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I have two datasets in ArcGIS Desktop. One is from the Ordnance Survey (UK National Mapping Agency) and, when I view the properties of the dataset it says that the Spatial Reference is

OSGB_1936_British_National_Grid

I want to set another file to the same spatial reference. I know I can use the Import function to import it from the first file, but how would I select this coordinate system from the built-in ArcGIS ones? I can find British National Grid under Projected/National Grids/Europe and I can find OSGB 1936 under Geographic/Europe, but I can't seem to find the combination of the two anywhere?

I'm not hugely experienced with coordinate systems, but I think that BNG is the co-ordinate system, and OSGB 1936 is the datum. Is that correct?

I know that when I select spatial references in ENVI I can choose a coordinate system of United Kingdom and a Datum of OSGB1936. Is there a way to do this in ArcGIS Desktop?

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In ArcGIS 10, if you go into, for example the Data Frame Properties, and go to the "Predefined" co-ordinate systems, you can click on two co-ordinate systems you mentioned in the question - OSGB 1936, and British National Grid, if you click "Modify" on both you will see that they actually both use the OSGB 1936 Datum (click on "Modify" again on BNG to see the Datum).

You probably want to use the British National Grid Co-ordinate system, because it is the basis of all Ordnance Survey Grid references- basically the projection is a set of mathmatical formulae that maps real world positions onto the co-ordinate system that is used in the UK. Not entirely sure what the OSGB_1936 co-ordinate system would be, but the major difference between a geographic and projected co-ordinate system is that:

"Unlike a geographic coordinate system, a projected coordinate system has constant lengths, angles, and areas across the two dimensions" (ArcGIS 10 Help File).

This obviously makes it much more useful for precision applications such as plans, although this accuracy will generally only be high over a relatively small area compared to a geographic co-ordinate system, which is suitable for describing a point with (relative) accuracy over the whole earth's surface.

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    The "file names" that you see when browsing the predefined coordinate reference systems don't always match the internal coordinate reference system name, thus the discontinuity. Each projected coordinate reference system contains a geographic coordsys as part of its definition.
    – mkennedy
    Commented Nov 9, 2011 at 20:34
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Define Projection (Data Management)

This tool overwrites the coordinate system information (map projection and datum) stored with a dataset. The only use for this tool is for datsets that have an unknown or incorrect coordinate system defined.

All geographic datasets have a coordinate system that is used throughout ArcGIS to display, measure, and transform geographic data. If the coordinate system for a dataset is unknown or incorrect, you can use this tool to specify the correct coordinate system. You must know the correct coordinate system of the dataset before using this tool.

http://help.arcgis.com/en/arcgisdesktop/10.0/help/index.html#//001700000077000000

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