22 PLACEoF A PLANET m 



complement .0000613, and the log. of « rz — 2.2178779 and 

 the feries for the upper half of the orbit 



will be, a = a -\ 3.4397266. z3 The negative fign 



4.0603053.2:5 prefixed to thefe 



-| 7.6959472. s7 logarithms affefts 



8.9982252. z9 8i.c. the index only, 



Foi- the lower half, a =:z 3.4543136. zi 



-| 4.2217638. zS 



6.8392607. z7 



-\ 7-4939405- S9 &c. 



For the logarithm of the dijlance in any part of the Orbit. 

 To the log. fine of a, add the comp. of the log. fine of the 

 true anomaly — the comp. of the log. of the conjugate femidiam.^ 

 the fum will be the true log. of the diftance. 

 Example of the Calculation. 

 The Sun's mean anomaly being IP 6^ 30' required the true 

 anomaly or equation. 

 Archof66°3o'=i.i6o64395 = 



J, log. = .0646990 

 Sub. I + X log. .0072323 



log z = .05746673=1.1414758 

 2:3 zr .1724001 

 + — 3-4397266 



— 3.6121267 zr + .0040938.01 



2:5 = .2873335 

 + — 4-0603053 



— 4.3476388 =: — .0002226.58 



%1 =: .4022669 



— 6.0982141 = + .0000012.54 



s;9 rr .5172003 



4 8.9982252 



— 7.5154255 = - - .0000003-27 



+ 1.1455708.5s 

 — .0002229.85 



a = 1. 1453478. 7=65?37'24*.96 

 Log. 



