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= (1 + μm) }

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0.08 sin. (-)

0.22 sin. (↳ — 2

-

+ 34.09 sin. (2 — K)
0.02 sin. 2 (- K)

+7x)

0.01 sin. (2 -3 ¥ + g) K

h

0.003404 t cos. ( — лỵ)
一匹)

0.01 sin. (h -Th)
팩)
0.28 sin. (-2 +πη)
1
0.54 sin. (2 ↳ — — πη)
h
0.02 sin. (2 ↳ -3 ¥ +TM1⁄2)
h
0.009134 t cos. (— an)

K

h)

0.14 sin. (2)

x)

0.42 sin. (2 − 2 l+ng)
0.02931 t cos. (¥ — ′′x)

0.01 sin. (2 + 2)
0.82 sin. (2 - Ķ — л2)
0.003727 t cos. (

--

+(1+μR)

0.02 sin. (K)

66

“8 r = the perturbation of Neptune's radius vector =

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(4n+1)+

--

0.00003 cos. (H
0.00666 cos. (2 K

+0.00001 cos. (2 ƒ
+0.00403 cos. (2

-0.00016 cos. (3 −4+л)

H

H5

+

— 6 1⁄2 + ̃1⁄2)
H 6K+

0.00004 cos. (4
-0.00002 cos. (5
0.00001 cos. (6 — 7K+л)
+0.000001362 t sin.

H

(

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H

H

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H

+0.00005 cos. (3 1⁄2 — μ

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+0.00003 cos. (H

+(1+

+++ 0.00005 cos. (4 -2 H

P

2 H

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- A

{+0.00310

+(tun)? +0.00275 cos. ( h − K)
| +0.00003 cos. 2 (1⁄2 — })

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H

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2 лу)

"H

0.00048 cos. (4 Ę
+0.00095 cos. (4 — 2 μ — 2 л)

F

H

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0.00002 cos. (h
π.)
+0.00002 cos. (−2 ¥ +лx)
(h x
0.0000002513 t sin. (—)

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− 2 K + πn)

-0.00004 cos. ( +(1+)+0.00008 cos. (2 — — πη) K +0.0000006742 t sin. (—)

h

( #1

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+(1+12)

+(1+μ2)

{

0.00004 cos. (îα)
(2

+(1+2)+0.00004 cos. (2-2 1⁄2 — τμ)

K

0.0000002163 t sin. (

"K) •л)

δυ

+ 0.00978

+0.00497 cos. (2 — Ę)

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+0.00012 cos. (2
+0.0000002751 t sin. (

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8.63 sin. 2 (HK) 1.70 sin. 3 (— K) — 0.54 sin. 4 (μ— K) 0.21 sin. 5(K) 0.09 sin. 6(K) 0.04 sin. 7(K) 0.02 sin. 8 (— K) 0.01 sin. 9(K) 0.01 sin. 10 (— Ķ) +18.60 sin. (h — F)

0.15 sin. 2(K)
0.02 sin. 3(K)
+34.09 sin. (2)
-0.02 sin. 2 (2K)
+0.02 sin. ( — K)
+k sin. (+ q) + A.

+ (1 + μg ' ' ' 8) 0.00006.

"These formulæ may be exhibited in the following form, which is similar to that adopted by the illustrious Leverrier, in his theory of Mercury, and very convenient for the construction of tables. The coefficients for the corrections of the masses are hereafter omitted.

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0.00003 cos. 2 (h)
+0.00497 cos. ( — K)
+h cos. ( 0) + B.

"In these equations, k, h, q, 0, A, and B are determined by the following formulæ :

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+

306 513)

k cos. q = 1.87 cos. (
+0.22 cos. [2 (μ )+171 28]
+1.76 cos. [3 (K) + 0 5]
+0.35 cos. [4 (K) +221 30]
+0.13 cos. 5(K)

+0.07 cos. 6(E)

+0.03 cos. [7(K) + 348]
+0.01 cos. [8(K) + 348]
(H
+0.44 cos. (h-K + 242 47)
+0.55 cos. [2 (h) + 271 3]
+0.44 cos. (2 - K +208 18)
+0.82 cos. [2 (2) + 348 9]

k sin. q = 1.87 sin. (E
(H
+ 306 5 13)
+0.22 sin. [2 (HK) + 171 28]
1.70 sin. [3 (HK) 178 45]

+0.32 sin. [4() + 180]

0.11 sin. [5(K) + 180] +0.05 sin. [6(-) + 180] +0.03 sin. [7(HK) + 168]

0.01 sin. [8(K) + 168] +0.51 sin. (h-F + 77 0) +0.55 sin. [2 (h)+268 55] +0.46 sin. [2 - Y K +64 0] +0.82 sin. [2 (2)+348 9]

h cos. 0 =

A =

h sin. 0 =

B

K

0.00011 cos. ( H +121) +0.00001 cos. [2 (H)+ 252] +0.00015 cos. [3 (HK) + 333]

0.00004 cos. [4 (HK) +333]
+0.00002 cos. [5 (μ — K) + 348]
(H
+0.00001 cos. [6 (HK) + 348]
0.00001 cos. (h+270)
+0.00008 cos. [2 (h) + 270]
+0.00005 cos. (2- K +90)
+0.00002 cos. [2 (2 −

) + 348]

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0.00011 sin. (H - K + 301) 0.00001 sin. [2 (-) + 72] 0.00015 sin. [3 (HK) + 333] 0.00003 sin. [4 (HK) + 333] +0.00002 sin. [5 (H )+348] 0.00001 sin. [6 (HK) + 348] +0.00005 sin. (h K + 325) +0.00008 sin. [2 (h) + 90]

0.00005 sin. (2)

0.00012 sin. [2 (2) + 168]

+

+

+

+

++

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+ 284 56 38) +38 24 43) + 188 42 10) +358 40 0)

+

0.022332 t sin. ( 187.33 sin. (HK 1724.04 sin. (2 - H 67.93 sin. (2-3 + 14.45 sin. (3-140 55 30) 0.15 sin. (4 - H + 90 0) 0.14 sin. (H +257 55) 73.23 sin. (4-2181 20 17) 0.59 sin. (5-2134 19) 2.85 sin. (6-387 47 23) 5.66 sin. (3-5 +358 16 47) 0.09 sin. (2-2300)

K + 179 56 48)

0.0000030384 t sin. (+257 27 18) 0.01326 cos. (H +0.00696 cos. (2 K 7 51 1) + 0.00462 cos. (22179 7 45)

H

+0.00005 cos. (3

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0.00116 cos. (4 K-2

+ 149)

+

3 29 5)

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