# Modifying Mercator projection in ArcMap?

I have a shapefile which is consistently drawing in the wrong place. Luckily I was given some information about it and am now wondering how to get the shapefile properly projected and drawn.

What I know:

1. It is in Mercator
2. The latitude and longitude of origin are 33 and 60 degrees, respectively
3. The scale factor is 1.15
4. There is no false easting or northing.

I am a bit confused because I can't seem to modify these parameters in various Mercator projections through ArcMap. I can usually only modify one or two of them (ex: scale factor and central meridian or only central meridian, etc).

What process do I need to go through to get this shapefile projected correctly and drawing in the right place?

What I've tried:

1. Creating a new projected coordinate system in Data Frame properties. Took projection "Mercator_Variant_A" and entered in the above central meridian (60) and scale factor (1.15). I then projected the .shp into this projection. Results: draws in the same incorrect place.
2. Assuming the projection of the .shp is wrong, I deleted the .prj file for my .shp, then used "Define Projection" to this same new projection defined from "Mercator_Variant_A". Results: draws in the same incorrect place.
• Where are the y values zero? At 33N? Or at the equator? Because Variant A assumes the latitude of origin is at the equator. Variant C allows you to set the latitude of origin but uses a standard parallel rather than a scale factor. What happens if you use the regular Mercator, standard parallel 1 = 33, central meridian = 60 (ignore the scale factor). BTW, what's the GeoCRS (datum/ellipsoid/anything?)? May 5, 2017 at 21:09
• @mkennedy the geographic coordinate system is GCS_WGS_1984. thank you--trying your suggestion now, will update. I am not sure where the y values are zero May 5, 2017 at 21:14
• @mkennedy, that worked splendidly. You rock, thank you! May 5, 2017 at 21:53
• The scale factor might be the value at the equator, given standard parallels at +/-33, but I haven't confirmed that. Glad to hear it worked! May 5, 2017 at 22:00
• Yes, I think it is-- approximately 1/cos(33). May 7, 2017 at 18:40

## 1 Answer

Mercator (called Variant B in EPSG terminology) and Mercator Variant A assume the latitude of origin is at the equator. Variant C allows you to set the latitude of origin but uses a standard parallel rather than a scale factor.

Try using the regular Mercator and set the standard parallel 1 = 33, central meridian = 60 (ignore the scale factor).

I am speculating that the scale factor is the scaling at the equator, given standard parallels at +/-33 latitudes.