It's difficult to believe that these are tube micrometers, given all the additional widgets and doodads in the boxes. It doesn't appear in a 1935 M&W catalogue, but I don't think the cat included the more specialised metrology equipment. It does, however, include a common-pattern tube mic., like a standard-framed one, but with a ball-ended anvil, No. 925.
I'd suggest that the mic. is intended for direct radius, rather than diameter, measurement (or, more correctly, comparison), and eccentricity measurement, on things like gears, cam discs, lobed 'wheels' with an odd number of lobes, etc., especially if the various doodads can be put in place of the anvil (or over it?), to fit different sized bores.
Interesting bit of kit. Let's hope someone can provide an evidence-based identification.