4 



Bowditch on the Oblateness of the Earth, 39 



-^ =.0,0053627 y . 0,1771 5 — 0,00095 = — a;(ll) 



-^ = 0,0053037 y . 0,12067 — 0,O00G4 = — ^-(8) 



0,0052471 ^.0,28778 — 0,00151= — a:Cl2) 



(12) 



0,0052384 V • 0,33980 — 0,00178 = 0^(4) 



(4) 



C14) 



^^^"^ 0,0052260 1/ . 0,40949 — 0,00214 = — x(.U) 



a 



0,0037136 w . 0,12387 — 0,00046= x{^) 



(6) 



The coefBcients of y in these equations are the values of h^^\ 

 n^% &c. hence h^'^ = 0.04052, h^^ = 0,14093, h^'^ ^ 0,13143, &c. 

 instead of which La Place has used the values of the coeflBclents 



^,^, &c. contained in the system (P') putting fe^^^ = 0,0067131, 



Ji^v = 0,0058886, &c. and in this consists the greatest of his mis- 

 takes. For by using these erroneous values of ¥^^, ¥^^, &c. their 

 sum becomes 0,0834899 ; which he puts equal to F, and as the 

 sum of the six first of these terms is 0,0368536 "^f F, and the sum 

 of the seven first of them is 0,041 9250 > ^ F, he puts r = 7, and 

 makes the error of the seventh of the equations (F'') equal to noth- 



ing, that is .r^"-' = 0, consequently^ = -^ =^JYi^^^'^^^^''*~^f 



and then the equation (B") gives z = 0,99933^^. 0,43539 

 0,99676, whence the ellipticity of the earth represented in gener- 

 al by 0,00865 — ^ becomes 0,003977^ = ^g. This is nearly the 



value given by La Place ; but if we use the correct values /i^ 

 0,01023, ¥'^ = 0,14095, &c. the sura of all of them will he F 

 4,03891', now as the sum of the seven first terms i^i 1,804^*9 -^if F. 

 and the sum of the eia^Jit first terms U 3,3l75i, k ^ Fj ^^ ought bv 



r- 



