75 



where the pressure scalar p ^) meanwhile is a function of the place 

 viz. of r. The radius R of the sphere and the mass m and (> are 

 related hy an equation which is found by integrating (H) from r :^ 

 to r = R. As for ?• = u is not zero, while for /• z= /? it has 



the value (see II equation (11)), we find 



« 



1 



R 



a = '^R^ 



3 

 and therefore 



m = Q^jiR' (29) 



This shows tliat q plays the part of density. 



Integrated from ?• = to an arbitrary upper limit r <^ /^ (6) gives 

 further ii as a function of r. We obtain : 



(30) 



I -r' 



3 



Now w and /> have still to be determined as functions of r. The 

 quantities io and p are connected by equation (7). This gives 



lo' dp 



■ -((> + />) = -/. • • (31) 



w dr 



so that 



dio 



— (q+p)^ — dp. 



This must be integrated. The integiation constant is determined 

 by the fact that at the spherical surface /> = and 



iv = c\/^ l—~ = c\x I — — R' (see II equation (12)). We llms 

 obtain the asked connection between iv and p : 



^a> I />)=^«lx 1-y^' ..... (32) 



Now p will be calculated as a function of r. Introducing in (5) 

 the expression (30) for u and simplifying the equation we obtain 



iv' / XQ \ X ^ 



(33) 



') We need not be afraid that this p will be confused with the quantity p which 

 in § 1 has been pul equal to 1. 



