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FOR COMPUTING THE APPARENT TIME.

Arg. Nat. number, answering to, numb. from Table XXVII.+Log. Sine alt. + numb. from Table XXVII.

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5000 4994 4987 4981 4975 4968 4962 4956 4949 4943 4937 4930 4924 4918 4912 4905 4899 4392 4886 4880 4873 4867 4861 4854 4848 4842 4835 4829 4823 4816 4810 4803 4797 4791 4784 4778 4772 4765 4759 4752 4746 4740 4733 4727 4720 4714 4708 4701 4695 4688 4682 4675 4669 4663 4656 4650 4643 4637 4630 4624 4617 4611 4605 4598 4592 4585 4579 4572 4566 45594553 4546 4540 4533 4527 4520 4514 4507 4501 4494 4489 4481 4475 4468 4462 4455 4449 4442 4436 4429 4423 4416 4410 4403 4397 4390 4384 4377 4371 4364 4357 4351 4344 4338 4531 4325 4318 4312 4305 4298 4292 4285 4279 4272 4266 4259 4252 4246 4239 4233

0

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

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2588 2581 2574 2567 2560 2553 2546 2539 2532 2525 2518 2511 2504 2497 2490 2483 2476 2569 2462 2454 2447 2440 2433 2426 2419 2412 2405 2398 2391 2384 2377 2370 2363 2356 2349 2341 2334 2327 2320 2313 2306 2299 2292 2285 2278 2271 2264 2257 2249 2242 2255 2228 2221 2214 2207 2200 2193 2186 2179 2171 2164 2157 2150, 2143 2136 2129 2122 2115 2108 2100 2093 2086 2079 2072 2065 2058 2051 2044 2036 2029 2022 2015 2008 2001 1994 1987 1979 1972 1962 1958 1951 1944 1937 1929 1922 1915 1908 1901 1894 1887 1879 1872 1865 1858 1851 1844 1837 1829 1822 1815 1808 1801 1794 1787 1779 1772 1765 1758 1751 1744 1736 1729 1722 1715 1708 1701 1693 1686 1679 1672 1665 1658 1650 1643 1636 1629 1622 1615 1607 1600 1593 1586 1579 1571 1564 1557 1550 1543 1536 1528 1521 1514 1507 1500 1492 1485 1478 1471 1464 1456 1449 1442 1435 1428 1420 1413 1406 1399 1392 1384 1377 1370 1363 1356 1348 134 1334 1327 1320 1312 1305 1298 1291 1284 1276 1269 1262 1255 1248 1240 1233 1226 1219 1211 1204 1197 1190 1183 1175 1168 1161 1146 1139 1132 1132 1125 1118 1110 1103 1096 1089 1081 1074 1067 1060 1052 1045 1038 1031 1024 1016 1009 1002 995 987 980 973 966 958 951 944 937 929 922 915 908 900 893 886 879 872 864 857 850 843 835 821 814 806 799 792 785 777 770 763 756 748 741 734 727 719 712 705 698 690 683 676 668 661 654 647 639 632 610 603 596 589 581 574 5671 560 552 545 538 531 523 516 509 501 494 487 480 472 465 458 451 443

625 618

50

51

3007 3000 2993 2986 2979 2972 2965 2958 2951 2945 2938 2931

50

4361

429 422 414 407 400

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TO FIND THE AUGMENTATION OF THE MOON'S SEMIDIAMETER, BY THE ALTITUDE OF THE NONAGESIMAL, AND THE APPARENT DISTANCE OF THE MOON THEREFROM.

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0.01

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0.00

6° 0' 0.00 0.29 0.59 0.901.221.541.88

0.00 0.270.56 0.85 1.161.46 1.78 0.00 0.260.53 0.80 1.09 1.38 1.69 0.00 0.24 0.490.76 1.02 1.301.59

0.00 0.230.460.71 0.96 1.221.49 0.00 0.21 0.430.660.901.141.40 0.00 0.19 0.40 0.610.83 1.06 1.30 0.00 0.18 0.37 0.560.770.98 1.20 0.00 0.160.33 0.520.700.901.11 0.00 0.140.30 0.47 0.640.821.01

0.00 0.130.270.420.580.740.91 0.00 0.110.240.37 0.510.66 0.82 0.00 0.100.21 0.33 0.450.580.72

0.00 0.08 0.170.280.390.50 0.63 0.00 0.06 0.14 0.230.320.420.53 0.00 0.05 0.110.180.26 0.34 0.43 0.00 0.04 0.090.160.230.30 0.39 0.00 0.03 0.08 0.130.190.260.34 0.00 0.02 0.06 0.110.16 0.220.29 10.00

0.02 0.05 0.08 0.130.18 0.24 0.01 0.03 0.060.100.140.19

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0 00

0.00

-16.0 0.26

+0.02 0.04 0.060.100.14

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CONTRACTION OF SEMIDIAMETERS OF SUN AND MOON.
Arg. App. Altitude of the Sun or Moon.

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12 13 14 16 18 20 24 32 5090 0"

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6713+56

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30

33

36

1789

7

39

8

10

8890

8

9

9

30

2

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2223 +++

3

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CORRECTIONS OF THE MOON'S PARALLAX, ARISING FROM

THE SPHEROIDAL FIGURE OF THE EARTH.

XXXIV.

XXXV.

GR. EFFECT OF PAR.

TABLE XXXVI.

REDUCTION OF

LATITUDE.

Reduct. Arg.

Latit.

IN LONDON.

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0"

0"

0"0

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of Lat.

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0.9

0.9

1.5

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2.3

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3.2

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10

3.9

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11 12

4.6

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246002

1

8

256464

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2 88

86

84

82

80

78

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Ap. T. aft.

EQUATION OF SECOND DIFFERENCE.

Arg.

Second Difference of the Moon's Place.
3" 4" 5" 6" 7" 8" 9" 10" 15" 20" 25" 150" 140′′ | 50′′

Ap. T. aft.
N. or M.

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0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.1 0.1 0.1 0.2 0.2 0.3
0.0 0.0 0.0 0.0 0.1 0.1 0.1 0.1 0.1 0.1 0.2 0.3 0.3 0.4 0.5
0.0 0.0 0.1 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.3 0.4 0.5 0.6 0.8
0.0 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0.3 0.4 0.5 0.7 0.8 1.0
0.0 0.1 0.1 0.1 0.2 0.2 0.2 0.3 0.3 0.3 0.5 0.6 0.8 1.0 1.3
0.0 0.1 0.1 0.1 0.2 0.2 0.3 0.3 0.3 0.4 0.6 0.8 0.9 1.1 1.5
0.0 0.1 0.1 0.2 0.2 0.3 0.3 0.3 0.4 0.4 0.7 0.9 1.1 1.3 1.8
0.0 0.1 0.1 0.2 0.2 0.3 0.3 0.4 0.4 0.5 0.7 1.0 1.2 1.5 2.0
0.0 0.1 0.2 0.2 0.3 0.3 0.4 0.4 0.5 0.5 0.8 1.1 1.4 1.6 2.2
0.1 0.1 0.2 0.2 0.3 0.4 0.4 0.5 0.5 0.6 0.9 1.2 1.5 1.8 2.4

0.3

11 50

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1 50

2 0

2. 10

2 20 230

2 40

2.50

30

3 10

3 20

3.30 340

3 50

4 0

4 20

4 40

5 0 6 0

0.1 0.1 0.2 0.3 0.3 0.4 0.4 0.5 0.6 0.6 1.0 1.3 1.6 1.9 2.6
0.1 0.1 0.2 0.3 0.3 0.4 0.5 0.6 0.6 0.7 1.0 1.4 1.7 2.1 2.8
0.1 0.1 0.2 0.3 0.4 0.4 0.5 0.6 0.7 0.7 1.1 1.5 1.8 2.2 3.0
0.1 0.2 0.2 0.3 0.4 0.5 0.5 0.6 0.7 0.8 1.2 1.6 2.0 2.3 3.1
0.1 0.2 0.2 0.3 0.4 0.5 0.6 0.7 0.7 0.8 1.2 1.6 2.1 2.5 3 3
0.1 0.2 0.3 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.3 1.7 2.2 2.6 3.5
0.1 0.2 0.3 0.4 0.4 0.5 0.6 0.7 0.8 0.9 1.3 1.8 2.2 2.7 3.6
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.7 0.8 0.9 1.4 1.9 2.3 2.8 3.8
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.5 1.9 2.4 2.9 3.9
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.5 2.0 2.5 3.0 4.0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.5 2.1 2.6 3.1 4.1
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.1 1.6 2.1 2.6 3.2 4.2
0.1 0.2 0.3 0.4 0.5 0.6 0.8 0.9 1.0 1.1 1.6 2.2 2.7 3.3 4.3
0.1 0.2 0.3 0.4 0.6 0.7 0.8 0.9 1.0 1.1 1.7 2.2 2.8 3.3 4.4
0.1 0.2 0.3 0.5 0.6 0.7 0.8 0.2 1.0 1.2 1.7 2.3 2.9 3.5 4.6
0.1 0.2 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.8 2.4 3.0 3.6 4.8
0.1 0.2 0.4 0.5 0.6 0.7 0.8 1.0 1.1 1.2 1.8 2.4 3.0 3.6 4.9
0.1 0.2 0.4 0.5 0.6 0.7 0.9 1.0 1.1 1.3 1.9 2.5 3.1 3.8 15.0

3.2

10 10

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Arg. Second Difference of the Moon's Place.
I' 2' 3' 4/ 5' 6'
8' 9' 10' 11'
00 00 00 0"0 0"0 00 0"0 0"0 0"0 0"0
0.8 1.2 1.6 2.1 2.5 2.9
3.3
3.7 4.1
2.4 3.2 4.1 4.9 5.7 6.5 7.3 8.1
3.6 4.8 6.0 7.2
8.4 9.6 10.8 12.0
4.7 6.3 7.9 9.4 11.0 12.6
14.2 15.7
7.8 9.7 11.6

Ap. T. aft.

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7.8 11.6 15.5 19.4 23.3 4.2 8.3 12.5 16.7 20.8 25.0 4.4 8.9 13.3 17.8 22.2 26,6 4.7 9.4 14.1 18.8 23.5 28.2 4.9 9.9 14.8 19.8 24.7 29.7 5.2 10.4 15.6 20.7 25.9 31.1 5.4 10.8 16.2 21.6 27.1 32.5 5.6 11.3 16.9 22.5 28.1 33.8 5.8 11.7 17.5 23.3 29.1 35.0 6.0 12.0 18.1 24.1 30.1 36.1 6.2 12.4 18.6 24.8 31.0 37.2 6.4 12.7 19.1 25.5 31.8 38.2 6.5 13.0 19.6 26.1 32.6 39.1 6.7 13.3 20.0 26.7 33.3 40.1 6.0 13.8 20.8 27.7 34.6 41.5 7.1 14.3 21.4 28.5 35.6 42.8 7.3 14.6 21.9 29.2 36.5 43.8 7.4 14.8 22.2 29.6 37.0 44.4 7.5 15.0 22.4 29.9 37.4 44.9 7.5 15.0 22.5 30.0 37:5 45.0

27.2

15.5 17.4 19.4
18.3 20.6 22.9 25.2
23.7 26.3 29.0
23.7 26.7 29.6 32.6 35.6
26.3 29.5 32.8 36.1 39.4
28.7 32.3 35.9 39.5 43.1
31.1 34.9 38.8 42.7
29.2 33.3 37.5 41.7 45.8 50.0
31.1 35.5 39.9 44.4 48.8
32.9 37.6 42.3 47.0 51.7
34.6 39.6 44.5 49.5 54.4 59.4
36.3 41.5 46.7 51.9
37.9 43.3 48.7 54.1
39.4 45.0 50.6 56.3
40.8 46.6 52.4 58.3 64.1
42.1 48.1 54.2 60.2 66.2
43.4 49.6 55.8 62.0 68.2 74.4
44.6
50.9 57.3 63.7 70.0 76.4
45.7 52.2 58.7 65.2 71.7 78.3
46.7 53.3 60.0 66.7 73.3 80.0
48.4 55.4 62.3 69.2 76.1 83.1

21.3 23:3

11 10

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57.0 64.2
58.3 65.6
59.3 66.7 74.1
59.8 67.3 74.8
60.0 67.5 75.0
1/ 2' 입 4/ 5' 6' 71 8' 9/ 10'
Second Difference of the Moon's Place.

49.9

71.3 78.4 85.6

720

51.0

72.9 80.2 87.5

17 0

51.9

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52.3

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52.5

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5 30

540

5.50

2 4 6

247 911 13 15
246811 13 15
8 10

17

6 0

2 4 6

8 10

12 14
12 14

16

16

6 10

6

810 12 14

16

6 20

6 30

6 40

6 50

2 4

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CORRECTION OF APPROX. TIME, ANSWERING TO EQUATION OF SECOND DIFFERENCE.
D's m.
Arg. Equation of Second Difference of the Moon's Longitude.

in 12 h. 1"2"|3" 14" 15"

6" 7" 8" 9" 10" 11" 12" 13" 14" 15" 16" 17" 18" 19" 20" 122′′ |24′′ |26′ 28

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17 20 22 24 26 28 30 33 35 37 39 41 43 48 52 57 61 19 21 23 25 27 29 32 34 36 38 40 42 47 51 55 59 18 20 23 25 27 29 31 33 35 37 39 41 45 49 53 57 18 20 22 24 26 28 30 32 34 36 38 40 44 48 52 56 17 19 21 23 25 27 29 31 33 35 37 39 43 47 50 54 6 8 9 11 13 15 17 19 21 23 25 26 28 30 32 34 36 38 42 45 49 53 67 9 11 13 15 17 18 20 22 24 26 28 30 31 33 35 37 41 44 48 52 79 11 13 14 16 18 20 22 23 25 27 29 31 32 34 36 40 43 47 50 9 11 12 14 16 17 19 21 23 25 26 28 30 32 33 35 39 42 46 49 9 10 12 14 15 17 19 20 22 24 26 27 29 31 32 34 38 41 45 48 2357 10 12 13 15 17 18 20 22 23 25 27 28 30 32 33 37 40 44 47 23 7 8 10 11 13 15 16 18 20 21 23 25 26 28 29 31 33 36 39 43 46 23 56 10 11 13 14 16 18 19 21 22 24 25 27 29 30 32 35 38 42 45 235 68 9 11 12 14 16 17 19 20 22 23 25 27 28 30 31 34 38 41 44

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Equation of Second Difference of the Moon's Longitude.
38" | 40" | 42′′ | 44′′ | 46′′ | 48′′ | 50′′ | 55′′ | 60′′ | 65′′ | 70′′ | 75′′ | 80′′

90′′

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