All you guys are not old enough. That is the attachment for a "Starrett test indicator". The rectangle end is attached to a height gage and use on a surface plate or flat surface on a machine in some cases. The rod end was attached to the holder on the side of the "test indicator which ws slipped over the body of the indicator.. They (Starrett) have made those things I'm sure since about 1945 or 50. I think they still make them. I have one in my dusty old toolbox.
dickr
...............Another shot of the OP's tool can be found at:
http://watchmaking.weebly.com/uploads/1/1/7/9/1179986/starrett_711_series_dti.pd