September 2S, 1883.] 



SCIENCE. 



425 



as other simple solids. Another fact is that 

 alreath- mentioned, viz.. the specilic heat of 

 compound solids per atom is less than that 

 of simple solids ; and to this it ma^- be added, 

 that the specific heat of simple solids is less 

 when the volume is made smaller b^- hammer- 

 ing, compression, or cooling, which facts will 

 be considered more at length later. 



It is shown in the kinetic theorj- of gases, 

 that, when molecules of unlike gases are jnixed. 

 the mean progressive energy of each molecule 

 is the same, whatever its weight. 



Now. when a gas is in contact with a solid, 

 ■will the collisions of the gaseous molecules 

 with those of the solid cause the latter to have 

 the same mean progressive energy of vibration 

 as those of the gas? That will depend largely 

 upon the duration of the collision. If tlie time 

 occupied by a collision is so brief that only a 

 small portion of a vibration of the solid mole- 

 cule is described during the collision, then the 

 laws of impulsive forces u\a.\ be applied, ac- 

 cording to which the effect of the finite forces 

 acting during the interval may be neglected. 



In case the collision is brief, the distribution 

 of the mean kinetic energy between the mole- 

 cules of the gas and solid will be very nearh* 

 the same as between ditferent gases, and the 

 mean kinetic energy of a simple solid mole- 

 cule will differ little from that of a gas at the 

 same temperature. 



In cases, however, in which the modulus of 

 elasticity of the solids considered is .so great as 

 to make the period of vibration of the mole- 

 cules also brief, their mean kinetic energy 

 would be materially smaller than in the previous 

 case ; and, if a solid could be found whose mole- 

 cules were immovably fixed, no vibratory energy 

 whatever could be imparted to its molecules. 



Now, Dulong and Petit's law seems to show 

 that all simple solids, even those having the 

 highest modulus of elasticity, h.ive an elas- 

 ticit}' so small, compared with that brought 

 into action between molecules at the instant of 

 free collision, th.at the distribution of kinetic 

 energ3- is approximate!}' the same as if tlie 

 body were gaseous and monatomic. But since 

 the laws of perfect elasticity require that the 

 mean potential energ\' shall be equal to the 

 kinetic, it follows that the specific heat of a 

 simple solid should be approximately twice 

 that of a monatomic gas at the same tempera- 

 ture and of the same atomic weight. 



The actual specific heats of mercury and 

 cadmium gas would be of great interest in this 

 connection, were they known, even though they 

 could only be determined at temperatures far 

 removed from those of their solids. 



The foregoing statement has been based 

 upon the assumption that any degree of free- 

 dom which suffers partial constraint, as do the 

 degrees of freedom of translation of a gaseous 

 molecule when it becomes solid, will have for 

 that reason less kinetic energy imparted to it 

 during molecular collision. This subject has 

 been treated somewhat at length in previous 

 papers upon the kinetic theory ; but in this 

 connection it may be useful to make a quota- 

 tion from Thomson and Tait : "-If a set of 

 material points are struck independently by 

 impulses, each given in amount, more kinetic 

 energy is generated if the points are perfectly 

 free to move, each independently of all the 

 others, than if they are connected in any 

 way." ' 



This mechanical theorem not only has spe- 

 cial application to the partial constraints intro- 

 duced into the freedom of motion of molecules 

 when they change from a gaseous to a solid 

 state, but it applies, also, to the additional con- 

 straints introduced into the degrees of freedom 

 of solid atoms when those atoms become more 

 closeh' bound together by chemism into groups, 

 i.e., into molecules. Evidently, the bonds of 

 union between the atoms of a compound solid 

 molecule are such that these degrees of free- 

 dom are considerably more constrained than 

 those which unite the atoms of different mole- 

 cules ; so that, in compound solids, the forces 

 of cohesion and chemism arc different, and 

 quite distinguishable the one from the other. 



Now, what, according to the mechanical theo- 

 rem above quoted, is the effect of introducing 

 the additional constraints required in order to 

 group a simple sohd, or mixture of simple sol- 

 ids, into molecules, and thus make it a com- 

 pound solid ? The effect will be to diminish 

 the mean kinetic energy of the system as de- 

 rived from tlie impacts of the molecules of any 

 gas surrounding it. This is, in fact, what 

 occurs, as appears from the experimental truth 

 previously mentioned, — that the specific heat 

 per atom of compound solids is less than that 

 for simple solids. How much the specific heat 

 per atom is diminished should depend upon 

 the intensity of the chemical attraction, wliich 

 certainly must be much greater than the cohe- 

 sion between atoms of simple solids, to cause 

 such marked deviations of specific heat per 

 atom as comjwund solids exhibit. This result, 

 when combined with that arrived at in connec- 

 tion with the discussion of Bcrthelot's law, in 

 my paper upon ' An extension of the theorem 

 of the virial,' etc., to the effect that the heat 

 evolved in chemical decomiwsition is greater 



1 .Val.pA«.,ari.315. 



