171-173] Adiabatic Model 173 



so that AF;(1) represents the change produced in F^(l) by the additional 

 term eP in the equation to the boundary (459). 



Let us further agree that &> is to be used to denote the value of o> in 

 the incompressible problem, the general value of a> a being henceforth denoted 

 by ft> 2 + Ao> 2 . 



With these conventions equation (457) becomes 



With the meaning now assigned to the symbols a, b, c and o> 2 , equation 

 (458) is also true. On subtraction of corresponding sides of the two equa- 

 tions, we obtain 



Equation (458) determines a solution when the mass is incompressible ; 

 equation (461) determines the relation between the new quantities intro- 

 duced by compressibility. More definitely, it connects P , the distortion of 

 the boundary from the shape suited to an incompressible mass, with p <r, 

 the range of density, and with A&> 2 , the change in o> 2 . 



173. The simplest solution occurs when all the changes from incom- 

 pressibility are measured by quantities so small that their squares may be 

 neglected. In this case (p <r)/p , eP and Ao> 2 are all of the first order of 

 small quantities, and equation (461) assumes the simple form 



In this equation we notice that E is multiplied by the small quantity 

 <r)/po, so that in evaluating E we may neglect all further small 



