The earliest tables of ΔT values were drawn up by Willem de Sitter (192?) and Dirk Brouwer (1952). The underlying observations (mainly of stellar occultations by the Moon) were reduced with the lunar theory of E.W. Brown in which a lunar (or tidal) acceleration parameter (n') of –22.44 "/cy/cy was adopted, based on the earlier studies of Spencer Jones (1939). A reanalysis of all the available observations between 1627 and 1860 by Charles F. Martin (1969) led to an improved set of ΔT values for this period.
The data of Brouwer and Martin was reanalysed by L.V. Morrison (1979), who further extended the range from 1620 to 19?? and reduced them using a lunar acceleration parameter of –26.0 "/cy/cy, based on the studies of Morrison & Ward (1975).
The values listed in the following table for the historical period (about up to 19??) are based on the analysis of F.R. Stephenson & L.V. Morrison (1984) of the times of stellar occultations of the Moon, solar eclipses and transits of the planet Mercury across the solar disk. The values for the more recent past are mainly derived from Very Long Baseline (VLB) observations of bright radio point sources such as quasars and radio stars.
year  +0  +1  +2  +3  +4  +5  +6  +7  +8  +9 
1620  124  119  115  110  106  102  98  95  91  88 
1630  85  82  79  77  74  72  70  67  65  63 
1640  62  60  58  57  55  54  53  51  50  49 
1650  48  47  46  45  44  43  42  41  40  38 
1660  37  36  35  34  33  32  31  30  28  27 
1670  26  25  24  23  22  21  20  19  18  17 
1680  16  15  14  14  13  12  12  11  11  10 
1690  10  10  9  9  9  9  9  9  9  9 
1700  9  9  9  9  9  9  9  9  10  10 
1710  10  10  10  10  10  10  10  11  11  11 
1720  11  11  11  11  11  11  11  11  11  11 
1730  11  11  11  11  12  12  12  12  12  12 
1740  12  12  12  12  13  13  13  13  13  13 
1750  13  14  14  14  14  14  14  14  15  15 
1760  15  15  15  15  15  16  16  16  16  16 
1770  16  16  16  16  16  17  17  17  17  17 
1780  17  17  17  17  17  17  17  17  17  17 
1790  17  17  16  16  16  16  15  15  14  14 
1800  13.7  13.4  13.1  12.9  12.7  12.6  12.5  12.5  12.5  12.5 
1810  12.5  12.5  12.5  12.5  12.5  12.5  12.5  12.4  12.3  12.2 
1820  12.0  11.7  11.4  11.1  10.6  10.2  9.6  9.1  8.6  8.0 
1830  7.5  7.0  6.6  6.3  6.0  5.8  5.7  5.6  5.6  5.6 
1840  5.7  5.8  5.9  6.1  6.2  6.3  6.5  6.6  6.8  6.9 
1850  7.1  7.2  7.3  7.4  7.5  7.6  7.7  7.7  7.8  7.8 
1860  7.88  7.82  7.54  6.97  6.40  6.02  5.41  4.10  2.92  1.82 
1870  1.61  0.10  –1.02  –1.28  –2.69  –3.24  –3.64  –4.54  –4.71  –5.11 
1880  –5.40  –5.42  –5.20  –5.46  –5.46  –5.79  –5.63  –5.64  –5.80  –5.66 
1890  –5.87  –6.01  –6.19  –6.64  –6.44  –6.47  –6.09  –5.76  –4.66  –3.74 
1900  –2.72  –1.54  –0.02  1.24  2.64  3.86  5.37  6.14  7.75  9.13 
1910  10.46  11.53  13.36  14.65  16.01  17.20  18.24  19.06  20.25  20.95 
1920  21.16  22.25  22.41  23.03  23.49  23.62  23.86  24.49  24.34  24.08 
1930  24.02  24.00  23.87  23.95  23.86  23.93  23.73  23.92  23.96  24.02 
1940  24.33  24.83  25.30  25.70  26.24  26.77  27.28  27.78  28.25  28.71 
1950  29.15  29.57  29.97  30.36  30.72  31.07  31.35  31.68  32.18  32.68 
1960  33.15  33.59  34.00  34.47  35.03  35.73  36.54  37.43  38.29  39.20 
1970  40.18  41.17  42.23  43.37  44.49  45.48  46.46  47.52  48.53  49.59 
1980  50.54  51.38  52.17  52.96  53.79  54.34  54.87  55.32  55.82  56.30 
1990  56.86  57.57  58.31  59.12  59.99  60.78  61.63  62.30  62.97  63.47 
2000  63.83  64.09  64.30  64.47  64.57  64.69  64.85  65.15  65.46  65.78 
2010  66.07  67.1(8)  68(1)  68(2)  69(2)  69(3)  70(4)  70(4)  –  – 
year  +0  +1  +2  +3  +4  +5  +6  +7  +8  +9 
values in light blue are predicted values (with estimated error in the last decimal) 
From 1973 onwards, precise daily values of ΔT can be obtained from the list of UT1–UTC values maintained by the Earth Orientation Department of the US Naval Observatory (view the readme file for more details). ΔT can be obtained from these values from the relation:
ΔT(s) = TAI–UT1 + 32.184 sec = (TAI–UTC) – (UT1–UTC) + 32.184 sec
where (TAI–UTC) is the cumulative number of leap seconds introduced since 1972.
Provisional daily ΔT values for the next 360 days can be obtained in a similar way from the predicted UT1–UTC values listed in the IERS Bulletin A issued bimonthly by the Earth Orientation Department of the US Naval Observatory.
The above table is also printed and updated each year in the Astronomical Almanac (pages K8K9), published annually by the Nautical Almanac Offices of the US Naval Observatory (Washington) and the Rutherford Appleton Laboratory (Cambridge). Click here for an ASCII version of the above list. A nearly identical table, in halfyearly intervals from 1657.0 to 1984.5, was published by McCarthy & Babcock (1986).
Note that the values before the mid 1950’s are mainly based on observations of stellar occultations by the Moon that were reduced with Brown’s lunar theory with an adopted lunar acceleration parameter (n') of –26.0 "/cy/cy. For other values of the lunar acceleration parameter, the values listed above before 1955.5 should be corrected by:
ΔT (s) = ΔT (table) – 0.91072 (n' + 26.0) u^{2}
with u = (year – 1955.5)/100, or the time measured in centuries since 1 July 1955.
Values after 1955.5 remain unchanged as they were obtained from observations that were compared directly against International Atomic Time (TAI).
Several polynomial representations for the ΔT values of the last few centuries have been proposed in the recent past to obviate the need of incorporating lengthy tables in a computer program. However, in order to account for the irregular fluctuations in the observed ΔT curve, these polynomial fits are of a high order with a necessarily limited range of validity.
Jean Meeus, in the second edition of his Astronomical Algorithms (1998), gives a 12thorder polynomial valid for the time span 1800 to 1997 with a maximum error of 2.3 seconds and two lowerorder polynomials covering the same time span with a maximum error of 0.9 seconds. The two latter polynomials are:
ΔT(s)^{ }=  –2.50 + 228.95 u + 5218.61 u^{2}
+ 56282.84 u^{3}
+ 324011.78 u^{4}
+ 1061660.75 u^{5} + 2087298.89 u^{6} + 2513807.78 u^{7} + 1818961.41 u^{8} + 727058.63 u^{9} + 123563.95 u^{10} 
(1800 < year < 1900) 
and
ΔT(s)^{ }=  –2.44 + 87.24 u + 815.20 u^{2}
– 2637.80 u^{3}
– 18756.33 u^{4}
+ 124906.15 u^{5} – 303191.19 u^{6} + 372919.88 u^{7} – 232424.66 u^{8} + 58353.42 u^{9} 
(1900 < year < 1997) 
with u = (year – 1900)/100, or the time in centuries since 1900.
These equations replace earlier and less precise polynomial fits valid for smaller time spans given in Schmadel & Zech (1979, 1988), in Montenbruck’s Practical Ephemeris Calculations (1989) and in Montenbruck & Pfleger’s Astronomy on the Personal Computer (1990, 1994, 199?).
The fourth edition of Montenbruck & Pfleger’s Astronomy on the Personal Computer (2000) provides the following 3rdorder polynomials valid for the period between 1825 and 2000 with a typical 1second accuracy:
Period  ΔT (s)  u = 
1825 to 1850  +10.4 – 80.8 u + 413.9 u^{2} – 572.3 u^{3}  (year – 1825)/100 
1850 to 1875  +6.6 + 46.3 u – 358.4 u^{2} + 18.8 u^{3}  (year – 1850)/100 
1875 to 1900  –3.9 – 10.8 u – 166.2 u^{2} + 867.4 u^{3}  (year – 1875)/100 
1900 to 1925  –2.6 + 114.1 u + 327.5 u^{2} – 1467.4 u^{3}  (year – 1900)/100 
1925 to 1950  +24.2 – 6.3 u – 8.2 u^{2} + 483.4 u^{3}  (year – 1925)/100 
1950 to 1975  +29.3 + 32.5 u – 3.8 u^{2} + 550.7 u^{3}  (year – 1950)/100 
1975 to 2000  +45.3 + 130.5 u – 570.5 u^{2} + 1516.7 u^{3}  (year – 1975)/100 
Edward M. Reingold & Nachum Dershowitz adopt the following approximate relations in the second edition of Calendrical Calculations (2001) and in their Calendrical Tabulations (2002).
Period  ΔT (d)  u = 
1620 to 1799  (196.58333 – 406.75 u + 219.167 u^{2})/86400  (year – 1600)/100 
1800 to 1899  –0.000009 + 0.003844 u + 0.083563
u^{2}
+ 0.865736 u^{3} + 4.867575 u^{4}
+ 15.845535 u^{5} + 31.332267 u^{6} + 38.291999 u^{7} + 28.316289 u^{8} + 11.636204 u^{9} + 2.043794 u^{10} 
(year – 1900)/100 
1900 to 1987  –0.00002 + 0.000297 u + 0.025184
u^{2}
– 0.181133 u^{3} + 0.553040 u^{4}
– 0.861938 u^{5} + 0.677066 u^{6} – 0.212591 u^{7} 

1987 to 2019  (100 u)/86400  (year – 1933)/100 
otherwise  (–15 + 32.5 u^{2})/86400  (year – 1810)/100 