REPRESENTING MEASURED ARCS OF THE MERIDIAN. 399 



thus we have M. error 



^ = 1-0-^60574 - "»""^=^ • ^^^ 



a = ^~^'?"!?^^^^ = 0-002498293 . + 0-00004002 

 400 



§. 5. 

 I have further only to seek for the two axes of the elliptic 

 spheroid of revolution, and to develop the numerical values be- 

 longing to it of some formulae which are of frequent application. 

 The reversion of the series (§. 2) 



3 45 , 525 , , 



2"^^+ 16^ +T28^^ + "-- 

 a = — 



4 64 



gives the expression of n in terms of u, namely 



2 1 23 



3 9 486 ^ ' 

 and by substitution of the found values of a, 



7 



n = , = 0-0016655304. 



a+ b 



Hence we obtain the proportion between the axes of the elliptic 

 spheroid of revolution, which corresponds most nearly to the 

 arcs which are under examination, 



2^ + 2" = 2^ - 4 ^ 300-7047 : 299-7047 ; mean error 



= + 4-81. 



Further, we obtain the axes themselves according to the for- 

 mulae given in §. 2. 



^ 180^ 



^~ i: {\ -nf {\ +«)N 



TT (1 + «)-(! -ra)N' 

 or, numerically expressed, 



T 



a = 3271953-854 log c = 6 . 5148071699 



6 = 3261072-900 log i = 6.5133605073. 



The length of the quadrant of the meridian, which according to 



the original view, ought to be 10,000,000 metres, is according 



to this determination. 



