[Proj] What is the meaning of the "Mercator 41" projection in EPSG:3752 ?

[Mikael Rittri]

Hello,
I am trying to understand the meaning of EPSG:3752, 
"WGS 84 / Mercator 41", used around New Zealand. 

I think the EPSG description of the projection is ambiguous:

        Map Projection: Mercator 41
        Projection Method: Mercator(1SP)

        Parameter Name:
        Latitude of natural origin      41° S
        Longitude of natural origin    100° E
        Scale factor at natural origin   1
        False easting                    0 metres
        False northing                   0 metres

Now, this description contradicts the EPSG Guidance Note 7.2 
(http://www.epsg.org/guides/docs/G7-2.pdf), Table 3 on pages 
14 - 15, "Summary of Coordinate Operation Parameters required 
for some Map Projections".  Because Table 3 says that 
"Latitude of natural origin" is indeed the first parameter of
Mercator(1SP), but it should be the equator.  Well, maybe 
Table 3 was meant to say that it is _usually_ the equator,
but that does not help me.  

>From the description of "Mercator 41", I think it is clear 
that the projected point with Easting 0 m and Northing 0 m 
represents the "natural origin" at 100° E, 41° S.

But where on the map is the local scale factor equal to 1 ??? 

Since the scale factor parameter is named "Scale factor at natural origin",
it would seem that the local scale factor is 1 at latitude 41° S 
(also at 41° N), because that's where the natural origin is located. 

On the other hand, if this is the intention, I would have expected 
EPSG to say that the projection method is Mercator(2SP), since it 
has two standard parallels. So, maybe "Scale factor at natural origin"
refers to the equator, after all, despite the inconsistent terminology. 

Does anyone know the truth out there?  A test point should suffice 
to settle the matter (if distinct from 100° E, 41° S).  

Best regards,

--
Mikael Rittri
Carmenta AB
Box 11354
SE-404 28 Göteborg
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mikael.rittri at carmenta.com
www.carmenta.com