116 



SCIENCE, 



[N. S. Vol. VIII. No. 187. 



many years later (1840) by Kegnault, who 

 in his first memoir* pointed out the diiBcul- 

 ties which attend the acceptance of the 

 statement of Petit and Dulong in the form 

 in which they gave it. He then discussed 

 the three principal experimental methods : 

 viz. (1) fusion of ice ; (2) mixture with 

 water or other liquid ; and (3) cooling ; 

 and decided in favor of the second, which 

 he used throughout his researches. The 

 general form of the apparatus used by the 

 great physicist has been a model for the 

 guidance of successive experimentalists 

 since his time. 



Another quarter of a century elapsed be- 

 fore the question of the specific heats of 

 the elements was resumed by Hermann 

 Kopp. His results were communicated to 

 the Royal Society, and are embodied in a 

 paper printed in the Philosophical Transactions 

 for 1865. After reviewing the work of his 

 predecessors he described a process by which 

 he had made a large number of estima- 

 tions of specific heat, not onlj' of elements, 

 but of compounds of all kinds in the solid 

 state. Concerning his own process, how- 

 ever, he remarks that " The method, as I 

 have used it, has by no means the accuracy 

 of that of Eegnault" (p. 84). 



In 1870 Bunsen introduced his well- 

 known ice-calorimeter. This is an instru- 

 ment in which the amount of ice melted by 

 the heated body is not measured by collect- 

 ing and weighing the water formed, but by 

 observing the contraction consequent upon 

 the change of state. The results obtained 

 by Bunsen himself are uniformly slightly 

 lower than those of Eegnault for the same 

 elements. 



Since that time experiments have been 

 made by Weber, Dewar, Humpidge and 

 others, in connection especially with the 

 influence of temperature in particular cases. 



Setting aside the elements, carbon, boron, 

 silicon and berry Ilium, as providing an en- 



*Ibid., 73, 5. 



tirely separate problem, the question is 

 whether the law of Dulong and Petit is 

 strictly valid when applied to the metals. 

 Kopp, in the discussion of his subject, came 

 to the conclusion that it is not ; but the 

 grounds for this conclusion are unsatisfac- 

 tory, since neither the atomic weights nor 

 the specific heats were at that time known 

 with sufficient accuracy. It has been cus- 

 tomary to assume that the divergences from 

 the constant value of the product. At. Wt. 

 X Sp. Ht. are due partly to the fact that at 

 the temperature at which specific heats are 

 usually determined, the difierent elements 

 stand in very difi'erent relations to their 

 point of fusion ; thus, lead at the tempera- 

 ture of boiling water is much nearer to its 

 melting point than iron under the same 

 conditions. The divergences have also 

 been attributed to temporary or allotropic 

 conditions of the elements. As to the re- 

 lation to melting point, the specific heats of 

 atomic weights seem to be practically the 

 same in separate metals and alloys of the 

 same which melt at a far lower temperature. 

 For example, the atomic heat of cadmium 

 is 6.35 ; of bismuth, 6.47 ; of tin, 6.63 ; and 

 of lead, 6.50 ; while the mean atomic heat 

 in alloys of bismuth with tin, and lead with 

 tin, ranges from 6.40 to 6.66 (Eegnault), 

 which is practically the same . Again, while 

 the melting point of platinum is at a white 

 heat, the metal becomes plastic at a low 

 red heat, and yet the specific heat at this 

 lower temperature is very little less than it 

 is near the melting point. The properties 

 of many other metals, notably zinc and 

 copper, change considerably at temperatures 

 far removed from their melting points with- 

 out substantial change in their capacity for 

 heat. 



As to allotropy, it is a phenomenon which 

 is comparatively rare among metals, and 

 in the marked cases in which it occurs we 

 have no information as to the value of the 

 specific heats in the several varieties, such 



