4 

 f 



40 



Boit'ditch on the Oblateness oftJie Earih.s 



8, consequently the error of ilie eigbtl 



the formulas (Q) to put r 



of the equations (P ') ought to be put equal to nothing, that is o?^"' 



0, which gives y 



',(15) 



ly 



^ 



(15) 



0,00225 

 U,41300 



(P") gives :^ = 0,99923 — y. 0^3529 



0,0054479. The equation 



■-J. 



0,99^86, and the ellipticity 



of the earth 0,00865 — y becomes 0,0032021 



1 



312 



- , instead of 



Thus we perceive the effect of this 



— ^„, found by La Place.* 



main error of the computation. 



There is also another error existing in the tenth of the eqaa- 

 lions (A") corresponding to the observation at Gotba, but as this 

 did not affect the result so materially as the preceding one, I 

 Lave thought proper to defer noticing it till this time in order that 

 the regular chain of the calculation might not be interrupted. 



-> 



This error consists in puttins: the coefficient of y 



equation 



equal to 0,57624, whereas its true value is 0.603 39. For the 

 latitude of Gotha being 56°,63 [corresponding to 50° 58' l",S ia 

 sexagesimals] its log. sine by Callet's Tables is 9,8902999, the 

 double of this logarithm is 9,7805998 corresponding to the natur- 

 al number 0,60339, which is the correct value of the coefficient of 



V 



If we decrease the \o 

 mz it 9,8802999, fwl 



taken from the table by 0,01, 



lake very 



ly made in 



4c 



r 



those tables, because the numbers 9,89 are marked at the top of 

 the column, and 9,88 at the bottom and the remaining five figures 



♦ To prove a posteriori that the corrected value of ^ makes the sum of the er- 

 rorsaW,a(^>, &c. less than La Place's value of ^; I computed that sum, with 

 both values to seven places of decimals. La Plact'a sum was, 0,00123, the cor- 

 rected sum O5OOII5, whence we evidently perceive that La Place's value does not 

 produce a minimum of error, as it ought to have dune if his calculation had been 

 made correctly. 



m 



