Generically, that's an dividing head (or indexer), with built-in provision for varying the worm gear ratio through a change gear set, mounted on a cross slide. The mounted-on-a-cross-slide strongly suggests it is part of some specific larger machine, and not a general accessory for a milling machine (for example).
If I had to guess what it's "off of", maybe a tool grinder of some sort? Perhaps a reamer flute grinder?
Added in edit: the currently unoccupied clamping bore is almost certainly for an overarm which would carry a bracket for either a dead center (most likely) or an indexing finger (much less likely). So this gizmo was intended for a grinding or machining operation, and not for measurement/inspection.
And a question for you, Mel in WA: Does the slide leadscrew interact with the worm wheel at all? I'm guessing not, but if it does, it would yield helical flutes in a tool-making application.