18 Prof. Encke on Olbers's Method of 



lation of g, G, k, H, and £, he has adopted a modification 

 which is easily found, and which, (as all formulae in the whole 

 paper,) supposes the use of his logarithmic tables, by which, 

 from the logarithms of two quantities, the logarithm of their 

 sum or of their difference is immediately found. Indeed, these 

 tables facilitate many calculations so much that every practical 

 calculator should not spare the trouble of getting expert in 

 using them. I will now place together all the formulae exactly 

 in the symbols used by Gauss, (with the sole exception that the 

 geocentric latitudes are by me denoted by 8,) as all alteration 

 would be for the worse. 



The data of the observations, viz. the three a, 8, 0, R, and t, 

 being given, we have to calculate successively, agreeably to 

 formulae (16), (19), (20), (22), (23), (24), 



M - *'""*' tan 8' sin (« - ©') - tan 8 sin (a' - 0') 

 t'-t ' tan 8" sin (a' - 0') - tan 8' sin (a" - ©') 

 R" cos (©"- 0) - R = g cos (G - 0) 

 R" sin (©" - 0) m g sin (G - 0) 



M — cos (a" -a) = h cos ? cos (H - «") 

 sin ( a " -a) = h cos ? sin (H - a") 



M tan 8" — tan 8 = h sin ?j 



cos £ cos (G — H) = cos <p 

 cos 8 cos (a — 0) = cos \[/ 



cos 8" cos (a" — ©'') = cos \J/' 

 g sin <p = A 



R sin ^ = B 



R"sinvf," =B" 



h cos 8 = b 



h cos 8" , 



-sr = 6 



g cos $ — b R cos 4» = c 



g cos $ — b" R" cos <J>" = c", then 



(I)- 



(II) 



"V((-/)* + *' B ") 



£ = \/(« m + AA) 



and the value of u must now be so determined that 

 ( r + 7 Ji + *)* _ ( r + r « - *)* = ^jp 



