464 Mr. J. Prescott on Convective Equilibrium 



solution has been obtained. Denoting by M the total mass 

 of the sphere, we know that 



M 



= 4-7T J pr 2 dr 



Jo 



the subscript ( ) indicating values of quantities whenjo = 0. 

 Substituting for p and r we get 



M, 4 J_^JM ^o^d 



l47r-K( 7 -l) ) 



I P 



Jio 



r „ T 



,!■ 



= l-20xlO n x^-i( ^dx 

 = l-20xlO u xg-h( °p{d* 



J CO «# 



= l-20xlO"x^(|) o 



= 1-20 x 10 11 x 6-98 x q-h 

 Therefore qk = 8*4 x 10 11 x M~ ] , 



p* = q-* 



M 



and 



8-4 x 10 11 * 



Hence 



/ 8-4xl0 l x Yl / 



\ M / x V 4ttK 



m —— II / 



(7-1) 

 and p = (p?/) 25 



10 



( M V 



y 25 - 



Thus, by means of the table given, the density at any 

 point can be obtained when the mass is given. 



Let us find the radius of the . sphere whose density at the 

 centre is 10 lbs. per cubic foot. At the centre 



/ M \ 10 



^ 10 =(^io") 10 - 



Therefore 8'4x 10 n 



M 

 And at the surface of zero density 



= 10 10 . 



r = 10" x — - x 25-5 x 10 8 feet 

 b'l 



= 12600 miles about. 



