THE ORBIT OF URANUS. 201 



Sum +0.68 +0.37 +0.06 —0.25 —0.57 —0.87 —1.19 



It will be seen that we have here computed twice as many numbers as are 

 necessary to interpolate with all attainable accuracy. 



The rest of the computation is fully given on the four following pages. First 

 we have the values of fj and the nine arguments for the intermediate dates, filled 

 in by successive addition of the nearly constant difference. The arguments thus 

 obtained for the last date may be compared with those just computed on the pre- 

 ceding page. 



The niunerals in the first columns of the sections of computation following 

 indicate the arguments with which tables arc entered to obtain the separate values 

 of the quantities (r.c.O)^ (r.,s.l), (?\c.l), etc. The negative terms in Table XVII 

 being taken from the sum of all the periodic terms from Tables VIII to XVI with 

 argument 1 to 9, we have the final values of (mc.O), («\.f!.l), etc. 



The final computation of the products {y.s.i] sin t*/, etc., and the addition of the 

 separate terms which make up the three co-ordinates, are shown on page 205. The 

 expressions c.O, s.l, etc., are employed for brevity, instead of (r.c.O), (r.s.l) sin </, etc. 



The longitude finally given by the tables is referred to the mean equinox, and 

 must therefore be corrected for nutation before being used to compute the geocentric 

 place. 



26 Jviue, 1873 



