• Measurements of different Portions of the Meridian. 345 



both as some test of their own exactness, and likewise in or- 

 der to judge what real ground there is for objecting to the 

 Swedish measurement. 



Applying now the data of the four first measurements in the 

 table to the formula (A), the four equations following will be 

 obtained, 



188510= A (3-11750- 6-2261. g+ 3-095. e*) 

 598630 =A (9-89589-18-1985.6+ 6-163. e 8 ) , R > 

 751567 =A(12-37030- 6-2811 .«- 10*266. e 2 ) W 

 172751 =A (2-84017- 0-3844. s- 2-166. e 2 ). 



It is known that e is not much different from ^^, and cer- 



e=-^r -M; 



We may therefore assume, 



300 ' 



tainly does' not surpass T ^. 

 j_ 



job * " ' ~ 90000 

 the correction t being a small fraction which we are sure is 

 less than 3^. The foregoing equations will now become, by 

 substitution, 



188510= A (3-09678- 6-206 t) 

 598630= A (9-83530- 18*157/0 

 751567 =A(12-34925- 6*350*) 

 172751 =A (2-83887- 0*399*). 

 In order to find a first approximate value of A, I add the 

 four equations, neglecting the terms containing t : thus 



1711458 = 28:1202. A; A = 60862. 



Next, put D =60862, A = D (1 + s) ; then, by substituting 

 in the four last equations, we shall get, 



= '3-097 5- 6-206* 



1 



D 



i) 

 33 



= 9-835 s -18*157* 



- ^ = 1 2-349 s- 6-350* 



- ~- v = 2-839 5- 0-399*. 

 New Series. Vol. 3. No. 17. May 1828. 



2Y 



These 



