

Atomic Laws of Thermochemistry. 7 



we will proceed with an account of another method of obtain- 

 ing more numerous values of I. This second method is 

 founded on a Kinetic Theory of Solids (Phil. Mag. 5th ser. 

 vol. xxxii.). The fundamental equation there established 

 relates to a collection of equal monatomic molecules of 

 diameter E or distance E between the centres of two mole- 

 cules when they are in contact, e being the average distance 

 apart of two adjacent molecules, so that e— E is the distance 

 through w r hich a molecule swings between an encounter on 

 one side and an encounter on the opposite side ; with the 

 same meaning as before for the other symbols, the equation 

 for a solid free from external force is 



&*(<?-E) 6e 3 



This equation applies to the metals : as before, 22r$(r)/6 

 reduces to lp, where p is the density, and e 3 =m/pj so that 



(it should be noticed that m denotes the actual mass of a 

 molecule, M its ordinary molecular mass (weight) referred to 

 hydrogen). Now 2-JmV 2 is the kinetic energy of the oscil- 

 latory translator^ motion of the molecules in unit mass, which 

 is equal to 2 Jc0 if the internal energy of the molecules is 

 negligible, where 6 is the temperature, c the specific heat, and 

 J the mechanical equivalent of heat, and e 2 (e— E) = E 3 (^/E — 1) 

 approximately : if the molecules are invariable with tem- 

 perature, <?/E — l = bd, where b is the coefficient of linear 

 expansion of the metal. But it was shown in " A Kinetic 

 Theory of Solids " that the metals behave as if E diminishes 

 with rising temperature in such a way as to make e/E — 1 

 = 7b6 approximately, and as W = m/p nearly, we have 



M2fe 2JcM(M/ P ) 



Lx.0 



In this cM, by Dulong and Petit's law, is nearly 6'4 for all the 

 metals : the values of b have not been found experimentally 

 for several of the most important metals, but can be obtained 

 by an empirical relation given in " A New Periodic Property 

 of the Elements " (Phil. Mag. [5] xxx. ; also xxxii. p. 540), 

 namely, if T is the absolute melting-point, &TM 1/6 =*044; 



