The several messages on EoT have pushed me to make a little investigation
on this subject to satisfy my curiosity.
I've searched for EoT on many books on Sundials and on Astronomy and
I've reached this conclusion : there is a great confusion on this argument.
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DEFINITION of EoT
Let be TA the Apparent Time (often called True Time) (marked by a Sundial)
and TM the Mean Time (marked by standard clocks)
The results of my search are the following :
n. 2 Italian books on Sundial EoT=TA-TM and EoT=TM-TA in different
pages
n. 2 Italian books on Sundial EoT=TA-TM
n. 1 Italian book on Sundial EoT=TM-TA
n. 6 handbook on Sph.Astronomy EoT=TA-TM
n. 2 French book on Sundial EoT=TM-TA
n. 1 French book on Sundial EoT=TA-TM
Rohr (It. Edition) EoT=TM-TA pag 41
in pag. 42 is said that in Anglo-Saxon
Countries is
EoT=TA-TM
Mayall-1994 - pag. 86
Waugh -1973 - pag.201
Duffett-Smith-1979 - pag.171 EoT=TM-TA
Meeus-Astr.Algh. - pag. 171 EoT=TA-TM In the book is said that
in older and in French texts is
EoT=TM-TA
HYR.Mills-Positional Astronomy EoT=TA-TM when Sun transits Meridian
Very good explanations
Explanatory Sup.Astronomical Almanac(ESAA) pag. 5 - 74
EoT=TM-TA
First conclusion :
in Astronomy handbook wins the definition EoT=TA-TM also if
this is not in ESAA. This occurrence probably because in Astronomy EoT was
used ( and also now is used at sea) to determine the True (Apparent)
Time when is known the Middle Time (from Clock)
in books on Sundials , where EoT is used to find the Clock's Time
knowing the Sundial's one (TA), wins ( 8 to 4) the definition EoT=TM-TA
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TABLE of EoT
I've looked for the value of EoT in a particular day (March the 1st)
in all my books on Sundials containing a table (13).
The values vary from 12m 19s to 12m 37s with an average of 12m 29s
In only two books is said that the EoT is calculated on 0 UT.
In 3/1 from 0h UT to 12h UT the change of EoT is -5.8 sec.
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VALUES of EoT from PC-Programs
I've examined 4 PC-Programs on Sundials (2 in Italian, Equadecl by de
Vries, and the one I've written) and with them I've calculated EoT in the
dates :
3/1/1997, 3/1/1998, 3/1/1999 and 3/1/2000.
After I've controlled the results with Jeffrey Sax's programs distributed
by Willmann-Bell and based on Astronomical Algorithms by J. Meeus -1991
All the programs, with the exception of mine, give the value of EoT
for the particular year entered , that is give different values of EoT in
different years : this is not useful to plan sundials and EoT's graphs
and may confuse the inexperienced.
Only the de Vries's program gives values equal to those produced by
Jeffrey Sax's one for 12h UT ( the differences are less then 0.7 sec )
(values are : 12m + 21.70s , +24.49s ,+ 26.56s , +18.16s for 1997,1998,
1999, 2000; average : 12m 22.728s )
My program gives always the same value for a given day (12m 23s)
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INSTANT
Almost always the EoT is defined as a function of time, that is as a
quantity whose value changes continuously : the difference from one day
to the following one may reach 20 sec.
This fact is correct in Astronomy but not when we deal with Sundials:
commonly the EoT is regarded as a "single" value for every day.
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CONCLUSION
I think that it wuold be useful for all the people interested to Sundials
if this subject wuold be arranged and unified.
Perhaps the Sundial's Associations ( NASS, BSS, ISSI, etc.) could promote
the matter.
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For the use of EoT with Sundials I suggest that :
- the definition is EoT=TM-TA so EoT is the correction to "add" to
Sundial's time (TA) to obtain the Middle Time (TM) : TM=TA+EoT
- the values to use for tables or graphs are those calculated in every day
in the istant of the Meridian transit of the True Sun ( True Noon)
( for Eurepean countries also at 12h UT)
In such a way the values in the same day in different places of the world
are not equal but the differences are small ( max. 20 sec.)
- the values to use are calculated (and printed in tables) with simple
algorithms and little precision (roughly 10 sec.: I remember that , because
of the Sun's diameter, the shadow of an infinitesimal point is a spot
"large" 2 minuts of time )
I propose to use the average of the values in 4 consecutive years
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Excuse me for the excessive lenght of this message
Gianni Ferrari
