Appendix IV

TABLE EQUATION OF TIME and DECLINATION OF THE SUN (1986 *)

00:00 in Universal Time (UT, GMT)

 Date               E              δ               Date                E              δ            Date                E              δ            Date                E              δ
         min. sec. ° ’          min. sec. ° ’          min. sec. ° ’          min. sec. ° ’
      Jan 0 –02 48 –23 07       Feb 15 –14 12 –12 51       Apr 1 –04 06 +04 20      May 17 +03 40 +19 13
  1 03 16 23 03   16 14 09 12 31   2 03 48 04 44   18 03 38 19 26
  2 03 44 22 58   17 14 06 12 10   3 03 30 05 07   19 03 36 19 40
  3 04 12 22 52   18 14 01 11 49   4 03 13 05 30   20 03 33 19 52
  4 04 40 22 47   19 13 56 11 28   5 02 55 05 53   21 03 30 20 05
  5 –05 07 –22 40   20 –13 51 –11 06   6 –02 38 +06 15   22 +03 26 +20 17
  6 05 34 22 33   21 13 44 10 45   7 02 21 06 38   23 03 22 20 29
  7 06 01 22 26   22 13 37 10 23   8 02 04 07 01   24 03 17 20 40
  8 06 27 22 19   23 13 29 10 01   9 01 47 07 23   25 03 12 20 51
  9 06 52 22 11   24 13 21 09 39   10 01 31 07 45   26 03 06 21 02
  10 –07 17 –22 02   25 –13 12 –09 17   11 –01 15 +08 08   27 +03 00 +21 13
  11 07 41 21 53   26 13 02 08 55   12 00 59 08 30   28 02 53 21 23
  12 08 05 21 44   27 12 52 08 32   13 00 44 08 52   29 02 46 21 32
  13 08 28 21 34   28 12 42 08 10   14 00 28 09 13   30 02 38 21 42
  14 08 51 21 24      Mar 1 12 31 07 47   15 –00 13 09 35   31 02 30 21 51
  15 –09 13 –21 13   2 –12 19 –07 24   16 +00 01 +09 56      June 1 +02 21 +21 59
  16 09 34 21 02   3 12 07 07 01   17 00 15 10 18   2 02 12 22 07
  17 09 55 20 51   4 11 54 06 38   18 00 29 10 39   3 02 02 22 15
  18 10 15 20 39   5 11 41 06 15   19 00 43 11 00   4 01 52 22 22
  19 10 34 20 27   6 11 28 05 52   20 00 56 11 21   5 01 42 22 29
  20 –10 52 –20 14   7 –11 14 –05 29   21 +01 09 +11 41   6 +01 31 +22 36
  21 11 10 20 01   8 –10 59 05 05   22 01 21 12 01   7 01 20 22 42
  22 11 26 19 48   9 10 45 04 42   23 01 33 12 22   8 01 09 22 48
  23 11 42 19 34   10 10 30 04 18   24 01 44 12 42   9 00 58 22 53
  24 11 58 19 20   11 10 14 03 55   25 01 55 13 01   10 00 46 22 58
  25 –12 12 –19 05   12 –09 59 –03 31   26 +02 06 +13 21   11 +00 34 +23 02
  26 12 26 18 51   13 09 43 03 08   27 02 16 13 40   12 00 22 23 07
  27 12 39 18 35   14 09 26 02 44   28 02 25 13 59   13 +00 09 23 11
  28 12 51 18 20   15 09 10 02 20   29 02 34 14 18   14 -00 03 23 14
  29 13 02 18 04   16 08 53 01 57   30 02 43 14 37   15 00 16 23 17
  30 –13 13 –17 48   17 –08 36 –01 33      May 1 +02 51 +14 55   16 –00 29 +23 20
  31 13 22 17 32   18 08 19 01 09   2 02 58 15 13   17 00 42 23 22
      Feb 1 13 31 17 15   19 08 01 00 46   3 03 05 15 31   18 00 54 23 24
  2 13 39 16 58   20 07 44 –00 22   4 03 11 15 49   19 01 07 23 25
  3 13 46 16 40   21 07 26 +00 02   5 03 17 16 06   20 01 20 23 26
  4 13 53 –16 23   22 –07 08 +00 26   6 +03 22 +16 24   21 –01 33 +23 26
  5 13 59 16 05   23 06 50 00 49   7 03 26 16 40   22 01 46 23 27
  6 14 04 15 46   24 06 32 01 13   8 03 30 16 57   23 01 59 23 26
  7 14 08 15 28   25 06 13 01 37   9 03 34 17 13   24 02 12 23 25
  8 14 11 15 09   26 05 55 02 00   10 03 36 17 29   25 02 25 23 24
  9 –14 13 –14 50   27 –05 37 +02 24   11 +03 39 +17 45   26 –02 38 +23 23
  10 14 15 14 31   28 05 19 02 47   12 03 40 18 00   27 02 50 23 21
  11 14 16 14 11   29 05 00 03 11   13 03 41 18 15   28 03 03 23 18
  12 14 16 13 52   30 04 42 03 34   14 03 42 18 30   29 03 15 23 16
  13 14 16 13 32   31 04 24 03 57   15 03 42 18 45   30 03 27 23 12
  14 14 14 –13 12       Apr 1 –04 16 +04 20   16 +03 41 +18 59      July 1 –03 39 +23 09
  15 14 12 –12 51   2 –03 48 +04 44   17 +03 40 +19 13   2 –03 50 +23 05

                                                                                                                    (Continued)

E: equation of time, δ: declination of the Sun, min: minutes, sec: seconds.

These values are for solar years 1986+4n (n=0,1,2,3,...). For 1987+4n, values corresponding to 6 hours earlier; for 1988+4n, values corresponding to 12 hours earlier (prior to March) and to 12 hours later (from March on); for 1989+4n, values corresponding to 6 hours later are used. For example, for 0 Jan. 1989 (31 Dec. 1988) the declination is determined as follows;

Declination (δ) = –23°27' - [-23°27' - (-23°03')] x 6÷24= -23°06'. Ibrâhîm Fezârî Baghdâdî was the earliest Muslim to devise the quadrant and use it to measure the Sun’s altitude. Among the very valuable books that he wrote are Zeyj-i-Fezârî, Amal-i-bi-l-usturlâb, and Kitâb-ul-mikyâs-uz-zawâl. He passed away in 188 [A.D. 803]. Two other extremely valuable books are Kitâb-ulusturlâb, by Usbu’ Ghirnâtî (of Granada), who passed away in 426 (hijrî), and Ridâyat-ul-mubtadî, by Alî bin Ahmad Baghdâdî (of Baghdâd) who passed away in 801 [A.D. 1398] in Egypt.

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Appendix IV (Continued)

TABLE EQUATION OF TIME and DECLINATION OF THE SUN (1986 *)

Oh UNIVERSAL (UT)

 

 Date               E              δ              Date                E              δ          Date                E              δ            Date                E              δ
         min. sec. ° ’          min. sec. ° ’          min. sec. ° ’          min. sec. ° ’
      July 1 –03 39 +23 09   16 –04 24 +13 54      Oct 1 +10 06 –02 59   16 +15 21 –18 36
  2 03 50 23 05   17 04 12 13 35   2 10 25 03 22 Nov 17 15 10 18 51
  3 04 02 23 00   18 03 59 13 16   3 10 44 03 46   18 14 58 19 06
  4 04 13 22 55   19 03 46 12 57   4 11 03 04 09   19 14 46 19 20
  5 04 24 22 50   20 03 32 12 37   5 11 21 04 32   20 14 32 19 34
  6 04 34 +22 45   21 –03 17 +12 17   6 +11 39 –04 55   21 +14 18 –19 48
  7 04 45 22 39   22 03 03 11 57   7 11 57 05 18   22 14 03 20 01
  8 04 54 22 32   23 02 47 11 37   8 12 14 05 41   23 13 48 20 14
  9 05 04 22 25   24 02 32 11 17   9 12 31 06 04   24 13 31 20 27
  10 05 13 22 18   25 02 16 10 56   10 12 47 06 27   25 13 14 20 39
  11 –05 21 +22 11   26 –01 59 +10 36   11 +13 03 –06 50   26 +12 55 –20 51
  12 05 29 22 03   27 01 42 10 15   12 13 19 07 12   27 12 37 21 02
  13 05 37 21 54   28 01 25 09 54   13 13 34 07 35   28 12 17 21 13
  14 05 44 21 46   29 01 07 09 33   14 13 48 07 57   29 11 57 21 23
  15 05 51 21 37   30 00 49 09 11   15 14 02 08 20   30 11 35 21 34
  16 –05 57 +21 27 Sept  31 00 31 +08 50   16 +14 16 –08 42 Dec 1 +11 14 –21 43
  17 06 03 21 17   1 –00 13 08 28   17 14 29 09 04   2 10 51 21 53
  18 06 08 21 07   2 +00 06 08 06   18 14 41 09 26   3 10 28 22 02
  19 06 12 20 57   3 00 25 07 45   19 14 53 09 48   4 10 04 22 10
  20 06 16 20 46   4 00 45 07 23   20 15 04 10 09   5 09 40 22 18
  21 –06 20 +20 34   5 +01 05 +07 00   21 +15 15 –10 31   6 +09 15 –22 26
  22 06 23 20 23   6 01 24 06 38   22 15 24 10 52   7 08 50 22 33
  23 06 25 20 11   7 01 45 06 16   23 15 33 11 13   8 08 24 22 40
  24 06 27 19 59   8 02 05 05 53   24 15 42 11 34   9 07 58 22 46
  25 06 28 19 46   9 02 26 05 31   25 15 50 11 55   10 07 31 22 52
  26 –06 28 +19 33   10 +02 46 +05 08   26 +15 57 –12 16   11 +07 04 –22 57
  27 06 28 19 20   11 03 07 04 45   27 16 03 12 36   12 06 36 23 02
  28 06 28 19 06   12 03 28 04 23   28 16 08 12 57   13 06 09 23 07
  29 06 26 18 53   13 03 49 04 00   29 16 13 13 17   14 05 40 23 11
  30 06 25 18 38   14 04 11 03 37   30 16 17 13 37   15 05 12 23 15
  31 –06 22 +18 24   15 +04 32 +03 14   31 +16 20 –13 56   16 +04 43 –23 18
       Aug 1 06 19 18 09   16 04 53 02 51  Nov 1 16 23 14 16   17 04 14 23 20
  2 06 16 17 54   17 05 15 02 27   2 16 24 14 35   18 03 45 23 22
  3 06 12 17 39   18 05 36 02 04   3 16 25 14 54   19 03 15 23 24
  4 06 07 17 23   19 05 58 01 41   4 16 25 15 13   20 02 46 23 25
  5 –06 02 +17 07   20 +06 19 +01 18   5 +16 24 –15 31   21 +02 16 –23 26
  6 05 56 16 51   21 06 41 00 54   6 16 22 15 50   22 01 46 23 27
  7 05 49 16 34   22 07 02 00 31   7 16 20 16 08   23 01 16 23 26
  8 05 42 16 17   23 07 23 +00 08   8 16 17 16 25   24 00 47 23 26
  9 05 34 16 00   24 07 44 –00 16   9 16 13 16 43   25 +00 17 23 25
  10 –05 26 +15 43   25 +08 05 –00 39   10 +16 08 –17 00   26 –00 13 –23 23
  11 05 17 15 25   26 08 26 01 02   11 16 02 17 17   27 00 43 23 21
  12 05 08 15 08   27 08 46 01 26   12 15 55 17 33   28 01 12 23 19
  13 04 58 14 50   28 09 07 01 49   13 15 48 17 50   29 01 42 23 16
  14 04 47 14 31   29 09 27 02 12   14 15 40 18 06   30 02 11 23 12
  15 –04 36 +14 13   30 +09 47 –02 36   15 +15 30 –18 21   31 –02 40 –23 08
    16 –04 24 +13 54 Oct 1 +10 06 –02 59     16 +15 21  –18 36   32   –03 09       –23 04

 

E = (true time)-(mean time).

The above values are determined when it was 00.00 in London at midnights. They are used after correction in direct proportion to the relevant longitude, and time. δ for a given time t in standard time is calculated from δ = δ2 + (δ2 - δ1) x (t-(S/15))/24 where δ1 and δ2 are the values on that day and on the following, respectively; S is the degree of the meridian determining standard time; all used with their algebraic signs.

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