Woodivard — The Relations of Internal Pressure, etc. 55 

 From (3) we get 



2m' ^ J- 2^ — r4^^y 

 dM CT, ^ dr '^P^ di- \drJ 



dr k p^ 



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

 reducing, we have 



<Pp 2<iy_l/.W+ .^0, (6) 



dr^ r dr p \dr ] 



which is the differential equation of the required relation. 

 In this equation, for convenience, I have written 



47r^ 



CT^' 



a. (7) 



To find the integral of (6), assume 



p = Ar^, 

 whence 



_P Anr^~^; 

 dr 



d^p 



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



Substituting in (6) we have 

 An{n — iy-^-\- 'lAnr"" " ^ — ^nV* - ^ + a^2,.2» _ q _ (^ § ) 



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

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

 n, we have 



+ 6— 4— 4 + a^ = 

 or 



A = '-; 



a 



