The latter distance properly belongs to 1822, but as the 

 preceding observations left it doubtful whether the distance 

 was then increasing or decreasing, I applied no correction to 

 it for adapting it to the year 1823. The distance for 1803-38 



was deduted from e,° -^ = o^ — ^ by means of the two 



at ^^ at -' 



values of Ap^ for one year; viz. for 1803, this value is =8"^ 20', 

 and for the interval 1820 to 1823 the same is = 2° 52'. The 

 other values are means of several numbers. Having carried 

 on the calculation with six decimal places, I give it here to 

 the same extent. Four places would have been perfectly suf- 

 ficient. The formulae (A) gave first, 



(0 12) = + 10-01579 (0 2 3) = + 2-79683 

 (0 1 3) =— 17-43508 (0 2 4) = + ] -28164 



(0 14)=- 19-02817 (0 34)=+ 3-08244 



and hence the formulae (B) and (C) 



(12 3) = 30-24770 (12 4) = 30-32560 

 (13 4)= 4-67553 (2 3 4)= 4-59763 

 (12 3 4) = 34-92323. 

 From (6) the following values resulted : 



% = 81° 17' 47"-3 log tang (45° + ? ) = 0-134021„ 

 ?i= 45 12 13 -9 log tang (45 + ?,) = 2-448786„ 

 C2= 44 43 21 -1 log tang (45 + ^ = 2-314900. 



The example was unfavourable as 45° + '^•^ and 45° + ^2 ^^^ 

 so near 90° that the equation of condition could not be per- 

 fectly fulfilled without arbitrary alterations. 



Next the following logarithms were calculated by (19) : 

 log N = 8-891624; log Ni = 1*543115; log N^ = l-409224„j 



and from the first, third and sixth equations of (20) for deter- 

 mining a came out thus : 



k = r8-333596 1 ^^ 4' (/3-«) + 0-42422 

 L J sm 2y ^ 



k = ro-179192„~l X^ 4/ (y-/3) +0-16628 

 L "J sm 2a ^' ' 



^ = r7-589418~|-?i^ rJ/(/3 + «) +100405 

 L J sm 2y ^ 



P 2 where 



