490 Mr. J. Prescctt on. the 



Whence 



-d __ 2x5 o) 



~ 26000 x *931 x 3-18 x 8tt ' n L 



10 



26000 x -931 x 3-18 x8tt 



»*§(•>« 



= 3 I gJ o pfW- 



If p were constant, in which case we could consider e 

 constant also, this would give 



_ 1 

 6 ~316' 



which does not agree with the result found by assuming p 

 to be constant in the equation obtained by considering the 

 equilibrium shape of a liquid earth. 



We shall now have to assume an expression for p in terms 

 of the radius which shall agree with all known facts, and 

 give a density decreasing from the centre outwards. We 

 know that, the density of water being taken as the unit, the 

 mean density of the earth is about 5*5 and the surface density 

 is 3 or 2-5. 



Also it is quite certain that p decreases from the centre 

 outwards. These facts tell us that 



f p/3M/3>2-5xl'R" 



and < 5*5 x -J B, 5 . 



The first of these conclusions is easily seen ; for at every 

 point in the earth 



p/3^2-5/3 1 ;; 



and therefore f E _ 



P ^dj3^2-oxlW. 



The second statement can be proved thus : — 

 We know that 



J' 



J c 



p/3 2 d/3=5'DX iRl 







Therefore 



3B 2 f R 02 



5*5 



d/3= ~-W. 

 5 



