the Elements Carbon, Boron, and Silicon. 299 



out introducing any serious error into the determination of the 

 specific heat, may now no longer be entertained. 



(2) The constant final values for the specific heats of carbon, 

 boron, and silicon are, in round numbers, 046, 0*50, and 0*205 

 respectively. The products of these numbers, multiplied into 

 the atomic weights 12, 11, and 28, are 



5*5, 5'5, and 5*8, 

 values which are in keeping with the atomic heats of the metals 

 and of the other non-metals. Carbon, boron, and silicon, which 

 hitherto formed the most marked exceptions to the law of Du- 

 long and Petit, are now shown to obey this law when a certain 

 temperature is reached. This law may therefore be accepted as 

 binding in the case of all the elements ; it must, however, be 

 formulated in a manner slightly differing from that ordinarily 

 laid down. Thus the specific heats of the solid elements vary 

 with the temperature; for every element, however, there is a 

 point (T ) from which the variation in the specific heat with in- 

 creasing temperature is entirely insignificant. The product of 

 the atomic weight into the value of the specific heat (estimated 

 at temperatures so that T> T ) is, for all the elements, a nearly 

 constant number varying from 5*5 to 6*5. 



The smallest relative quantities of the elements carbon, boron, 

 and silicon hitherto found in the molecules of their gaseous com- 

 pounds, viz. 12, 11, and 28, really represent the atomic weights 

 of these elements. 



(3) All opaque modifications of carbon (graphitic, dense and 

 porous) have the same specific heats. From a thermal point of 

 view there are, below a red heat, but two allotropic modifica- 

 tions of carbon, the opaque and the transparent. The specific 

 heats of these two modifications differ considerably at low tem- 

 peratures; with increasing temperatures, however, their values 

 are gradually equalized, until at about 600° they become the 

 same. A consideration of the specific heat of carbon tends to 

 show that from a red heat upwards there are no different allo- 

 tropic modifications of this element ; from the point at which 

 the optical difference between the two modifications of carbon 

 lessens, the thermal difference begins to disappear also. 



In the year 1864 Kopp deduced the rule that the different 

 allotropic modifications of a substance have the same specific 

 heats. The allotropic forms of carbon have hitherto stood in 

 direct opposition to this rule; now, however, it is proved that 

 from a certain temperature those modifications obey Kopp's rule. 



VI. Further Problems. 

 The foregoing researches point to a whole series of new pro- 

 blems ; of these the most important are the following : — 



X2 



