Rigidity of the Earth 



Consequently 



* x = 0*0544 X 

 =0-325^. 



7-5 x 0-796 ha 

 9 



495 



(57) 



In order to test the effect of varying the law of density 

 while keeping the mean and the surface density the same, 

 I have calculated the ellipticity with the same rigidity, 

 8 X 10 8 grams per square centimetre, and the density 



^„(u-i2- 5 r). 



(58) 



With this expression for p the density at the surface is clearly 

 2'5w and the mean density is 5*5 w as in the previous 

 calculation. 



The differential equation (21) is now satisfied by 



'Ao+AiJ+A,^ 



+ A 3 ^-+A 4 



(59) 



By the same process as in the preceding case we find 

 A =-3G18xl0-V 

 A l = 



A 2 = + 1282xl0" 4 v 

 A 3 =+6088xl0- 5 v 

 A 4 =-2244xl0- 5 v 

 A 5 =-1614xl0" 5 r 

 A 6 =+ 345 xl0~ 6 u 

 A 7 =+2016xl0" 6 r 

 A 8 =4 732 xl0- 7 t> 

 A 9 =-1370xl0" 7 « 



where 



Aio— — 



176 x 10" 7 o 



An= + 



77xl0" 7 r 



A 12 = + 



98xl0" 8 « 



Ai3= — 



llxl0" 9 r 



(60) 



v= -1-535 



ha 



(61) 



In the actual working of the problem it is necessary to 

 compute the coefficients as far as A 13 to get accurate results, 

 because the coefficient of Am in the boundary condition (30), 



