178
March 2017
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
Founti is: α
o
= 109° 19´ 36˝ . A subsequent Polaris observation
(2 pointings) was not adopted.
The French North African ellipsoidal Bonne projection was
used for the Reconnaissance Triangulation, and this Grid
continues to influence mapping systems in North Africa to this
day. Proper computation of these Grid coordinates must be
performed from the series form of the equations for millimeter
accuracy. Texts that suggest the universal use of spherical
formulae with the equivalent authalic radius and latitudes are
wrong! The Latitude of Origin (
f
o
) = 35° 06´ North, and the
Central Meridian (
l
o
) of zero degrees from Paris corresponds
to 2° 20´ 13.95˝ West of Greenwich. The False Origin is 100
kilometers for both Eastings and Northings. This Grid has
perplexed novice cartographers (and many “old pros”) for
decades. Even more confusing, some implementations of this
Grid display no False Origin. The active use of this Grid was
terminated in 1942, but it continues to confound, as I shall
explain later.
The second type of French triangulation commenced in
1922, and is known as the Triangulation Réguliere (regular
triangulation). This work was carried out entirely by
Topographic Brigades of the Service Géographique de l’Armee
(Army Geographic Service), sent from Paris to Morocco. All
computations were performed in Paris. The Réguliere Datum
of 1922 is based on the origin at the astronomic station
Merchich 1921 (south of Casablanca), where: Φ
o
= 33° 26´
59.672˝ North, Λ
o
= 7° 33´ 27.295˝ West of Greenwich. The
azimuth to stationMohammed El Kebir is: α
o
= 46° 52´ 11.291˝
(from south), and the ellipsoid of reference is the Clarke
1880 where: a = 6,378, 249.145 meters, and
1
/
f
= 293.465.
During the same era, of 7 baselines that were measured for
the classical triangulation, Ber Rechid and Agourai were
locally adopted as temporary datum origins. The Ber Rechid
1920 Datum is defined where: Φ
o
= 33° 17´ 41.6˝ North,
Λ
o
= 9° 56´ 02.05˝ West of Paris. The azimuth from North
Base to South Base is: α
o
= 169° 34´ 15.3˝ . The geodetic
definition of the Agourai Datum seems to be lost, but it may
exist somewhere in Rabat or Paris. The remaining baselines
of the Réguliere Datum of 1922 included Marrakech, Guercif,
Taroudant, Bon Denib, and Sidi Ben Zekri, where “sidi” is an
Arabic term of obeisance, similar to “my lord.” In the 1950’s,
the U.S. Army Map Service (AMS) found the Réguliere
classical triangulation to be intrinsically correct.
The Lambert (partially conformal) Conic projection is
used for the Réguliere Datum of 1922, and this Grid also
confounds cartographers to this day. There are two original
zones: for Zone Nord, the Latitude of Origin (
f
o
) = 33° 18´
North (or 37
G
where 100 grads = 90°), the Central Meridian
(
l
o
) = 5° 24´ (6
G
) West of Greenwich, and the Scale Factor
at Origin (m
o
) = 0.999625769. For Zone Sud, the Latitude
of Origin (N
o
) = 29° 42´ North, the Central Meridian (
l
o
) =
5° 24´ West of Greenwich, and the Scale Factor at Origin
(m
o
) = 0.999615596. The False Origin is 500 kilometers for
Eastings and 300 kilometers for Northings
for both zones
. The
formulae used with this Grid have a long and lurid history
dating back to the 19
th
century, courtesy of the French way
of doing things.
During the 19
th
century, France was the center of cartographic
research in the mathematics of map projections. Because
projection table computations were performed by hand, all
formulae were commonly truncated past the cubic term to ignore
infinite series terms considered at the time, too small to warrant
the extra effort. For instance, the Lambert Conformal Conic
projection was used only to the cubic term in the formulae for
the tables of the developed meridional distances. This resulted
in French Army projection tables that have become part of the
arcane lore of computational cartography. This “secret” has
been explicitly detailed in the French literature for a century,
but apparently ignored by readers of English-only papers.
Standard Lambert formulae will not work for Morocco, and the
use of fully conformal formulae will yield computational errors
that exceed 15 meters! Note that mathematical elegance is not
what matters in a country’s coordinate transformations; what
matters is computational conformity to local
legal
standards. In
Morocco, one had better use the French Army Truncated Cubic
Lambert Conic projection. Watch out for that “shrinkwrap”
software in perfect conformity with United States Standards.
The Maroc Nord and Maroc Sud zones have an eastern
limit to their Grids that are defined by the 448,000 meter
Easting (X) coordinate of the North African ellipsoidal
Bonne projection. The intersection of this Grid limit with
the graticule was a graphical simplicity but a computational
nightmare until the paper of Karl Rinner was used at AMS. In
the 1930’s, Professor Rinner published a paper (in German)
detailing his development of the formulae for the ellipsoidal
Bonne projection in series form. AMS developed a reversion
of his series, and computational algorithms were developed
for the North African Bonne in Morocco among other places.
In the past 50 years or so, a couple of other places on the
Atlantic coast have been rumored to be datums in Morocco.
Those places are Modagor and Sidi Ifni. Neither of these are
datums; rather, they are local Grids based on the Réguliere
Datum of 1922. In particular, the Sud d’Ifni 1955 Hatt Azi-
muthal Equidistant Grid is defined at the origin point (Camp
monument at Maison Guizol) where: (
f
o
) = 29° 02´ 06˝ North,
the Central Meridian (
l
o
) = 10° 30´ 06˝ West of Greenwich, and
the Scale Factor at Origin (m
o
) = 1.0. The False Origin is 50
kilometers each for Eastings and Northings. The orientation
of the Grid is defined to “Fourmi” as: α
g
= 40° 19´ 47˝ . The
Mogador 1957 Lambert Grid origin is: (
f
o
) = 31° 30´ North,
the Central Meridian (
l
o
) = 10° 00´ West of Greenwich, and
the Scale Factor at Origin (m
o
) = 0.999932968. The False
Origin is 200 kilometers each for Eastings and Northings.
In 1921, the position of Mogador Mat on the Reconnaissance
Triangulation was:
f
= 31° 30´ 36.7˝ North,
l
= 9° 46´ 31.2˝
West of Greenwich. The same point on the Réguliere Datum
of 1922 is:
f
= 31° 30´ 13.178˝ North,
l
= 9° 46´ 23.643˝ West
of Greenwich. The Mosque d’Agadir has also been recomputed
on the Réguliere Datum of 1922 as:
f
= 30° 25´ 54.785˝ North,
l
= 9° 37´ 36.811˝ West of Greenwich.
