Problem: Data with Projections of NAD 83 Harn and NAD 27 do not align in the Map
Data sources with coordinate system datums of NAD 83 Harn or NAD 27 do not align in the map.
ArcMap has the ability to project data on the fly. This means that data of different projections will align as long as they are defined correctly. In the case of data with datums that differ from the coordinate system of the data frame, a transformation must be applied to the data.
When projecting data from NAD 27 to NAD 83 Harn it takes a two step transformation to accomplish this. First the data needs to be transformed from NAD 27 to NAD 83 then it needs to be transformed from NAD 83 to NAD 83 Harn.
While the project tool can handle a 2 step transformation the data frame cannot. As a result it is not possible to specify both datum transformations necessary to align the data in the map.
Solution or Workaround
There are two options:
Use the Project tool to project either the data in NAD 27 to NAD 83 or the data in NAD 83 Harn to NAD 27: ArcToolbox > Data Management > Projections and Transformations > Features.
The data frame then applies the appropriate datum transformation to align the data. No transformation is necessary if all the data is projected to the same coordinate system.
Change the Data Frame Coordinate system to NAD 83: View > Data Frame Properties and click the Coordinate System tab. Under 'select a coordinate system' browse to North American Datum 1983 through Predefined > Geographic Coordinate Systems > North American. When working with a projected coordinate system the same solution can apply by using NAD 83 as the datum of the coordinate system.
When the data frame is set to NAD 83 it only needs one transformation to get to NAD 83 Harn and NAD 27.