214 



C. F. GAUSS ON THE GENERAL. THEORY OF 



abridged and facilitated, and at the same time the important 

 object of security against errors of calculation will be materially 

 promoted. 



For the construction of the table the values of the coefficients 

 were brought into the following form : 



X = a" + c' cos {X + A') + a" cos (2\ + A") + 

 a"' cos (3 \ + A'") + a}"" cos (4 \ + A^'') 



Y= b' cos (X + B') + b" cos (2 X + B") + 



b'" cos (3 X + B'") + b'"" cos (4 X + B'") 



Z = c« + c' cos (X + C) + c" cos (2 X + C") + 

 c"' cos (3 X + C") + c^^ cos (4 X + C'^). 



The first table contains those parts of X and Z which are in- 

 dependent of X. In the four next tables are found the values of 

 the auxiUary angles A', A", &c., and the logarithms of a', a", &c,, 

 all for the several degrees of latitude <}> = 90" — u. The table is 

 placed at the end of the memoir. 



The calculation for Gottingen is given as an example. 

 For latitude 51° 32' we find from the tables : 



aP = + 500-8 cO = + 1465-2 



log b' = 2-18900 



log i" = 2-03220 



log bf" = 1-46845 



log A'v= 0-70016 



B' = 358° 24' 



B" = 64 50 



B'" = 318 13 



^iv_ 232 26 



log a' = 2-28980 



log a" = 1-79403 



log a'" = 1-32522 



log aiv= 0-59391 



A' = 249° 30* 



A" = 311 45 



A'" =234 10 



^iv_ 142 26 



log c* = 2-20204 



log c" = 2-12777 



log c"' = 1-43199 



log ci^= 0-59091 



C = 105° 44' 



C" = 165 15 



C" = 42 22 



C'v= 322 26 



And for longitude 9° 56'i, the parts of X, Y, Z, are found as 



follows : 



