POLYMORPHIC TRANSFORMATIONS OF SOLIDS. 103 



In addition to these very rough values at the triple point, there 

 have been several other determinations at atmospheric pressure. 

 It has been shown directly that the relations of I and II are abnormal 

 both in regard to expansion and specific heat. The form II has a 

 negative coefficient of expansion. We have no accurate measurements 

 of it at the transition point. The best are by Fizeau ^^ on cr^-stals. 

 He found at 40° for large crystals the average contraction of 0.0648 

 and for the precipitated salt b}^ a dilatometric method 0.0674 cm^./gm. 

 (I have taken the density at room temperature as 5.67 from data of 

 Rodwell ^^). Fizeau and Rodwell have both shown, however, that the 

 coefficient increases rapidly with rise of temperature. Rodwell's data 

 would give an average coefficient between 70° and 150° of — O.OaSSS. 

 From data of Rodwell we also find that the mean expansion of 

 I between 150° and 450° is about O.O55. These measurements of 

 the expansion are too uncertain to justify us in making calculations 

 of the difference. The data for specific heat are somewhat more 

 concordant. Two observers agree in finding that I has a smaller 

 specific heat than II. At the transition point Bellati and Romanese ^^ 

 give for the specific heat of I 0.0577 cal. and for that of II 0.0654, 

 making a difterence of 0.0077 cal. Mallard and Le Chatelier ^^ give 

 for the specific heat of I between 154° and 347° 0.055, and for II 

 between 20° and 127°, 0.059. Since however, they estimate the 

 accuracy of the individual measurements as only 3%, we evidently 

 cannot place much reliance on their difference. If we assume the 

 value of Bellati and Romanese for the difference and combine with 



the values given above for —. — (= —0.0653) and —. — (= 0.005), 



dp dp 



we find A/3 = — .00002, whereas we know A/3 to be positive. If A/3 is 



to be positive with the above values for —, — and , — , the difference 



dp dp 



of specific heats must be at least twice as great as it is. We can get a 



much better value for Aa. If we assume A/3 = 0, and it evidently is 



very small, we find Aa is of the order of 0.065, the same as found above 



at the triple point. We may accept this value with some confidence 



therefore. Combined with the value of Richards and Jones ^° for the 



compressibility of the ordinary variety, this means that I is about 



twice as compressible as II, although it has the smaller volume. The 



19 Fizeau, Pogg. Ann. 132, 292 (1867). 



20 T. W. Richards and G. Jones, Jour. Amer. Chem. Soc. 31, 158-191 

 (1909). 



