19 () THE ORBIT OF UK ANUS. 



CHAPTER IX. 



GENERAL TABLES OF URANUS. 



Enumeration of the Quantities contained in tlie several Tables. 



THE first six tables are designed to give the values of the three arguments of 

 the elliptic motion, g, o, and 0, and of the nine arguments of the tables of pertur- 

 bations. The argument w is, however, diminished by 3', the sums of the constants 

 added to the perturbations of (r.c.O) to make these quantities positive, and 6 by 

 10", the constant added to the reduction to ecliptic. The expressions for the argu- 

 ments of perturbations are as follows, the mean longitude of each planet, counted 

 from the perihelion of Uranus, being represented by the initial letter of the planet. 

 All these arguments are expressed in units, of which 600 make an entire circum- 

 ference, so that each unit is 36'. The time t is counted in Julian years from the 

 fundamental epoch, 



1850, January 0, Greenwich mean noon. 



Arg. 1 = J U =219.190 + 43.44028* 



2= S- U =577.349 -f 13.22717* 



3= U- N = 88.884-j- 3.50035* 



4 = J2S =497.6 + 9.8445* 



5 = 3- U J= 79.8 + 3.3825* 



6 = 4 2Z7- J= 57.1 -f 16 - 610 * 



7 = 2J 3# 3 U= 238.7 -f 18.633* 



8 = 2,7 --4S 2T= 261.3 + 5.4058* 



2J -3*7=136.9 19.992* 



Table I gives the corrections which must be applied to the values of the argu- 

 ments at any time during the nineteenth century to reduce them to the corresponding 

 time in any preceding or following century between the Christian era and the year 

 2300. Since G> and each contains a term proportional to the square of the time, 

 the correction for these quantities is not constant during each century, but is of 

 the form 



o-fo'Z 1 



o and o' being constant during each century, and T being the fraction of the 

 century counted from its beginning. 



Table II gives the value of g, M 3', 6 10", and the above nine arguments for 

 Greenwich mean noon of Jan. of each leap year from 1752 to 1948, and for 

 January 1 of the years 1800 and 1900, corresponding to December 30 of the years 

 1799 and 1899. The corrections for the perturbations of long period are not 



