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I created two different MXDs, one for City of Tucson and another for US States. If you click on the ArcGIS.com Map link above (in the services page), you will see that City of Tucson Layer is overlaid on the basemap properly but the US States is projected somewhere in the ocean. I know this is a projection issue but if you look at the metadata in the services link, both are showing Spatial Reference: 102100 (3857).
Now the projection of the City of Tucson is NAD_1983_HARN_StatePlane_Arizona_Central_FIPS_0202_Feet_Intl in the ArcMap and the US States is WGS_1984_Web_Mercator_Auxiliary_Sphere in ArcMap. I tried to change the projection to WGS84 but the layer is still not projected properly.
How can I correct it? By "correct it" I mean that the projection should be like City of Tucson where it is projected properly over the basemap in ArcGIS.com.
You should leave your data in its own coordinate system. Then set the DATA FRAME properties to Web Merc aux sphere and refresh your service. (You should also clear your REST cache after changing a service)
WGS_1984_Web_Mercator_Auxiliary_Sphere
Projection: Mercator_Auxiliary_Sphere
False_Easting: 0.000000
False_Northing: 0.000000
Central_Meridian: 0.000000
Standard_Parallel_1: 0.000000
Auxiliary_Sphere_Type: 0.000000
Linear Unit: Meter
GCS_WGS_1984
Datum: D_WGS_1984
I just checked the data frame properties and it is already Web Merc Aux Sphere,
Also how do I clear the REST Cache? I found this link for clearing REST Cache but it seems that I need to Generate Admin Token. Is that the right process?
http://server/arcgis/rest/admin/
or in your case
http://msgist2011.grd.arizona.edu/ArcGIS/rest/admin/
log in, clear cache, clear cache now.
Looking at your States map service, the spatial reference is web mercator, but the coordinate bounds look like geographic (latitude and longitude, probably WGS84) coordinates.
Did you use Define Projection to set your data's projection to web mercator? Define projection doesn't actually reproject data, it only changes a dataset's metadata. If you did do this, I would run your layers back through Define Projection and specify WGS84. You can leave your data frame set to web mercator or set it to WGS84. In either case, re-publish your service. ArcGIS Server will take care of re-projecting your data on the fly when you use it as an ArcGISDynamicMapServiceLayer or when you use it in a webmap on ArcGIS.com.