88 THE ORBIT OF URANUS. 



Action of Jupiter and Saturn Continued. 

 (Terms multiplied by the product of their masses.) 

 /' i' 



(0.c.0)=+ 0.08 sin ^ 2 +0.51 cos N. 2 

 + 0.04 sin N 3 + 0.01 cos N 3 



0.01 sin N t + 0.05 cos N 4 



0.35 sin N, 1.30 cos N, 



( 0.55 sin N 9 0.03 cos N 6 ) 

 I +40.65 sin N 7 10.50 cos N 7 J 



0.05 sin N s + 0.03 cos ^ 8 



(v.c.l)=+ 0.06 sin JV, - 0.27 cos JV X (w..l)=+0.26 sin ^ +0.27 cos JV, 



+ 0.18 sin N 2 +0.01 cos N 2 -0.04 sin N, -0.17 cos N 3 



0.03 sin ^3 + 0.08 cos ^3 +0.08 sin N 3 +0.03 cos N 3 



0.02 sin JV 4 + 0.09 cos ^ 4 0.02 sin JV 4 +0.08 cos .V 4 



0.44 sin Nf, 0.61 cos N & +0.30 sin ^V 5 0.58 cos N t 

 f 4.238^^ 3.87 cos JV 6 ) f +2.64 sin N, +4.64 cos JV 6 1 

 I +8.06 sin ^ 7 8.38 cos JV 7 J 1+7.35 sin N 7 +4.41 cos N 7 ) 



0.10 sin ^ g + 0.03 cos N s 0.04 sin ^ 8 +0.00 cos N s 



0| O O I O 



(w.e.2)= f 0.24 sin N 6 0.22 cos N t ) (w.s,2) f +0.16 sin N 6 +0.26 cos N 6 1 

 } +0.47 sin ^V 7 0.54 cos N 7 J t +0.54 sin JV 7 +0.47 cos N 7 j 



(p.c.0)=+ll sin N b 3 cos N & 



Two of these arguments, namely, 5$ 2/, and 3^ + 6^ 2/, are of very 

 long period, that of the first being about 880, and that of the second about 1590 

 years. It will, therefore, be convenient to tabulate them both as functions of the 

 time for the time during which the theory is to be used. To make their effect as 

 small as possible during the period for which the provisional ephemeris is to be 

 computed, we shall suppose the longitude of epoch, mean motion, and longitude of 

 the perigee to be affected with the negative of the following corrections : 



^= + 27.27, 

 fa = + 27.27, 

 n = - 0.1172. 



Reducing these corrections to corrections of the co-ordinates, and adding them to 

 the terms of long period in the true longitude and logarithm of radius vector, we 

 shall have for these terms, 



// // 



(w.c.O) = 0.546 sin N 6 0.032 cos # 6 



+ 40.650 sin N 10.500 cos N, + 27.27 11.72 T 



// // // // 



(v.s.l) = 2.63 sin N e + 4.64 cos N 6 + 7.35 sin N 7 + 4.42 cos N 7 



(v.c.l) = 4.22 sin N e 3.87 cos N, + 8.06 sin N 7 8.39 cos #" 7 1.10 T 



