METHOD PURSUED. 



Ixxvii 



and can construct the following table of geocentric coordinates and constants for the nine obser- 

 vatories which have furnished materials for our discussion : 



OBSERVATORY-CONSTANTS. 



The longitudes (L.) in this table being all easterly from Washington, the negative sign is 

 unnecessary ; <p and <p' denote, respectively, the astronomical and the corrected latitude ; p the 

 distance from the centre of the spheroid, expressed in terms of the major semi-axis of the gene- 



)o 

 in the expression for ^d oT > which is con- 

 stant for the observatory ; and c the constant used in reducing the sidereal time to mean Wash- 

 ington time by means of the sidereal time at Greenwich mean noon, given in the London 

 Nautical Almanac being the longitude east from Washington, added to the reduction to mean 

 time which belongs to the longitude from Greenwich. 



4. EPHEMERIDES AND AUXILIARY TABLES. 



The ephemerides here given are derived from Lindenau's tables of Mars and Venus, and 

 comprise the entire period of Lieutenant Gilliss's observations of each of these planets. Inasmuch 

 as the employment of the ephemerides is, in fact, only differential in character, it did not appear 

 necessary to incorporate the recent modifications and improvements of Lindenau's tables, given 

 by Breen and Peirce. They are consequently accordant with the Nautical Almanac and Berlin 

 Jahrbuch . 



The approximate values which have been employed for the semi-diameters at the unit of 

 distance from the earth are 



For Mars, t = 4". 66393, (Oudemans, Astron. Nachr. XXXV, 351.) 

 For Venus, ? = 8".6625, (Wichmann, Astron. Nachr. XXXII, 74.) 



The ephemerides for the two oppositions of Mars, and the two inferior conjunctions of Venus, 

 here follow in their order. 



