July I, 1875] 



NATURE 



169 



with the atcmic weight gave a constant value, or, in other 

 words, the atoms of all the elements experimented with 

 have the same capacity for heat. The investigation of 

 Regnault confirmed this law, showing that it is valid for 

 most of the solid elements with tolerable exactness ; but it 

 should be remembered here that the specific heats of these 

 elements must be determined at temperatures which are 

 sufficiently below the melting points of the elements 

 in question. Only carbon, boron, and silicon proved 

 exceptions to this remarkably simple, natural law ; for 

 these three elements far smaller atomic heats were found. 

 It was also found that the different allotropic modifications 

 of these three elements possess cjuite different specific 

 heats, and that none of these specific heats were in 

 accordance with Dulong and Petit's law. Later on 

 similar results were obtained by De la Rive and Marcet, 

 Wiillner and Bcttendorf. We must not forget to men- 

 tion, for the sake of completeness, that with regard to the 

 difference in the specific heats of the allotropic modifica- 

 tions of an element, Kopp has already, in 1864, stated 

 his belief that all allotropic modifications of each element 

 possess the same specific heat in all cases, and that the 

 results of experiments which are contradictory to this view 

 must be considered as caused either by a faulty method of 

 observation or else by impurities in the substances used. 

 Hcrr Weber of Hohenheim has succeeded lately in prov- 

 ing the validity of Dulong-Petit'slaw,also for carbon, boron, 

 and silicon ; his experiments were made with Bunsen's 

 ice-calorimeter. In order to heat the substances experi- 

 mented upon to a series of temperatures below red heat, 

 oil baths were used, and various temperatures between 

 0° and 300° C. were applied ; in order to cool them, 

 solid carbonic acid and a cold mixture, consisting 

 of one part of snow and \ part of common salt, w-ere 

 employed. All these teinpe'ratures were read off directly 

 from an ordinary air-themiometer. For higher tempera- 

 tures (between 500° and 1000°) an indirect method was 

 made use of, which allowed of the determination of the 

 temperatures by means of the indications of the calori- 

 meter. This indirect method is based on the correctness 

 ofPouillet's determinations (published in 1836) of the 

 cjuantity of heat which a certain unity of weight of 

 platinum requires to become heated from temperature 

 Tq to T. (These determinations are given by Pouillet for 

 the interval T = 0° X.o T = 1200° C.) The results which 

 Herr Weber obtained may be stated as follows : — The 

 specific heats of carbon, boron, and silicon increase 

 regularly as the temperature rises, from the lowest 

 obtainable degrees of temperatures upwards, and finally 

 remain nearly constant after a certain degree has been 

 reached. The nature of the function, which expresses the 

 dependence of the specified heat y from the temperature 

 T, seems to be the same for all the three elements, and to 

 possess the following formula : — 



where A, B, q and /^ express constant positive values, and 

 A>B, q>h, and also T is the temperature counted up- 

 wards from the absolute zero. 



The temperature from which the specific heat of 

 carbon remains nearly constant is somewhere near 600° 

 C, and it is immaterial whether the carbon is in the 

 form of diamond or in that of graphite. From red heat 

 upwards this element shows no greater variability in its 

 specific heat than the other elements which follow Dulong- 

 Petit's law. (At lower temperatures, however, for in- 

 stance when the temperature rises from — 50° C. to 

 + 600°, its specific heat increases sevenfold). The 

 specific heats of graphite and diamond are perfectly iden- 

 tical above 600° C., if we neglect small differences, which 

 do not exceed the numerical value of the specific heat by 

 more than 0*5 to 2 per cent. The specific heats of 

 graphite, of the dense amorphous coal, and of the porous 

 charcoal, are within the interval from 0° to 225° C. per- 



fectly identical from degree to degree. Thus all opaque 

 modifications of carbon (the graphitic, dense and porous 

 forms) have the same specific heat. We may say that 

 below red heat, from a thermal point of view, there are 

 only two different allotropic modifications of carbon, the 

 transparent and the opaque one. The specific heats of 

 these modifications differ all the more the lower their 

 respective temperatures; if the latter rise, they ap- 

 proach each other steadily and become identical at 

 about 600°. Above red heat there are no different allo- 

 tropic modifications of carbon with regard to specific 

 heat ; from that point in the scale of temperature, where 

 the optical difference of the two modifications of carbon 

 ceases, the thermal difference ceases also. Kopp's view 

 as quoted above is thus completely affirmed. 



With regard to the specific heat of crystallised silicon, 

 it approaches (analogous to the specific heat of carbon) 

 as the temperature rises a nearly constant limit, which is 

 reached at about 200°, after having passed through highly- 

 variable values. At that point of the scale of temperature 

 the variability of the specific heat of silicon is no greater, 

 than that of the metallic elements. With regard to the 

 experiments with crystallised boron, it has been found that 

 within the interval of temperature from - 80° to -h 260° C> 

 the specific of this element behaves in a manner which is 

 perfectly analogous to the specific heats of opaque and 

 transparent modifications of carbon. This great coinci- 

 dence in the behaviour of the specfic heats of both ele- 

 ments justifies the supposition that also the specific heat 

 of boron in a rising temperature approaches a nearly con- 

 stant limit, and that this lies somewhere near a moderate 

 red heat. Unfortunately, Herr Weber could not prove 

 the correctness of this supposition by direct experiments 

 through want of sufficient material. 



The nearly constant final values, which are reached as 

 the temperature rises by the specific heats of both carbon 

 and crystallised silicon, were found to be, in round 

 numbers— 



For carbon o'46 



„ crystallised siUcon 0*205 



For crystallised boron, as we have said before, this final 

 value could not be experimentally determined, but from 

 the measurements that were made, and from the nature 

 of the function which represents the specific heat of 

 boron in its dependence upon temperature, we may con- 

 clude that this final value lies somewhere near 0-5. 

 The atomic weights of the three elements, as found by 

 the determination of their vapour densities, are — 



Carbon 12 



Silicon 28 



Boron \i 



The products of these figures when muhiplied by the 

 specific heats of these elements as mentioned above, give 

 for their atomic heats the values — 



S'S 5-8 5-5 



z.^., values which closely correspond to the atomic heats of 

 metals and the other solid metalloids. 



Hence it follows that beyond a certain temperature, 

 carbon, sihcon, and boron also follow Dulong and Petit's 

 law, and continue to do so as long as the temperature 

 rises. Dulong and Petit's law has thus become one 

 without exceptions. The wording of this law ought, how- 

 ever, to be somewh£.t different to what it has been up till 

 now ; the following would, perhaps, be best : — 



" The specific heats of the solid elements vary acording 

 to temperature ; but for each element there is a point T^ 

 in the scale of temperature beyond which, as the tempe- 

 rature T rises, the variability of the specific heat becomes 

 insignificant. The product obtained by multiplication of 

 the atomic weight with that value of the specific heat 

 which belongs to the temperatures T > T^, is a nearly 

 constant value for all s#lid elements, and lies between 5-5 

 and 6-5." S. W, 



