518 Mr. Rankine on the Centrifugal Theory of Elasticity y 

 acts on the two lateral faccs^ its total amount for each being 



t^KKdu, 

 2gk 



The transverse components of this pair of forces balance each 

 other. Their radial components, amounting to 



nu ^ ^gr^"^""- 2gku ' 



constitute a centrifugal force relatively to the atomic centre, 

 acting on the pair of triangular frusta whose mass is 



pfli^du 

 2 • 



The condition of permanent, or periodical equilibrium of this 

 pair of frusta, requires that this centrifugal force shall be ba- 

 lanced by the variation of the mean elasticity of the atmosphere 

 at the two surfaces of the spherical layer, combined with the 

 attraction of the nucleus. The action of the former of these 

 forces is represented by 



—b^dux'^T-. 

 du 2 



Let the accelerating force of attraction towards the nucleus be 

 represented by 



__ (t>rRu) 

 R ' 



(j) being a function, which, by the definition of an atomic bound- 

 ing surface in article 8, is null at that surface, or when m=1. 

 Then the attraction on the pair of frusta is 



_ pfhdu<l)(Ru) 

 2 * 

 Add these three forces together ; let the sum be divided by 



2 pfhdu, 



and let the density p be denoted, as in article 10, by 



then the following differential equation is obtained, as the con- 

 dition of a permanent state of the atomic atmosphere : 



gku "^{u) du T* * 

 This equation will be realized for each layer at its mean posi- 

 tion, on each side of which its radial oscillations are performed. 



