84 



THE ORBIT OF URANUS. 



(u.c.O) = 



^_o.oor/ 



_ 4.110 sin 2A^ 



— 0.824 sin 3^^ 



— 0.228 sin 4A^ 

 _ 0.074 sin 5J^ 



— 0.025 sin 6.4., 



Action of Satw) 

 A.,= l' — g 



-f 8.580 cos A^ 



—0.009 cos 2 J, 

 —0.019 cos 3Aj 

 —0.008 cos 4J, 

 —0.003 cos bA, 



•n. 



(v.c.\) = {^ h\nA.,-^[^ ^ 



^ ' V_ 1.03 r/ ' ' V_ ( 



45.005 



(u.s.l) = 



(u.c.2) = 



)cos.4„ 

 



_ 2.121 sin 2^, —0.793 cos 2^, 



— 0.302 sin %A., —0.308 cos 3^ 



— 0.109 sin 4^2 —0.099 cos \A^ 



— 0.038 sin bA^ —0.027 cos bA, 



— ii'Mir 



/-52020\i„^_^/+llC.73 x^^^ (^^, 

 V_0.27r/ ' \— 1.3877 ' ^ 



— 0.CG5 sin 2A^ —1.847 cos 2A^ 



— 0.081 sin 3^, —0.153 cos 3^, 

 _ 0.013 sin 4.4., —0.044 cos 4A^ 

 0.005 sin bA„ —0.016 cos 5.4, 



— 0'".65 2' 



f+143"52 i„^ /-12.'554N^^ 

 \— 0.94r/ \+ LOST/ ' 



+2.037 cos 2 J, 



—2.421 sin 2A., 

 —0.226 sin 3^., 

 — 0.055 sin iA^ 

 —0.027 sin 5J, 

 —9". 



4-0.318 cos 3^2 

 +0.097 cos 4^, 

 +0.038 cos bA, 

 1ST 



Icos. 



(u.e.S) = 



(v.cA) = 



(p.r.O) 



— 2.265 



— 1.163 

 + 0.026 

 + 0.005 

 + 0.002 



— 0.126 



— 0.503 

 + 0.053 



+ 106 

 o 



sin A.^ 

 sin 2A^ 

 sin 3A^ 

 sin 4Jj 

 sin bA, 

 — 0" 



sin A^ 

 sin 2A^ 

 sin 3^2 



sin A.J 

 sin 2.4, 



+5 



+2 

 — 

 — 0, 

 — 

 04 T 



+0, 

 — 



+ 

 + 

 + 

 + 



(p.r.l) = + 1364 sin A.^ — 



— 46 sin 2 A., + 



— 7 sin 3.4, + 



— 3 sin iA, + 



+98 T 



(p.c.2) = - 



279 sin A.^ — 

 27 sin 2A^ + 

 3 sin 3A, 



\-1T 



(p.c.3) = 



+ 



61 sin A.^ 

 24 sin 2A, 



+ 



656 cos A, 

 ,956 cos 2^, 

 .063 cos 3.4j 

 .013 cos 4.4, 

 .004 cos 5^2 



.329 cos A^ 

 .378 cos 2J, 

 .032 cos 3 A, 



761 cos A, 



89 cos 2A, 



19 cos 3A, 



5 cos iA, 



43 cos A^ 



45 cos 2.4j 



9 cos 3.:4j 



2 cos 4.4, 



103 cos A^ 

 9 cos 2A„ 



24 cos A^ 

 9 cos 2J. 



/+116.650 \ . . , / 51.954 \ 



= 1 )sin.4.,+ ( Ic 



V— 1.38 T/ '^^+ 0.27 T/ 



—1.813 sin 2.4, +0.631 cos 2A, 



—0.177 sin 3^, +0.013 cos 3^, 



—0.044 sin 4.4, +0.013 cos iA, 



—0.016 sin bA., +0.005 cos bA, 



— 0".54T 



(u.s.3) = +5.656 sin J, +2.265 cos A, 

 +2.956 sin 2.4, +1.163 cos 2^ 

 —0.063 sin 3.4^ —0.026 cos 3A, 

 _0.013 sin 4J, —0.005 cos iA, 

 —0.004 sin 5.4, —0.002 cos bA, 

 — 0".03r 



(y.s.4) = +0.329 sin A, +0.126 cos A, 

 +0.378 sin 2A, +0.503 cos 2A, 

 —0.032 sin 3^, —0.053 cos 3A, 



(p.s.l) = - 



(p.s.2)=- 



(p.s.3) = 



