Woodward — The Relations of Internal Pressure, etc. 55 

 From (3) we get 



dM CT, ^ dr ^^' dr' \drl 



dr ^ k ' f • (^) 



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

 reducing, we have 



dr^^ r dr pUrJ ^ ' • ^ ^ 



which is the differential equation of the required relation. 

 In this equation, for convenience, I have written 



4:7rk 



V'T,^ 



(7) 



To find the integral of (6), assume 



p = Ar^, 

 whence 



dr 

 ^, = An(n^l)r--'. 



Substituting in (6) we have 



An (n — l)r«-2 + 2Anr''-^ — An?r''-^ + a^V^" = 0. (8) 



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

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

 n, we have 



+ 6— 4— 4 + a^ = 

 or 



A = h, 

 a 



