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N.

21 19 59 10 410 6 11 44 20 6 23 22 19 45 10 190 29 12 4 20 19 23 23 19 31 9 570 53 12 24 20 30 23 24 19 17 9 351 17 12 44 20 42 23 25 19 39 131 40 13 4 20 53 23 26 18 488 502 413 23 21 4 23 27 18 33 8 28 2 27 13 43 21 34 23

28 18 17 8 52 51 14 2 21 24 23 19 19 7 9 53
29 18 1 3 14 14 21 21 34 23
30 17 45
3 37 14 39 21 43 23
3117 28
21 521

14

6

53 17 20 23 00

7 15 17 37 23 5
38:17 53 23 9
8 018 9:13 13

7

8

23 18 25 23 16

8

45 18 40 23 19 9 7 18 55:23 22 9 29 19 10:23 24 9 5119 24 23 26 10 13 19 3823 27

S.

28 20 35 12 170 52 10 34 19 51 23 27
28 20 23 11 570 29 10 56 20 5 23 25
27 20 12 11 370 611 17 20 18:23 27
27 19 59 11 160 18 11 38 20 30 23 27
25 19 47 10 560 4111 59 20 4223 25
24 19 34 10 351 512 20 20 5423 24
22 19 20 10 14 1 28 12 40 21 523 22
52/13 0 21 16/23 19

17 18 53 9 32 2 15 13 21 21 27 23 16
13 18 39 9 10 2 38.13 40 21 37 23 18
18 24 8 49
14 이 123

of refraction and parallax upon the distance; it is also necessary to calculate the apparent time from an obsered altitude of the sun at a distance from the meridian, the latitude being given; or ta compute the time of the sun's setting or rising; which, though a less accurate method than the former of obtaining the time, may yet be useful when that cannot be had. For any of these purposes the sun's declination must be found to the time given nearly, re duced to the meridian of Greenwich, making proportion accord ing to its daily increase, or decrease, by the help of table 14, as in the following examples.

1st Required the Sun's Declination at noon in New-York, in Longitude 74° 8' West, on the 1st of April, 1811.

Dec. for April 1st, 1811, at Greenwich, in Tab. 134° 18' N.
Equation for Long. Table 14.

=

+450"

Required Declination 4° 22' 50".N.

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Sun's Declination for the Years 1811, 1815, 1819, 1823.

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Feb. Mar. April. May, June July Aug. Sept! Oct. Nov. Dec.

N. N. N. N. N. N. s. S.

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2

1 16 42 22 47

1621

123 4117 36

48 4 18 14 53 25 5923 11 18 13 8 32 2 56,14 15 21 44 2 22 591 26 59 7 251 4 42115 11 22 7123 217 588 u 3 19 14 34 21 53 322 5416 417 3 5 915 29 22 1523 217 42 7 49 3 43,14 53 22 4 22 48 16 24 6 405 28 15 47 22 22 22 5817 2717 27.4 615 12 22 11 5 22 41 16 6 6 17 5 50 16 4 22 2922

5217 12 4 2915 31 22 19 6 22 35-5 47,5 53 6 13 16 21 22 36 22 47 16 556 42 4 52 45 49/22 27 7 22 27 15 29 5 306 3616 38 22 42 22 4116 38 6 20 5 15 16 7 22 34 8 22 20 15 105 7 6 5846 55 22 48 22 3516 22 5 57 5 38 16 25 22 41 9 22 12 14 514 43 7 2117 11/22 53 22 28/16 4 5 35 6 100 22 314 32'4 20 7 4347

27 22 5922 2115 47 5 121 6 24!16 19 22 53 1121 54 14 133 578 517 43 23 . 3 22 13'5 30 4 496 47 17 16 22 58 12/21 4513 53 3 33 8 2717 38123 722 51'5.12 4 371 7 10 17 33 23 3 1321 35 13 333 9 8 4918 14 23 11 21 5714 54 4 4 7 3217 49 23 8 14/21 2513 1312 46 9 11 18 28 23 1521 4914 363 41 7 55 18 523 12 1521 1412 5212 22 9 33 18 43 23 18 21.4014 1713 17 8 17 18 21 23 16

312 321 59 9 54 18 57 23 21 21 30 13 582 54: 8 4018 36 23 19 1720 5212 35 10 1519 11/23 23/21 20 13 402 31: 9

2 18 5! 23 21 18 20 40111 5011110 36119 2523 25/21, 10113 2012 8, 924119 6 23 24 19 20 28" 290 47110 57 19 38/23 2621 013 11 45' 9 46 19 21 23 25 20 20 15" 7° 2411 1819 $123 2720 49 12 413 21:10 719 35 23 271 9.

N.
N

S. 21 20 210 4610 011 39/20 3|23 28 20 38 12 22 0 58 10 29 19 48 23 27 22119 49 10 240 241 59 20 16123 28 20 2612 20 35 10 $0 20 323 28 2319 35 10

20 47 12 19 20 28:23 27 20 1411 410 " 12 20 14 23 28 24 19 21 9 491 012 3920 39:23 2720 211 210 12 11 33 20 27123 27 25 19 6 9 181 35 12 5920 50:23,2619 50 u IO 36 11 54 20 39:23 26 2618 52 8 56'1 58 13 19 21 1123 24 19 37110 400 59 12 15 20 5023 24 27 18 36 8 33 2 22 13 3821 12,23 22 19 2410 191 23 12 3521 223 22 28118 21 8 11 2 4513 57 21 22 23 20 19 10 9 581 46 12 5521 13 23 20 29 18 5 3 9 14 1621 32'23 17118 561 9 372 9.13 16:21 24:23 17 3017 491 3 32 14 35 21 41:23 14/18 43 9 152 33 13 36 21 34 23 13 31,17 321 (3 55

21 Sol
18 28 8 541

23 91

13 55

N. B. To find the equations in Table 14,-seek the Sun's de'clination to the nearest degree in the top line of the table ; then, under this declination and against the given Lon. in the left hand column, is found the equation for Lon, and in the same column with the dec. and against the given time from Noon, in the right hand column, is found the equation for time ; both which equations must be added, or subtracted, according to the directions at the head of the Table.

2d Required the Sun's Declination on the 1st of May, 1811, at 5 h. 48 min. P. M. in Longitude 720 W.

Dec. May 1st, 1811, table 13. = 190 53' N.
Equat. for Lon.

+ 341"
Equat. for Time

+ 4 27

Reduced Dec.

F 15

| 8 N.

444

147

150

99

102

123

126

Add in W. lon.
Sub. in E. lon

Lon.

105

108

129

132

135

138

141

93

96

III

114

117

120

45

48

51

54

57

60

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When Sun's dec. increases.

When Sun's dec. decreases.
Add af. noon. | Sub. in W. lon. | Sub. af. noon.
Sub. be.noon. Add in E. lon.

Add be noon.

2o

Sun's Declination.
6% 80 9o
o'q

10°

0'0

d'o"

o'o oh om

o'0" 0'0"
11 0 15

O 12 O 12, 0.12 0 1.

0 110 110 12

0 240 24 0 24 0 23
0 350 350 35 0 34

0 230 220 2210 210 24
0 340 330 32 0.320 36
O 470 470 471 0 46; 45 440 430 420 48
0 59 590 580 570 560 550 540 53 1

I II I 10 I 10 I 9 1 7 I 6 5 3 1 12
221 22 122 I 21
117 116 1 14 1 24
I 34
I 341 33 1 32
I 271 24 136
145 144 143
38 35148
57
I 56

128

I 18 I 29 141 15451

I 46

1.39

1 58

1 49

I 481 45 2

3 32 3 31

3 43 3 42
3 55 3 54

D

2 10 2 10 2 8

2 22 2 21

2 19 2 31

2 332 32

2 45 2 442 43

2 57 2 56 2 54251
3-93 8.3 6
3 20 3 19 3 18

3 30

4

0'0"

345
3 52

4 7 4 6 4 4
4 19 4 18 4 16

7 39 7 37
7 57 49

2 6 2 3 2

2 17 2 14 2 12
239

2 25

2 23

2 40

2 36

2 34

2 47

3 3 3 15

3 26

3 37

3 48

4 0 4 12

2 59

3 10

2 44

2 55

3

6

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I 59 1.55 2 12

2 10 2 6

2 20

2 31

2 41

4 3 4 30 4 27 4 23
4 43 4 42 4 39 4 34)
4 54 4 534 594 45
5 6 5 5 5 2 4 57
5 18 5 17 5 14
530 5 28 5 26
5 41 5 40 5 37
553 552 548

5

440
9 5 1456 451
5 20 5 12 5 7
5 31 5 23 5 18
5 42-5-34 5 29
5 54 5.46

6 5 6 4 6

5 415.34
6 17 6 15 6 12 6 6 5 57 5 52 5:45
6 27 6 23 6 17 6 8 6 3 5 56
6 39 6 35 6 28 6 19 6 14 6 7
6 51 6-46 6 39
6 30
6 24 6 17
7 4 7 2 6 586 51 6 41 6 35 6 28

6 28
6 40

6 52

7 157 14
7 27 7 26

4 38

4 50 445

2 52

3 3

3 14

3 25

3 35

4 8

4 19

4 29

5 2 5 13 5 23

Ti. fr.

119 noon.

2 2

2 16 2.36

2 27

2 48

2 38

857 848
9 88 58

2 49

3 C

3 10

3 21

3 3

7 44 7 37

7 227 128 12
7 337 22 8 24
7 43 7 338 36
27 54 7 438 48
8 21 8 13 8 4 7 54 9
8 45
8 33
8 24 8 15
9 11 9 6 8 57 8 44 8 35 8 26
9 25 9 239 18 9 8 8 55 8 46 8 37

7 10 7 3 6 52 6 46
7 22 7 15 7 3 6 57
7 33 7 26 7 14 7 8
7 25 7 18
8 3 8 1756 7 49 7 37 7 29
814 8 13 8 8 8 07 48 7 40
8 26 8 24 8 20 8 11 7. 59 7 51
8 38 8 36 8 31 8 22 8 10 8
8 50 8 48 8 42 8 33

9 I 8 59 8 54

9 13

8 5 9 12 8 15 9 24 8 26 9 36 8 36 9 48 8 47 10 0

9 37 9 359 29 9 19

9 19 9 9 8 57 10 12

9 6 9 48 9 45 9 40 9 30 9 17 153 10 0 9 57 9 52 9 42 9 28 156 10 12 10 9 10 49 54 9 39 9 30 9 20 9 8 10 24 159 10 24 10 21 10 16 10 5 9 50 9 41 9 319 18 10 36 162 10 36 10 33 10 27 10 16 10 9 52 9 42 9 29/10 48 165 10 47 10 44 10 38 10 27 10 12 10 39 52 9 39 11 0 10 59 10 56 10 50 10 39 10 24 10 14 10 11 1111 811 210 51 10 35 10 25 10 14 10 011 24 174 11 2311 2011 1411 310 46 10 36 10 25 10 11 11 36 177 11 3411 31 11 25 11 14 10 57 10 47 10 36 to 21 11 48 180 11 46 11 4312 37 11 2511 8105 1046'

168

39 50 11 12

171

O

30

3 12

3 24

3 36

3 48

4 0

3 42 4 12

3 52 4 24 4 3 4 36

4 13 4 48

4 23 5 0 4-34 512

4 445 24

4 555 36
5 5 5 48
5 16 60

527 6 12
5 37 6 24
5 48 6 36
5 58 6 48
69 70
6 19 7 12
6 39 6 307 24
6 50 6 40 7 36
1 6 5 7 48
7
7 117

1 8 0

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When Sun's dec. increases. When Sun's dec. decreases.
Adu in W. len. Add af. noon. Sub in W. lon./Sub.af.noon.
Su" in E. Jon. Sub be noon. Add in E. lon. J Addbe.noon.
Lon.
Sun's Declination.

Itimefr.:
120
139 140 1150 16"

179 180 19°1

Noon. o'omlo'n lo ou o ou ooo'o lo'on o'o'

oh om 3 0 100 100 gjo 9 910

O 12 2010 2010 180' 18 0 180 160 1610 14

024 9 O 3110 305 280 27

270 240 240 21

0 36 12 O 4110 400 380 370 360 320 3110 28 0 48 15 0 510 50 10 4810 461 0 440 4110 3910 35

Io 18

010 38 10 5510 530 4940 460 42
21
I 120 9 70 sli

210 570 54 49
24

1221 19 ! 171! 141 III 511 20 56 1 36 27 1 324 29 27 1 231 1201 1411 101

3

148 30 1 431 391 36! 32 I 281,231_1811

O 33 1 531 49 1 461 42 1 371 311 251 18 2 12 36 31 591 561 ST 1.46: 39' 33/1 25 2 24 39 2 14/2 912 52 1 5511 471 411 322 36

2 24/2 1912 1512 10 411 361 491 39
45 2 34/2 29 2 24) 19 2 1212 si 571 46) 3
48

2 442 392 34 2 282 212 1312 411 53) 3 12 51

2 5512 492 44/2 381 2 3012 212 12 2 54 3 51? 5912 532 47 2 39/2 29/2 20/2 71 3 36 57 3 15 3 93 312 56 2 4812 382 282 15 3 48 60

3 25 3 193 133 51 2'562 472 36 e 23) 4 0 63 33513 293 223 14 3 5 2 552 432 29 4 12 66

3° 4613 39 3. 3213 23 3 14 3 3/2 5112 36.4 24 69 3 56/3 49 3. 42 3 32 3 23 3. 112 5912 43 4 36 72 4 63 593 513 413 32 3 19/3 712 50 4 48 75

1 3 5 3 403 28 3 1512 585 78 4 194 114 0 3 493 363 22 3 5 5 12 4

4 29 4 2014 9 3 583 4413 303.125 24 84

4 474 39 4 30 18] 4 713 52 3.3813 19 5 36 87 4 58 4 49 4 40 4 27 4 16 113 46 3 26 5 48 90 5 4 594 49 4 37 4 25/4 103 543 34

O 93 *5 18 5 94 5914 46 4 34 4 18 4 113 411 6 12 96

5 28 5. 195 94 55) 4 434 2614 93 48 6 24 99 5 395 295 1815 4 52 4 34 4.1713.556 36 102 5 4915 395 28 5 141 5

[4.434 2514 21 6 48 105 59 5 49 5 375 23 5 814 324 33 4 917 Q :08 6

95 595 4715 32 5 175 04 40 4 16 7 12 I11 6 206 915 565 421 265 8

4 23 7 24 114 6 30 6 1916 615 5 5 35 5 164 564 30 7 36 117

6 4016 296 1516 15 4415 2515 4 4 38 7 48 I 20 6 516 596 25 10 5 5315 3415 12 4 46 8 0 123 7 1 ó 496 35 6 19 6 25 425 194 53 8 12 1 26

116 596 4416 28 6 115.505 2715
129 7 227

6
54 6 37 6

195 $815 355 71 8 36 132 7 3217 18 7 416 46 6 2816 6 5 435 14 8 48 135 7 427 287 136 56 6 366 1515 5115 211 9 o 138 7 527 3817 237 51 6

456 2315 58

5 28

9 12 8 317 487 3317 14

6
546 3116

S 351924 144 8 13 7 5817 4217 23 7 36 396 14 5 42 9 36 147

8 238 87 527 32 7 12,6 4816 22 5 49 9 48 150 8 338 1818

27 42) 7 21 576_301 5 5710 153 8 43 8 2818 12 7 517 3017 516 376 4110 12 156

8 548 38 18 2118 o 7 397 136 45 6 11 10 24 159 9 418 48 8 31 8 10 7.48

1810 36 162

9 14,8 388 4118 19 7 5717.2917 116 25110 48 165 9 249 818 5018 28 8 517 387 96 3211

O 168 9 359 1819 03 38 8 1417 467 166 39 11 12 171 9 4519

110 8 47 8 2317 5417 24 6 46" 24 1749 5519 39 19 5 578 328 317 3716 5311 36 177 TO 619 419 2410

6 8

4:18 127 4017 DU 48 180 10 16

44 2017 487

O

4 48

ol 8 24

141

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Add in W. lon.
Sub. in E. lon

Lon.

153

156

72

75

78

81

141

144

159

162

69

84

87

90

123

126

135

138

147

150

33

36

39

42

45

48

63

66

93

96

129

132

J-2

15

18

21

24

27

30

9

When Sun's dec. increases,

3

O

0 14

070 60 60 50 40 39 20 6 0 130 12 O II O 10 90 80 60 40:4 0 200 18 0 17 0 15 0 12 0 10 0 705 0 270 250 230 21 0 19 0 16 0 14 0 90 1017 0 340 320 29 0 27 0 24 0 210 18 0 12 0 9 0 400 380 350 32 0 29 0 250 21 0 14 10 470 440 41 0 38 0 340 29 24 170 12 0 540 500 470 440 39 0 34 0 28 0 19 14 I 10 570 53 10 500 44 0 390 320 220 15 18140 59. 0.55 0 490 43 0 360 250 17 1.14 10 I 41 0 0 530 47 0 390 270 19 1 211 16 I 10 I 50 580 510 42 0 300 20 2822 I 16 10 I 30 550 46 0 320 22 I 351 29 22 I 16 I 8 50 0 340 24 281 22 I 13 54 0 360 25 33 27 I 18 570 390 27 1551 481 391 32 1 23 I 12 OO 42 0 29 2 2 5445 38 281 16 1 30 44 0 30 57 2 9 2 1 I 521 4433121 70 470 32 2 16 2 II 0 490 34

59

I 421 36

4

I 481 42

8

51

I

54

I

60

8

59 I 49 139 26

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2 22 2

14

2 29 2 20

2 36 2 26
2 432 33

2 50 2 40
2 56 2 46

3 32 52
3 10 2 58

2 454431 30
2 101 59 I 481 34
2 16 2 4 1 531 38
2 21 2 10 1 58 1 42
2 27 2 16 2 3 1 47
2 33 2 21 2 8

2 39 2 26 2 13

2 45 2 52 2 59

3 303 18

3

3 37 3 24

4 2 49 2 32
92 54 2 37

3

2 13
2 17
2 2
2 25

99

3 44 3 30

102

3 15 2 59 2 42 3.51 3 37 3 213 5 2 47 3 583 44 3 27 3 11 2 52 108 4 43 503 33 3 16

105

2 30

III
4 113 56 3 39
114
4 18 4 2 3 46
117 4 25 4 93 52
120 4 32 4 16 3 59

3 12 2 48 2 20

7 48
8.0

3 17

8 12

2 57 2 34 29
712
3 2 2 38 2 12 31 I 2 7.24
3 7 2 43 2 161 341
4736
37 5
2 53 2 23 1 39 17
4 384 22 4 4 3 44 3 22
2 57 2 261 4
4 454 28 4 10 3 49 3 27 3
12 29 44
4 524 34 4 16 3 54 3 32 3 5
4 59 4 41 4 22 3 59 3 37 3 9
5 64 48 4 28 4 5 3 42 3 13
5 124 54 4 34 4 10 3 47 3 17
5 19 5 0 4 404 15 3 52 3 21

3 26
3 30
3 35

1 9 8 24 I 10 233 1 46 1 12 8 36 2 36 49 1 14 8 48 2 401 511 15 90 2 43 54 17 9. 12 2 461 561 19 9 24 5 26 5 6 4 46 4 21 3 57 50 1 59 1 20 9 36 5 335 134 52 4 27 4 2 2 54 2 1 1 22 9.48 5 40 5 20 458 4 33 4 7 2 58 2 4 1 24 10 0 5 465 26 5 3 4 38 4 1 3 39 3 12 6 1 25 10 12 5535 32 5 9 4 43 4 16 3 43 3 4 2 9 1 27 10 24 6 05 38 5 15 4 48 4 213 47 3 8 2 11 1 29 10 36 6 75 45 5 21 4 54 4 26 3 51 3 12 2 13 1 30 10 48 6 145 52 5 26 4 31 3 56 3 16 2 15 1 32 11 0 6 205 58 5 3256 4 36 4 0 3 19 2 17 1 34 11 12 6 27,6 4 5 38 5 11 4 4 4 4 3 22 2 20 135 11 24 6 34 6 10 5 44 5 17 4 46 493 26 2 22 1 37 11 36 177 6 416 17 551 5 23 4 51 4 14 3 30 2 25 1 39 11 48 558 15 291 4 56 14 19 3 34 2 28

165

168

171

174

185

6 48 6 24

13 O

1 40

-317 3 5

3 24 3 12

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Add aft. noon.
Sub, bef. noon.

time fr

2030 210 21030/22° 22°30/23° 23°15' Noon.

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obom

0 12 0 24

0 36

0 48

10

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When Sun's dec. decreases.
Sub. W.
Sub. aft.
Add in E. lon.

Sun's Declination.

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3 21 3 27 3 33 3 39

2 32 2 181
2 382 23 2
2.44 2 28 2 9

4

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14 0 510 35

17

0 540 37
210 56 0.39
250 59
40
1 29 1
425.0
51 32 4 44 5 12
55 135 60 45 5 24
9 0 47
536
1 43110 495 48
1 471 140 50 60
I 50 160 52

59

1 39

6 12

531 19 0546 24

571 21 0 55

6 36
6 48

7 0

I I 24 O 57

51 26

129

1 48 20

59
O

2 12 2 24

36

2 48

30
3 12

3 24

3 36

348

40

4 12

4 24 4 36 4 48

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