198 



THE ORBIT OF U RAX US. 



whenever the coefficient to be multiplied is less than 32". The values of these 

 coefficients, (v.s.3), (v.c.3), etc., corresponding to the entire degrees of y, may be 

 either formed by interpolation at sight from those corresponding to the dates of 

 computation, or the values of the arguments 2 and 3 corresponding to the 

 required degrees of g may be computed, and the values of (.s.3), etc., correspond- 

 ing to these values of the arguments may be taken from Tables IX and X, while 

 Table XVII must be entered with the corresponding dates. 



If the heliocentric ephemeris is computed for ten years at a time, the last of 

 these modifications in the mode of computation will greatly facilitate the computa- 

 tion of the smaller terms. We first find the date, and the values of arguments 1, 

 2, and 3, to one place of decimals, for some entire degree of g preceding that which 

 corresponds to the first date, and then find the dates and the values of the arguments 

 corresponding to successive values of g, differing by 2 or 4, until we pass the last 

 date of computation. We then take out the values of (v.s.3\ (.c.3), (v.s.4), (v.cA), 

 (p.s.3), (p.c.3), (i.c.O), (i.s.l), (6.C.1J, (6.s.2), and (i.c.2), with these values of the 

 dates and arguments, form their products by the sines and cosines of the corre- 

 sponding multiples of rj by means of the supplementary tables, and add the proper 

 products together so as to form three small tables with g as the argument. These 

 terms are then interpolated to the values of g corresponding to the original dates 

 of computation. 



As a first example of the use of the Tables we will compute the heliocentric 

 co-ordinates of Uranus for Greenwich mean noon of the date 1753, Dec. 3. In 

 computing the arguments we shall make use of Table I, though it is not necessary 

 to do so. The computation of the arguments is as follows : 



