10 



On the Constitution of Matter, 



I undertook the investigation originally, for the purpose of 

 determining the laws of expansion and change of specific heat, 

 but I have been led to conclusions having reference to phenomena 

 of far greater interest and importance. 



The law of force, which I have assumed, afi'ords a 

 reasonable general explanation of some of the phenomena relating 

 to gases and vapours ; such as the change of specific heat with 

 change of temperature, and condensation at the dew point. It 

 points also to an essential distinction between gases and vapours 

 in the nature of the encounters between the molecules. I must, 

 however, defer the consideration of these and many other questions 

 to some future occasion, briefly stating the principle upon which the 

 change ofspecific heat, of which the absorptionof heatin liquefaction 

 and in vaporization are particular cases, seems to depend. If any 

 system, not subject to loss of energy by friction or any similar 

 cause, be vibrating about a position of stable equilibrium, the 

 average proportion of the energy in a potential state, depends 

 greatly upon whether or not there is any position of unstable 

 equilibrium within, or nearly within, the scope of the motion. 

 When the system passes slowly through such a position, a large 

 proportion of the energy becomes potential ; and if the motion 

 constitutes heat, a large proportion of the heat becomes latent. 

 The existence of the position of unstable equilibrium B, appears 

 to be the chief cause of the various changes which are observed 

 in the specific heats of solids, gases and vapours. 



Let there be n equal atoms in a straight line, acting upon one 

 another according to the law already assumed, and slightly dis- 

 turbed in that line from their positions of stable equilibrium. 



Let the displacements at time t, be represented by x^ x^ 



a?r The equations of motion, to a first approximation, are 



1 d- Xi 

 m- df ^ ^' '''- 



1 d"x. „ 

 mr dt- 



Xi 



or putting q for ~ \~^ + 2, 



(j — 1) «i = X. 



qx., = Xi + a-'s 





q x, = x,_, + x^^, 



■ 



(q—l)x^ = x^^i ^ 





;a) 



