EXPERIMENTAL KNOWLEDGE OF THE PEOPERTIES OF MATTER. 481 



showed how nearly the molecular Leats calculated according to his theory 

 agreed with those observed chiefly by himself and by Neumann, Regnanlt, 

 and Pape. The principle of Kopp's theory is that each element in com- 

 bination has the same atomic beat as when free in the solid state at such 

 temperatures that both the element and the compound are so far removed 

 from their melting-points that they may be considered to approximate to 

 the state (if one may use the expression) of ' perfect ' solids ; for most of 

 the elements the atomic heat is known by direct experiment ; in other 

 cases, according to Kopp, a value can be assigned to the atomic heat such 

 that the molecular heats calculated by assuming it for compounds of this 

 element shall agree well with those found by direct experiment, the mole- 

 cular heat of a compound being thus supposed to be independent of its 

 constitution, but dependent only on the number and specific heats of the 

 elements composing it. As an example of his method of finding on his 

 theory a theoretical specific heat of an element in the solid state take the 

 case of oxygen ; for oxides of the formula RO, where R is the atom of 

 coppei', magnesium, and a number of other metals whose atomic heats are 

 for each not far from 64 which is the average value, Kopp finds the 

 molecular heats of all, including for each the results of several experi- 

 menters, and calculates for all a mean value ll'l . Subtracting from this 6'4 

 the remainder 4' 7 is the atomic heat of oxygen as deduced from the mole- 

 cular heats of those oxides. Similarly for oxides of the general formula 

 R2O3 lie gets the mean molecular heat 27 1. Now, as R includes metals, all 

 of which are shown to have atomic heat about 6'4, and the average atomic 

 heat is 0-4, three times the atomic heat of oxygen =27'1 —12-8=14-3 ; 

 and the atomic heat of oxygen, as deduced from these oxides is 4'8. Other 

 values obtained in a similar way are 37, 4-1, 4 2, 4-0, 34, 39. From all 

 the separate values Kopp deduced an average of 4'0 for the atomic heat of 

 oxygen ; for that of sulphur and of phosphorus, 5'4 ; fluorine, 5 ; silicon 

 3-8; boron, 27; hydrogen, 2-3; and carbon, 1-8. For the rest of the 

 elements in general, including the well-known metals except beryllium, 

 together with nitrogen and bromine, he gives the atomic heat 6'4.^ 



Specific Heats of Carhon, Boron, and Silicon — Weher. 



Among the exceptions to Dulong and Petit's law, Kopp was obliged to 

 admit carbon, boron, and silicon. Weber^ was struck by the agreement 

 of several experimenters as to the fact of the specific heats of different 

 forms of carbon being unlike, and the atomic heats calculated from them 

 having different values; and on comparing the temperatures within which 

 Regnault, De la Rive, and Marcet, Kopp, Wiillner, and Bettendorf 

 obtained their numbers for charcoal, gas-carbon, natural graphite, blast- 

 furnace graphite, and diamond, he noticed that although for each form 

 the different observers got different numbers, there was this peculiarity, 

 that the lower numbers for each form of carbon always corresponded to 

 lower temperatures : for example, the mean specific heat found by De la 

 Rive and Marcet for diamond was •1146, the range of temperature being 

 3° to 14° ; and that found by Regnault was -1469, the range being 8^ to 98°. 



On investigation Weber found that the specific heat of this substance, 

 carbon, increases more rapidly than that of any other substance with rise of 

 temperature, the specific heat of diamond near 200° being three times as 

 great as it is near 0°. In order to get correct values of the specific heat 



' Zoc. cit. p. 329. ^ Ber. 5, 1872, p. COS. 



1888. I I 



