Woodward — The Relations of Internal Pressure^ etc. 55 

 From (3) we get 



2nr^P J. 2^^P r4^^^\ 



dM a 



dr ~ k p'^ 



(5) 



Equating the right hand members of (4) and (5), and 

 reducing, we have 



d^p 2 dp 1 /dpY , 2 n ,a^ 



which is the differential equation of the required relation. 

 In this equation, for convenience, I have written 



47^^• 



C^T^ 



= a. (1) 



To find the integral of (6), assume 



whence 



^ = Am— ^; 

 dr 



-J^^ = An(n-l) r--\ 



di 



Substituting in (6) we have 



An {n — \ )?•" - 2 + 2 J.nr" " ^ — An V " 2 + aAh^^"" = . ( 8 ) 



Equation (8) is homogeneous in r if n — 2 = 2?i, or 

 n =—2. Dividing (8) by A/-''-^ and substituting —2 for 

 n^ we have 



+ 6— 4— 44-aA = 

 or 



^ = ?; 



a 



