or Centrifugal Theory of Elasticity. 357 



tion only of the expansive pressure which depends on density 

 and heat jointly, and is the means of mutually converting heat 

 and expansive power ; that is to say, the pressure at the bound- 

 aries of the atomic atmospheres, which I shall denote by 



j»=r(v,Q). 



Pressures, throughout this paper, are supposed to be measured 

 by units of weight upon unity of area; densities, by the weight 

 of unity of volume*. 



(3.) Determination of the External Pressure of an Atomic 

 Atmosphere. — Let a body be composed of equal and similar 

 atomic nuclei, arranged in any symmetrical mannei", and enve- 

 loped by an atmosphere, the parts of which are subject to 

 attractive and repulsive forces exercised by each other and by 

 the nuclei. Let it further be supposed, that this atmosphere at 

 each point has an elastic pressure proportional to the density at 

 that point, multiplied by a specific coefficient depending on the 

 nature of the substance, which I shall denote by h. (This coeffi- 

 cient was denoted by b in previous papers.) 



Let p and y denote the density and pressure of the atomic 

 atmosphere at any point ; then 



Let 



d^ d<^ _ d^ 



~^1^\ ~^V ~^~d^ 



be the accelerative forces operating on a particle of atomic atmo- 

 sphere, in virtue of the molecular attractions and repulsions, 

 which I have made explicitly negative, attractions being sup- 

 posed to predominate. The property of the surfaces called the 

 boundaries of the atoms is this, — 



Or'' Or'' (f),-' 



the suffix 1 being used to distinguish the value of quantities at 

 those surfaces. Hence 4>, is a maximum or minimum. Those 

 surfaces are symmetrical in form round each nucleus, and equi- 

 distant between pairs of adjacent nuclei. Their equation is 



Let M denote the total weight of an atom, /^ that of its atmo- 

 sj)heric part, and M — yu, that of its nucleus; then 



* Sept. 1855. — There is reason to believe that in many substances the 

 ehiHticity of fi^^ure depends on more than three independent coeffieients; 

 Ijut as the present pa])er rehitcs to elasticity of volume only, the above 

 equations are nevertheless sutlicient to illustrate the classification of elastic 

 pressures. 



