Bowditch on the Oblateness of the Earth. 



41 



I 



03999 arc found in the column itself}, the double of the logarithm 



will become 9,7005998, corresponding to the number 0,r>76^ 

 used by La Place. Whence we readily perceive the cause of 

 this mistake. We shall now proceed to calculate the corrected 

 values of z and ij, and the ellipticity of the earth by rectifying both 



- M 



these mistakes. The tenth of the equations (A") will become 



' 1,G0006 



z 



y. 0,60339 = 0?^^°^, the others remaining unchang- 



1 



ed ; this will increase the coeiRcient of ^ in (B") by — th part of the 



difference between 0,60339 and 0,57624, or 

 that the equation (B ") will become 



0,02715 

 15 



.-df 



0,00181, so 



0,99923 



.-r. 



ij. 0,43710 



(B") 



and wlien this is subtracted from each of the equations, (A") 

 to obtain the equations (O"), it will produce a correction of 

 + y. 0,00181, in each of those equations, besides the correction of 

 the tenth equation — y. 0,02715, so that these corrected equa- 

 tions will be 



0,00254 +y . 0,43710 

 0,00234+^ . 0,40958 

 0,00213 -fi/ . 0,39440 

 0,00178+ J/ . 0,34161 

 0,00195+1/. 0,33694 

 0,00046 + y , 0,12568 

 0,00027 — y .0,03841 

 0,00064 — y ,0,11886 

 0,00077—^.0,12962 



0,00083 — 7/ . 0,16629 



0,00095 — y . 0,17534 

 0,00151 — y . 0,28597 =.t(12) 



0,00178 — ^ . 0,31199 



a (4) 



a.-(8) 



a (10) 

 x(il) 



J* 





0,00214 — y . 0,40768 

 0,00225 — y . 0,41119 



a;(l3) 



x04i) 



.r(15) 



V 



^ 1CV 



^. 



Xf 



