[tz] TIme in Belize

Brian Inglis Brian.Inglis at SystematicSw.ab.ca
Sat Nov 7 16:08:12 UTC 2020

On 2020-11-07 01:18, Paul Eggert wrote:
> On 11/6/20 1:59 PM, Michael H Deckers wrote:
>>> -Zone America/Belize    -5:52:48 -    LMT    1912 Apr
>>> +Zone    America/Belize    -5:52:48 -    LMT    1912 Apr  1
>>    but the source is quite clear that it should be
>>       +Zone   America/Belize   -5:52:43 -   LMT  1912 Apr  1
> Unfortunately it's not so clear. Here's a citation to the source:
> # Definition of Time Ordinance, 1927 (No.4 of 1927) [1927-04-01]
> # Ordinances of British Honduras Passed in the Year 1927, p 19-20
> # https://books.google.com/books?id=LqEpAQAAMAAJ&pg=RA3-PA19
> It says that standard time was established as -06 on 1912-04-01, and that -06
> was 00:07:17.27 later than the local mean time at Belize. However, by my
> calculations -05:52:42.73 is longitude 88° 10′ 40.95″ W, which Google Maps says
> is in the ocean east of Belize city, so this was not LMT in Belize city.
> To my mind what matters here is what was the legal time in Belize city before
> 1912-04-01. If there was no law or it was just LMT, no change needs to be made.
> If it was -05:52:42.73 then we need to find out when that legal time was
> instituted (perhaps for all of British Honduras?), and insert a transition from
> LMT to -05:52:42.73 at the appropriate date.
> One constraint we like to follow is that the LMT longitude corresponds to the
> longitude in zone1970.tab.

You can't really make accurate judgments about anything based on Google Maps
(notice they do not show any geographical grid or claim any geographical
accuracy), except maybe within the Continental US, possibly because they use a
WGS84 spherical Mercator projection, rather than the ellipsoid, which results in
errors (except where that projection matches the ellipsoid), apparently higher
at higher elevations, and they seem to use the NAD83 North American Datum in
North America, but the datum used must vary elsewhere, and lacks documentation
in some areas.
Compare published geographic coordinates of current geodetic control points with
where those coordinates appear on Google Maps and you will see the local errors
and their magnitudes.
I have friends who get numerous drive-bys of their acreage apparently due to
"Google Maps" leading those who blindly follow such to believe their county road
crosses a "near grade" railway line, despite online maps showing the nearest
such roads 2-3 sections away, and the actual railway line elevation in the area
varying from the terrain by a couple of metres either way.

"Google Maps ... use a spherical-only Mercator projection based on the World
Geodetic System (WGS) 1984 geographic coordinate system (datum). This Mercator
projection supports spheres only, unlike [other] Mercator implementation, which
supports ... ellipsoids. To emulate the sphere-only Mercator, it is necessary to
use a sphere-based geographic coordinate system (GCS) to use the correct
Mercator equations. This sphere-based geographic coordinate system is called
'WGS 1984 Major Auxiliary Sphere'."

Historically and currently, other, possibly more local datums, were and are used
for geographic coordinates, nowadays often based on WGS84 spheroid models,
corrected by continuous GNSS observation cross-references, VLBI observations,
and gravimetry at active control points, to some ITRF, and usually more accurate
Original (astronomically referenced) survey accuracies are often of the order of
a metre, compared using modern methods, and modern corrections made, even at
remote locations, tend to be on the order of only metres in 3D, mainly due to
changes in reference frames, spheroid models, and datums (causing the largest

"		Table 1. Parameters of Some Spheroids
Spheroid Name	Semi-major	Semi-minor	Flattening, f	Eccentricity
		Axis, a (m)	Axis, b (m)			squared, e2
Clarke 1858	6378293.645	6356617.938	1/294.26	0.006785
Clarke 1866	6378206.400	6356583.800	1/294.9787	0.006769
Clarke 1880	6378249.145	6356514.870	1/293.465	0.006804
Clarke 1880	6378249.145	6356514.966	1/293.4663	0.006803
South American	6378160.000	6356774.719	1/298.25	0.006695
International	6378388.000	6356911.946	1/297		0.006723
		Table 2. Projections Adopted
Country	 Datum			Spheroid	Projection
Belize	 NAD 1927		Clarke 1866	TM & UTM
	 British Honduras 1922	Clarke 1858	TM Colony Coordinates
Honduras NAD 1927		Clarke 1866	TM (with UTM grid)
	 NAD 1927		Clarke 1866	Honduras Lambert N&S
	 Fort Charles Flagstaff	Clarke 1866	Jamaica Lambert Metre

"The original datum established for Belize is the Sibun Gorge Datum of 1922
where the astronomical coordinates of the origin are: Φo = 17º03’40.471”S,
Λo = –88º37’54.687”W, and the ellipsoid of reference is the Clarke 1858 where:
a = 6,378,293.645 m, 1/f = 294.26.
The Colony Coordinates used the datum origin for the Transverse Mercator
projection with a scale factor at origin of unity, a False Northing =
445,474.83ft, a False Easting of 217,259.26ft, and the unit of measure is where
1 meter = 3.28086933 Jamaican feet.
Another datum known to exist is called the Jesuit College Flagstaff, probably
being the origin for a local hydrographic survey.
With aerial photography flown in 1969 and 1972, a series of 1:50,000 scale
topographic maps were produced by the British Directorate of Overseas Surveys
The coordinate reference system currently used in Belize is the North American
Datum of 1927, presumably introduced in the 1950s by the U.S. Army Map Service’s
Inter-American Geodetic Survey.
The available 1:50,000 scale maps of Belize on the NAD27 are over-printed with
the UTM Grid. According to TR 8350.2, the three-parameter datum shift for
Central America including Belize From NAD27 To WGS84 is: ΔX = 0m±8m, ΔY =
+125m±3m, ΔZ = +194m±5m, and is based on a 19-point solution in 1987."

So with some GIS software and experimentation, current accurate values could be
recalculated, but historically and navigationally, time and latitude were
important, and as accurate as the technology of the day could make it.

Take care. Thanks, Brian Inglis, Calgary, Alberta, Canada

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[Data in binary units and prefixes, physical quantities in SI.]

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