PEINCIPLES OF THE MECHANICAL THEORY OF HEAT. 277 



If we iiulicate the atomic weight of a compound body hy P, its specific heat by 



S, and by N the number of single atoms which are associated witli one atom of 



P • S 

 the compound body, then, according to Garnier, we have very nearly ___=«, 



if a represent the mean atomic heat of the solid eleuients, and, therefore, the 

 value G.4. In efi'ect there results, for example, for 



Cinnabar 



Eock salt 



Ked copper 



Water 



Specular iron, {Eisenglanz) 



Chemical 

 formula. 



H^S 



N a A 



■e«2 



H,0 



FC.2O3 



232. 



r)8. .5 



142. rt 



]8.0 

 IGU.O 



0.0:') 17 

 0.219 

 0. 1 1 1 



].0() 

 0. 154 



PS 



N 



(i.O 

 6.4 

 5.3 

 6.0 

 5.0 



Now the temperature of a boily depends, according to the mechanical theory 

 of beat, entirely on the living force with which the atoms composing it move. 

 Two bodies have a like temperature when the living force with which each atom 

 in the one vibrates is equal to the living force of an atom in the other. For the 

 temperature of two bodies to be raised in an equal degree it is necessary that the 

 oscillatory work of the atoms in both should undergo an ecpial augmentation. 



From this it might well be expected tliat like quantities of heat will be needed 



to produce a like elevation of temperature in two masses of diflerent substance 



of whicli one contains just as many atoms as the other; or, in other words, it 



would be ex])ected that the magnitude, which we have above indicated as atomic 



heat, sh(nild for all elements lie alike; that, hence, the Dulong-Petit law should 



not only be ajijjrosimatch', but rigorously, correct, that for chemicaHy com- 



}»ounded substances the quotient which we obtain when we divide the atomic 



heat of the combination by the number of single atoms which are associated with 



P S 

 one atom of the composition, being the value -^jrr-, must under all circumstances 



be perfectly equal to the atomic heat of the simj)le substance. This, however, 



esperinaent does not verify. The numbers of the last cohunu of the above table, 



P S 

 in part, desnate considerably from 6.4, and thus the quotient -Trf— is not equal for 



all combinations, as we have also seen above. 



The contradiction in which experiment and the mechanical theory of heat 

 seem here involved entirely vanishes, however, when it is considered that the 

 quantity of heat which must be sup})lied to a body in order to raise its tenqiera- 

 ture is by no means wholly cnqdoyed in exalting the living force of its molecular 

 vibrations, but that a considerable i)art of the heat, which we designate as specific 

 beat, is consumed in the performance of internal and external work. 



Let us indicate the specific heat of a simple substance by s; then is, 



s^Jc + i + e .... (1), 



if by Jc we denote the augmentation of the vibratory work wliich the unit weight 

 {Getvichtseinhcil) of the substance in question undergoes from an elevation of 

 tenqjerature (jf 1°, while i and e denote the heat c<piivalent of the internal 

 and external work sinuiltaneously executed. If we designate tlie atomic weight 

 of the substance by j;, then, according to the ])rineiph'S dl' the mechanical theory, 

 the product Icp naist, of course, be the same for all sinq)le suhslances; but it by 

 no nu'ans follows that S}) also is a constant magnitude, since c and i are qiumli- 

 ties which vary, not only fn^m one substance to another, but for the same sub- 

 stance with the conditions of aggregation. 



We can realize the absolute validity 



