or Centrifugal Theory of Elasticity. 361 



^, 0), and G approximate to constant quantities. In the limit- 

 ing or perfectly gaseous condition, therefore, 



H -^ 



and 



(6.) Equilibrium of Heat : Nature of Temperature and Real 

 Specific Heat. — When the atmospheres of atoms of two different 

 sabstanc•e^5 arc in contact at their common bounding surface, it 

 is necessary to a permanent condition that the pressure in passing 

 that surface shoukl vary continuously. 



Let («) and [b] be taken as characteristics, to distinguish the 

 specific quantities peculiar to the two media respectively. Let 

 dm denote the volume of an indefinitely thin layer close to the 

 bounding surface. Then the following equations must be ful« 

 fil!ed to ensure a permanent condition : — 



M«)=;H^);|-[(«) = ||-Wwhen;y=;>. . (12) 



By making the proper substitutions in equation (1), it appears 

 that 



p' =pe -J-^ • — . 



Cl)^ Y 



Hence 



^'"^^'M^'-^-^^y 



Now p is the same for both media :—•-- = e is 



cither a maximum or a minimum, so that its differential is null ; 



and dm is a continuous function of M, so that , («) = -A-iZ (^), 



dm dm ^ ' 



There remains only the function of heat. 



Therefore the condition of a permanent state of molecular 

 motion, that is to say, the condition of equilibrium of Itcat, is 

 that this function shall be the same for the two substances ; or 

 that 



20,^20,. 



K^a hh 



Hence tcvuperalurc depends on the above function only ; for 

 Phil. May. S. 4. Vol. 10. No. 07. Nov. 1855. 2 B 



