodynamic formula 



(dc;\ fdh\ , , , , , fdh\ 



I T— ] = ^ r I —^ I , so that when the average value oi I t-^ I over 



the temperature range vanishes Cp will have a maximum. All of 

 the curves show this maximum at the same pressure. 



This universal reversal in the sign of ( ^-^ 1 is a fact of no little 



interest and importance, and seems not to have been anticipated. 



In fact, the natural hypothesis of the contrary behavior, namely that at 



fdh\ 

 high pressures (^ij = 0, has recently been made the basis of an 



empirical theory of liquids by Tammann as was pointed out in the 



introduction. This hypothesis of Tammann is based on very plausible 



evidence from the data of Amagat, which seem to indicate that at 



fdh\ 

 high pressures ( t-^ 1 does vanish. But this apparent evidence from 



Amagat is founded on an accident, and a rather remarkable accident, 

 as will be evident from an inspection of Figure 99 for Cp. The re- 

 versal in the sign of ( vi] takes place for nearly all the twelve 



liquids at pressures which are in the neighborhood of 3000 kgm., the 

 maximum pressure reached by Amagat. As a matter of fact, 

 Amagat 's data do show in some cases the reversal of the effect, but 

 the experimental error was fairly high, and Amagat himself did not 

 credit the reversal as genuine. Only six of Amagat 's liquids can 

 yield evidence on this point, because they are the only ones for which 

 readings were made at more then two temperatures; of these six 

 liquids, ether, ethyl alcohol and carbon bisulphide show the reversal 

 at 3000 kgm., while methyl and propvl alcohol and ethyl chloride 



show a positive I - j J over the entire range. 



