5. Interval 284, rate 25 losing, interval 1084, accumulated rate+4m 30°, Green. date May 19d oh 29m 10', red. decl. 19° 48′ 39′′ N., red. eq. T. 3m 4581 subt. from A.T., true alt. 30° 41′ 2′′, sum of logs. 9'340198, hour-angle 3 43m 95, M.T. ship May 19d 3h 39m 235. Longitude 47° 33′ 15′′ E.

By Raper: True alt. 30° 40′ 55′′, log. sine sq. 9'340227, hour-angle 3h 43m 10. Longitude 47° 33′ 30′′ E.

6. Interval 22, rate 94 gaining, interval 33d 18h, accumulated rate 5 175 3, Green. date June 14 17h 56m 42", red. decl. 23° 20′ 14′′ N., red. eq. T. + om 6a, sum of logs. 9'277995, hour-angle 3h 26m 32°, M.T. ship June 14a 20h 33m 34. Longitude 39° 13′ E.

By Raper: True alt. 39° 50' 18', log. sine sq. 9.278041, hour-angle 3h 26m 33. Longitude 39° 12′ 45′′ E.

7. Interval 26d, rate 47 gaining, interval 34a, accumulated rate -2m 40°, Green, date July 5d oh 33m 8o, red. decl. 22° 47′ 11′′ N., red. eq. T. + 4m 159, true alt. 48° 47′ 5, sum of logs. 9'166615, hour-angle 3h om 12. Longitude 52° 16′ W.

By Raper: True alt. 48° 46′ 55", log. sine sq. 9'166672, hour-angle 3h 0m 138. Longitude 52° 16' 15" W.

8. Interval 21a, rate 2a·6 gaining, interval 104d 2h, accumulated rate 4m 31, Green. date August 13d 2h 20m 42o, red. decl. 14° 36′ 29′′ N., red. eq. T. 4TM 3816 add, true alt. 27° 23′ 29′′, sum of logs. 9:163652, hour-angle 2h 59m 33, M.T. ship August 12d 21h 5m 5a. Longitude 78° 54′ 15′′ W.

By Raper: True alt. 27° 23′ 25′′, log. sine sq. 9°163683, hour-angle 2 59m 34". Longitude 78° 54' 30" W.

9. Interval 28d, rate o7, interval 32d 19h, accumulated rate 224, Green. date August 31d 19h 12m 18%, red. decl. 8° 18′ 26′′ N., red. eq. T. 0TM 48·24 subt., truo alt. 44° 44′ 40′′, sum of logs. 9'057066, hour-angle 2h 37m 54, M.T. ship September 1d 2h 37m 50. Longitude 111° 23' E.

By Raper: True alt. 44° 44′ 36′′, log. sine sq. 9'057044, hour-angle 2h 37m 53°. 11° 22′ 45′′ E.

IO.

Longitude

Interval 36, rate 487 gaining, interval 974 83h, accumulated rate 7m 38%, Green. date October 25d 8h 35m 428, red. decl. 12° 17′ 42" S., red. eq. T. 15m 5286 subt., true alt. 40° 31′ 1′′, sum of logs. 9012568, hour-angle 2h 29m 425, M.T. ship October 25d 2h 13m 49*. Longitude 95° 28′ 15′′ W.

By Raper: True alt. 40° 30′ 56′′, log. sine sq. 9'012622, hour-angle 2h 29m 435. Longitude 95° 28′ W.

II. Interval 20d, rate 67, interval 184 7h, accumulated rate 2m 256, Green. date November 27d 7h 13m 53°, red. decl. 21° 13′ 53′′-S., eq. T. 12m 5s subt., true alt. 34° 50′ 6′′, sum of logs. 9'420025, hour-angle 4h 6m 518, M.T. ship November 26d 19h 41m 4o. Longitude 173° 12′ 15′′ W.

By Raper: True alt. 34° 49′ 57′′, log. sine sq. 9°420039, hour-angle 4h 6m 51. Longitude 173° 12′ 15′′ W.

12. Interval 284, rate 93 losing, interval 148a 18h, accumulated rate + 23m 3, Green. date December 24d 18h 37m 428, true alt. 10° 42′ 56′′, sum of logs. 9.638730, hour-angle 5h 30m 14", M.T. ship December 24d 18h 30m 0o. Longitude 1° 55′ 45′′ W.

By Raper: True alt. 10° 42′ 44′′, log. sine sq. 9.638761, hour-angle 5h 30m 15o. Longitude 1° 56' W.

13. Interval 31a, rate 6o·9 losing, interval 80d 14a, accumulated rate 9TM 16′, Green. date January 1d 14h om 38°, red. decl. 22° 56′ 41′′ S., red. eq. T. + 4 98.87, true alt. 39° 9′ 31′′, sum of logs 9.362235, hour-angle 3h 49m 258. Longitude 151° 45′ 45′′ W.

By Raper: True alt. 39° 9′ 28′′, log. sine sq. 9°362253, hour-angle 3h 49m 255. Longitude 151° 45′ 45′′ W.

14. Interval 314, rate 83 gaining, interval 71d 22h, accumulated rate 9m 569, Green. date February 10d 21h 33m 26, red. decl. 13° 59′ 12′′ S., red. eq. T. 14m 275.6 add, true alt. 12° 17′ 54′′, sum of logs. 9:176958, hour-angle 3h 2m 29′′. Longitude 5° 21′ 45′′ W.

By Raper: True alt. 12° 17′ 48′′, log. sine sq. 9°177030, hour-angle 3h 2m 30o. 5° 22′ W.

Longitude

15. Interval 34d, rate 25 losing, interval 52 days, accumulated rate + 2m 10, Green. date October 26d ob 26m 103, red. decl. 12° 31′ 15′′ S., red. eq. T. 15m 568.6 subt., true alt. 25° 10' 24", sum of logs. 9'286497, hour-angle 3h 28m 44". Longitude 62° 42′ 45′′ W.

By Raper: True alt. 25° 10′ 13′′, log. sine sq. 9.286565, hour-angle 3h 28m 45o. Longitude 62° 43′ W.

16. Interval 184, rate 54 losing, interval 17 days (nearly), accumulated rate 1m 32, Green. date February 5d 23h 59m 40%, red. decl. 15° 33′ 6 S., red. eq. T. + 14m 1984, true alt. 21° 21′ 7′′, sum of logs. 9:466313, hour-angle 4h 21m 590. Longitude 69° 9′ 30′′ E. By Raper: True alt. 21° 20' 57', log. sine sq. 9'466348, hour-angle 4h 22m 0o. 69° 9′ 45′′ E.

Longitude

17. Interval 484, rate 33, interval 72d 19h, accumulated rate 4m os, Green. date April 30d 18h 54m 3o, red. decl. 15° 3′ 56′′ N., red. eq. T. 2m 566 subt., true alt. 28° 18′ 45′′, sum of logs. 9-460500, hour-angle 4h 20m 1o. Longitude 140° 45′ 15′′ E. By Raper: True alt. 28° 18' 32", sine sq. 140° 45′ 30′′ E.

9°460546, hour-angle 4h 20m 28. Longitude

18. Interval 584, rate 16, interval 99d 16h, accumulated rate -2m 394, Green. date April 20d 15h 48m 558.8, red. decl. 11° 48′ 12′′ N., red. eq. T. subt. 1m 18", true alt. 31° 59′ 23′′, sum of logs. 9.360584, hour-angle 3h 48m 56′. Longitude at sight 179° 40′ 30′′ E., diff. longitude+29′ 54 give longitude at noon 179° 49′ 36" W.

By Raper: True alt. 31° 59′ 19′′, sine sq. 9°360594, hour-angle 3h 48m 56a. Longitude at noon 179° 49′ 36" W.

19. Interval 48d, rate 1*25, interval 113d 8h, accumulated rate + 2m 217, Green. date August 21d 8h 22m 23, red. decl. 11° 57′ 40′′, red. eq. T. + 2m 53°, true alt. 34° 2′ 1′′, sum of logs. 9°330311, hour-angle 3h 40m 25. Longitude at sights 179° 53′ 30′ W. + 29′ 54′′ W. Longitude at noon 179° 36′ 36′′ E.

By Raper: True alt. 34° 1′ 51′′, log. sine sq. 9'330352, hour-angle 3h 40m 25o. Longitude 179° 36′ 36′′ E.

20. Interval 27a, rate 0*3 gaining, interval 20d, accumulated rate - 6, Green. date March 20d 1h 32m 46, red. decl. o° 3' 28" S., red. eq. T. +7 338, true alt. 29° 1′ 4′′, sum of logs. 9'410710, hour-angle 4b 3m 56, M.T. ship March 19d 20h 3m 37°. Longitude 81° 17′ 15′′ W. 21. Interval 32d, rate oo8 gaining, interval 113d 15h, accumulated rate Im 31°, Green. date September 22d 15h 38m 0, red. decl. o°, red. eq. T. — 7m 473, hour-angle 4h 3m 50o, M.T. ship September 22d 19h 48m 23". Longitude 62° 35′ 45′′ E.

By Raper: True alt. 29° 2′ 15′′, hour-angle 4h 3m 518. Longitude 62° 35′ 30′′ E.

SUMNER'S METHOD, Page 299.

I. 1st red. decl. 7° 42′ 55′′ S; 1st red. eq. T. 12m 378 47 (added to A.T.); 1st true alt. 29° 57′ 17′′; lat. 49° 10′ gives hour-angle 1h 27m 53°; long. 178° 27′ 30′′ E. (A). Lat. 49° 40′ gives hour-angle 1h 21m 5s; long. 180° 9′ 30′′ E., or 179° 50′ 30′′ W. (A'). 2nd red. decl. 7° 38' 10' S.; 2nd red. eq. T. 12m 3584 (added to A.T.); 2nd true alt. 15° 55′ 57′′; lat. 49° 10' gives hour-angle 3h 38m 34'; long. 180° 5' o' E., or 179° 55′ W. (B). Lat. 49° 40′ N. gives hour-angle 3h 36m 34; long. 179° 35′ E. The line of bearing when the first altitude was taken trends E.N.E. and W.S. W. (nearly). The position of ship when the second altitude was observed was lat. 49° 25′ N., long. 179° 49′ E.

2. 1st red. decl. 19° 47′ 20′′ N.; 1st red. eq. T. 3m 468; true alt. 49° 8′ 2′′; lat. 48° 30′ gives hour-angle 2h 25m 6; M.T. ship May 18d 21h 31m 8; long. 7° 37′ W. (A). Lat. 49° o' gives hour-angle 2h 23m 11; M.T. ship May 184 21h 33m 3s; long. 7° 9′ W.; 2nd. red. decl. 19° 50′ 19′′ N.; red. eq. T. 3m 4584 subt.; true alt. 40° 56′ 2′′; lat. 48° 30′ gives hourangle 3 19 50*; long. 5° 18' W. (B). Lat. 49° o' gives hour-angle 3h 18m 51; long,

5° 38′ W. The line of bearing when the first altitude was taken trends N.E. by N. (northerly) and S. W. by S. (southerly). The position of ship at the time of the second observation is lat. 49° 58' N., long. 6° 1′ W.

3.

W.

2nd red. eq. T. 16m 68 Lat. 48° 40′ N. gives

1st red. decl. 16° 37′ 15′′ S.; 1st. red. eq. T. 16m 78.4 subt.; 1st true alt. 19° 58′ 31′′; lat. 48° 10' N. gives hour-angle 1h 59m 6o; long. 11° 34′ W. (A). Lat. 48° 40′ N. gives hourangle 1h 53m 498; long. 9° 44′ W. (A'). 2nd red. decl. 16° 41′ 6′′ S.; subt.; lat. 48° 10' gives hour-angle 3h 22m 48; long. 10° 33′ W. (B). hour-angle 3h 20m 93; long. 11° 13' W. (B'). The line of bearing at first observation trends N.E. by E. E. and S.W. by W. The ship's position at time of second observation is lat. 48° 5' N., long. 10° 27′ W. 4. 1st red. decl. 16° 28′ 46′′ S.; 1st red. eq. T. 14m 459 add; 1st true alt. 19° 59′ 26′′; lat. 48° 10' gives hour-angle 21 om 28a; long. 0° 54′ W. (A). Lat. 48° 40′ gives hour-angle 1h 55m 17; long. 0° 23′ E. (A'). 2nd true alt. 11° 0′ ‍53′′; lat. 48° 10′ gives hour-angle 3h 24m 30%; long. 0° 21′ E. (B). Lat. 48° 40' gives hour-angle 3h 21m 54"; long. 0° 17′ W. The line of bearing at first observation runs N.E. by E. E. and S. W. by W. W. The ship's position at second observation is lat. 48° 22' N., long. 0° 4}' E.

5. 1st red. decl. 19° 10′ 24′′ S.; 1st eq. T. 12m 22o add; 1st true alt. 9° 46′ 49′′; lat. 51° 15' gives hour-angle 2h 55m 368; long. 15° 33′ W. (A). Lat. 50° 45′ gives hour-angle 2h 59m 88; long. 16° 263′ W. (A'). 2nd red. decl. 19° 7′ 58′′ S. ; 2nd red. eq. T. 12m 24°*77 add; lat. 51° 15' gives hour-angle oh 57m 358; long. 17° 16′ W. (B). Lat. 50° 45′ gives hour-angle 18m 515; long. 14° 27′ W. (B). The line of bearing at first observation trends N.E.E. (easterly) and S.W. W (westerly). The position of ship at second observation is lat. 50° 56′ N., long. 15° 26' W.

2nd red. eq. T. 180° 15′ E., or

6. 1st red. decl. 2° 27' 0" N.; 1st red. eq. T. 5m 368.45 add; 1st true alt. 36° 48′ 53′′; lat. 50°40′ gives hour-angle 1h 36m 228; long. 180° 42′ 30′′ E., or 179° 17′ W. (A). Lat. 51° 10′ gives hour-angle 1h 41m 35o; long. 179° 24}′ E. (A'); 2nd red. decl, 2° 33′ 2′′ N.; 5m 3187 add; 2nd true alt. 15° 23′ 33′′; hour-angle 4h 32m 38; long. 179°0′ W. (B). Lat. 51° 10' gives hour-angle 4h 33m 32"; long. 181° 28′ E., or 178° 31}′ W. The line of bearing at first observation trends N.E. by E. E. and S.W. by W. W. The position of the ship at the second observation is lat. 51° 12′ N., long. 178° 37}′ W.

7. 1st red. decl. 7° 31′ 34′′ S.; 1st lat. 49° 15'; hour-angle 1h 29m 498;

red. eq. T. 12m 3185 add; 1st true alt. 29° 55′ 26′′; long. 1° 23′ W. (A). Lat. 49° 45′ gives hour-angle 1h 23m 7; long. 0° 17′ 30′′ E. (A'). 2nd red. decl. 7° 36′ 50′′; 2nd red. eq. T. 12m 29a add; lat. 49° 15' gives hour-angle 3h 38m 575; long. 1° 9′ E. (B). Lat. 49° 45′ gives hour-angle 3h 36m 588; long. 0° 39′ E. (B'). The line of bearing at first observation trends N.E. by E. E. (easterly) and S.W. by W. W. (westerly). The position of the ship at the second observation is lat. 49° 45′ N., long. o. 39' E. 8. 1st red. decl. 16° 33' 0" S.; 1st red. eq. T. 14m 38.14 add; 1st true alt. 20° 11′ 0′′; lat. 47° 10' gives hour-angle 2h 7m 10s; long. 83° 19' 15" E. (A). Lat. 47° 40′ gives hour-angle 2h 2m 255; long. 84° 30′ 30′′ E. (A'). 2nd red. decl. 16° 29′ 2′′ S.; 2nd red. eq. T. 14TM 4o49 ; 2nd true alt. 11° 17′ 59′′; lat. 47° 10' gives hour-angle 3h 26m 49; long. 86° 14′ 45′′ E. (B). Lat. 47° 40′ gives hour-angle 3h 24m 19; long. 85° 37′ 15′′ E. (B'). The line of bearing at the first observation trends N.E. by E. and S. W. by W. The position of the ship at the second observation is lat. 47° 53' N., long. 85° 20' E.

9. 1st red. decl. 19° 3′ 46′′ S.; 1st red. eq. T. 12m 28-88 add; 1st true alt. 9° 46′ 38′′; lat. 51° 15' N. gives hour-angle 2h 56m 30s; long. 180° 18′ E., or 179° 41′ W. (A). 2nd red. decl. 19° 1′ 20′′ S.; 2nd eq. T. 12m 318; 2nd true alt. 18° 40′ 21′′; lat. 50° 45′ gives hourangle 2h 59m 11; long. 179° 38′ E. (A') Lat. 51° 15′ N. gives hour-angle oh 55m 43"; long. 180° 34' W., or 178° 26' E. (B). Lat. 50° 45′ gives hour-angle 1h 7m 188; long. 178° 40′ W. The line of bearing at first observation trends N.E. N. (northerly) and S.W.S. (southerly). The position of the ship at the second observation is lat. 50° 53′ N., long. 179° 24′ W.

10. 1st red. decl. o° 15′ 23′′ N.; 1st red. eq. T. 7m 188.5 add; lat. 50° 10' gives hour-angle 3h 31m 16; long. 0° 43′ W. (A). angle 3h 28m 48; Long. 0° 6' E. (A'). 2nd red, decl. 0° 20′ 58′′ N.;

1st truo alt. 22° 59′ 25′′; Lat. 50° 50' gives hour. 2nd red. eq. T. 7TM 14°3

add; 2nd true alt. 32° 40′ 10′′; lat. 50° 10' gives hour-angle 2h 13m 22; long. 0° 26' E. (B). Lat. 50° 50′ gives hour-angle 2h 8m 228; long. 0° 48′ W. (B'). The line of bearing at the first observation trends N.E. } N. and S.W. S. The position of the ship at the second observation is lat. 50° 14' N., long. 0° 19' E.

II. 1st red. decl. 2° 7′ 36′′ S.; 1st red. eq. T. + 9m 4s4; 1st true alt. 14° 22′ 43′′; lat. 49° o' gives hour-angle 4h 20m 173; long. 1° 16′ W. (A). Lat. 49° 40′ gives hour-angle 4h 18m 43s; long. 0° 52′ W. (A'). 2nd red. decl. 2° 0' 6" S.; 2nd eq. T. + 8m 5954; 2nd true alt. 23° 27′ 13′′; lat. 49° 0′ gives hour-angle 3h 18m 40s; 49° 40′ gives hour-angle 3h 15m 53°; long. 1° 22′ W. (B'). observation trends N. by E. E. and S. by W. W. observation is lat. 49° 22′ N., long.

12. 1st red. decl. 16° 1′ 57′′ N.; 47° o' gives hour-angle 1h 57o 10o; 2h om 35; long. 52° 19′ W. (A'). N.E.N. and S.W. S. The 46° 28′ N., long. 51° 45′ W.

1° 4′ W.

long. 0° 40′ W. (B). Lat. The line of bearing at the first The position of the ship at the second

1st red. eq. T. 3m 2352; 1st true alt. 50° 40′ 55′′; lat. long. 51° 27′ W. (A). Lat. 46° 20′ gives hour-angle The line of bearing at the first observation trends position of the ship at the second observation is lat.

13. 1st red. decl. 23° 23′ 23′′ N.; 1st red. eq. T. + oTM 325; 1st true alt. 52° 1′ 30′′; lat. 48° 50' gives hour-angle 2h 23m 35o; long. 48° 13′ E. (A). Lat. 48° 10′ gives hour-angle 2h 25m 453; long. 47° 41′ E. (A'). 2nd red. decl. 23° 23′ 36′′ N.; 2nd red. eq. T. + om 338*7 ; 2nd true alt. 63° 45′ 6". Lat. 48° 50' gives hour-angle o 32m 44s; long. 47° 29′ E. (B). Lat. 48° 10' gives hour-angle oh 43m 41s; long. 50° 13′ E. (B'). The line of bearing at the first observation trends N.E. by N. N. (northerly) and S.W. by S. S. (southerly). The position of the ship at the second observation is lat. 48° 30' N., long. 48° 49′ E.

14. 1st red. decl. 13° 34′ 51′′ S.; 1st red. eq. T. subt. 16m 11869; 1st true alt. 28° 28′ 14′′; lat. 47° 30′ gives hour-angle oh 33m 11s; long. 74° 38′ E. (A). Assumed lat. 47° 50′ (not 48°, which would give the sum more than 180°), this gives hour-angle ob 16m 55*; long. 70° 34′ E. (A'). Red. decl. 13° 37′ 45; eq. T. 16m 138.6 subt.; lat. 47° 30′ gives hour-angle 3h om 37; long. 73° 42′ W. (B). Lat. 48° o' gives hour-angle 2h 57m 43s; long. 74° 25′ W. (B'). The line of bearing at the first observation trends E. N. (northerly) and W. S. (southerly). The position of the ship at the second observation is lat. 47° 46′ N., long. 74° 12′ W.

N.B.-It is scarcely necessary to warn the intelligent navigator against making an assumption of latitude that shall render the computation of the hour-angle impossible: the sum of the altitude, latitude, and polar distance, can never exceed 180°.

No.

Green. date.

1. Jan. 23423h 46m 7 2. Feb. 28 9 43 4 3. Mar. 27 0 34 12 4. April 2 19 o 8 5. May 25 21 9 32 6. June 20 6 55 44 July 31 1 6 46 Aug. 23 2 57 38 9. Aug. 31 18 33 2 10. Nov. 25 7 30 28 11. Dec. 16 22 58 2 12. July 21 16 18 50 13. Jan. 6 249 30 14. April 25 1 43 33 15. Jan. 29 6 53 47 16. Feb. I 2 22 23 17. Mar. 26 0 29 58 18. Feb. 25 15 40 19. June 21 7 3 20 20. Sept. 10 20 16 21. April 24 14 32

Red. decl.
19° 9' 30"S
7 44 I S
2 40 49 N
5 18 4 N
21 18 32 N
23 27 4 N

18 14
II 21 44 N
8 19 2 N
20 51 43 8
23 22 28 S
22 59 26 N
22 27 49 S
13 16 17 N
17 47 45 S
17 0 41 S
2 17 N

8

23 27 N

4 33

о

13 8 50

22. Feb. 28 20 15
23. Dec. 31 21 25 30

7 34

23 1

AZIMUTHS, Page 312.

True alt. Sum of logs. True azimuth.

38°34' 32" 27 7 43 29 41 3 II 50 42 43 19 41 16 49 1 43 35 48 7 43 28 30 14 51 34 2 21 51 13 O 14 19 37 26 46 54 18 52 57 13 47 28 40 7 21

19'731159
19'295153
19.703487
19:651755
19'418154
19.808282
19'601312

19'759124
19:556169
19'696611
19'712137
19'259073
19'732709
19:439408
19:242075
19'651011

19:422946

32.50 39 19 362660
60 48 32
15 46 28
42 38 43
43 34
66 26 29
45 22 20

19 8417,6
18:930809
19:785877
18.043319
19891183

N 94°24′ 44′′E
S 52 44 38 W
S 90 35 56 W
S 84 5 20 W
S 61 33 50 E
S106 37 52 W
S 78 22 58 E
S 98 32 36 E
N 73 43 34 W
N 89 41 22 W
N

91 45 50 E
N 50 26 36 E
N 94 38 OW
N 63 15 44 E
8 49 24 O W
N 83 59 54 W
S 57 23 OE
S 61 56 30 W
S112 54 32 W
N 33 57 20 E
S102 48 OE
S 12 4 2 W
N123 49 48 E