I 



498 Mr. J. Prescott on the 



Therefore, when n = 8 x 10 8 grams per square centimetre, 



P-^X T * e ) dr:=2 '5 Wa5e l+ 1 5 Wa5 \ y A 0+ qA 2 + yjA 4 f.. j- 



= 2-5 wa b ei + 15 iva? (90 x 10" 4 5) 



= 2-5 iva^ + 15 wa 5 (0'1655 e x ) 



=4'98iua% (73; 



The total potential near the earth's surface is 



Y'~{-ihr 2 P 2 = Y / + iJia 2 P 2 , .... (74) 



a being written for r in the second term which is small. 



Over an equi potential surface the expression in (74) is 

 constant. That is, 



9^ + i 77 |^ 2 (4-98)wa^ 1 + i/ia 2 P 2 = a constant. (75) 



But the mean density of the earth being 5*5 w we find that 



$yird(5'5w)=g. (76) 



Hence, after being divided by ga (75) becomes 



-7 + -^— j7- <?iP 2 + g-P 2 = a constant. . . (77) 



The constant in (77) depends on the particular equi- 



potential surface we are dealing with. Since — is nearly 



unity and the other two terms are small, the constant is also 

 nearly unity for all equipotential surfaces near the earth's 

 surface. For the particular equipotential surface with the 

 same mean radius as the earth, the constant is exactly unity. 

 Thus for this surface 



a 1 /3x4-98 /t\ D 



And therefore 



i-+ (*$?-#?■ • • ■ ™ 



approximately. 



The ellipticity of this surface is 



3x4-98 , ha T6x4-98 ,„ OKl1 l ha 



=1-353^ (79) 



2g 



