Defining a spatial reference 

Release 9.3
Last modified November 13, 2008 
Print all topics in : "Projections and Transformations toolset" 
A spatial reference is the georeferencing and coordinate system assigned to any geographic data, including raster datasets and raster catalogs. The spatial reference defines how geographic data is mathematically transformed onto a flat map with the least amount of distortion. There will always be some sort of distortion in geographic data since you are trying to project threedimensional data onto a twodimensional plane. When you choose a spatial reference, you must choose which type of distortion you want to minimize.
Many predefined spatial references have already been defined and are available for use. If none of these spatial references represent the projection that is desired, you are able to modify the current projections or create your own. If you want to use the same spatial reference of an existing feature class, feature dataset, or a dataset, you can import that exact spatial reference as well.
Converting from one projection to another can also change the shape and area a cell represents on the surface of the earth. Each projection treats the relationship between a threedimensional world and a twodimensional one differently. You should be aware of the properties and assumptions for each projection before selecting one.
When you display and perform analysis with raster datasets, they should be in the same coordinate space and in the same projection. If two raster datasets are in different coordinate systems, the values of the coordinates are on different scales. Errors will occur when comparing such datasets because they will represent different locations. ArcGIS will apply an onthefly transformation of the input datasets that are in different projections so that the layers can be processed together.