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[Larry_S]

Hi,

I'm working with early USGS 'Geologic Atlas of the United States' folios that I believe where drafted using the USGS's historical Polyconic projection with a local parallel and prime meridian. When georeferencing these over to UTM NAD27 I am noticing a misalignment scaling issue east to west.

I am working with:

Darton Oelrichs Folio #85, Page 8 (from 1902)

I computed the corners, in meters, using the equations and tables on pages 129-133 (with examples starting on 304) from the USGS Professional Paper 1395, "Map Projections - A Working Manual"

http://pubs.er.usgs....spubs/pp/pp1395

Then cross-referenced these against GDAL's gdaltransform and Proj's cs2cs (same result) using the following for the GCP's and map's projection:

Where gdaltransform and cs2cs calculate...
GCPs (e.g. solving for y,x SE corner of 43,-103 in deg): +proj=longlat +ellps=clrk66 +no_defs
to
Local Polyconic Projection: +proj=poly +lat_0=43 +lon_0=-103.25 +x_0=0 +y_0=0 +ellps=clrk66 +units=m +no_defs
(Proj definition based off of GeoTIFF Definition)
results with y=20385.786913m, x=30.331823m

With the equations from the USGS Manual I get a practically identical result: y=20385.7869228 x=30.3318229278


However, once GCPs are embedded and the file reprojected to UTM 13N NAD27 and placed next to modern geologic quads, there is a noticable east-west shift of up to 600 meters of the map's content, even though the actual corners register perfectly. North-south content it is pretty close. The east-west offset is not linear, changing in scale, with the error becoming larger the further away from central meridian. So I am guessing this is an issue with whatever reference datum the map was based on (or lack thereof).

Does anyone have experience with georeferencing these types of historical USGS maps, or what datum was used? I realize the Polyconic projection is not conformal, but there must be some method the USGS back then to come up with the placement of the initial parallels and meridians.

Side Note: Why does the PROJ.4 definition for Polyconic start with '+proj=stere' as noted on the GeoTFF page?

Thanks,

Larry