Figure of the Earth. 491 



Hence 



±^R5_ p pd/3=^-\ p pdj3-\ p/Fd/S 



Jo ° J o Jo 



Now -~ is always negative and the remaining factors 



under the integral sign are positive. Thus 



5.5 r*R 



-^-R 5 = p/3 4 <i/3 + a positive quantity, 

 Jo 



which proves the second statement. 



A law o£ density which gives roughly the type of variation 

 to be expected is 



,.C-D(g)-. 



To make p = 3 at the surface we get 



3 = C-D. 



C is the density at the centre and can be given any 

 arbitrary value. By making the mean density 5*5, n is 

 determined thus : — 



p/3 2 d/3 = rro\ /3*d/3. 



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This gives 



C |oD=5'5. 



n + 6 



But also 



C-D = 3. 



Therefore 



15 





n 20-11 



Let m denote the 



value of 





J 





J 



