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Some historical projections, specifically the Max Eckert series (Eckert I-VI) can be successfully defined in the Custom CRS dialog and saved in the Custom CRS database, but are not listed as User Defined Coordinate Systems in the Project Properties-->Coordinate Reference Systems dialog. Hence, while I can define these projections, I can not use them.

My procedure is as follows:
1. Settings-->Custom CRS...
2. Click Star icon in Define section to create a new Custom CRS database entry
3. In Define section: Name = "Eckert I [ESRI:53015]"; Parameters = "+proj=eck1 +lon_0=0 +k=1 +x_0=0 +y_0=0 +a=6371000 +b=6371000 +units=m +no_defs"
4. In Test section: Parameters = "+proj=eck1 +lon_0=0 +k=1 +x_0=0 +y_0=0 +a=6371000 +b=6371000 +units=m +no_defs"
Geographic/WGS84 North = 25 returns Destination CRS result of 2,561,146.4404
Geographic/WGS84 East = 25 returns Destination CRS result of 2,205,431.6570 (i.e., Test succeeds)
5. Click Floppy Disk icon in Define section to save Eckert I projection in Custom CRS database
6. Click OK to exist Custom CRS dialog
7. Settings-->Project Properties-->Coordinate Referenece System (CRS) tab
8. Activate "Enable 'on the fly' CRS transformation'
9. In "Coordinate reference systems of the world" list box, scroll down to "User Defined Coordinate Systems"
10. Find that my custom Eckert I projection is not listed.

I have tried the above procedure with a Van der Grinten projection (+proj=vandg +lon_0=0 +x_0=0 +y_0=0 +R_A +a=6371000 +b=6371000 +units=m +no_defs) and have found that it does show up as a User Defined Coordinate System.
Also, adding a shapefile layer that has been projected to Eckert I projection in other GIS software results in QGIS not recognizing the shapefile's projection.

There was a recent OSGeo changeset to GDAL's OGRSpatialReference that specifically added definitions for these very projections (see http://trac.osgeo.org/gdal/changeset/22786). Perhaps QGIS has not incorporated this changeset?

Using OSgeo4w's command shell, "gdalsrsinfo -V +proj=eck1" returns a successful validation in GDAL version 1.7.3.

I am conducting research with historical maps (hence the need for historical projections), and I need the Eckert I projection to approximate the ancient Trapezoidal projections. I would like to use QGIS for this research, but I cannot because of this bug. Many thanks in advance for your help!