This is the device to which you are referring :
Science Museum - Home - Maddox wing test instrument, c 1920-1937.
It's called a MADDOX WING (presumably after a Mr or Dr Maddox, but no other information ). I have one here, but it's rarely used nowadays.
I didn't realise, though, that it was old enough to be a museum exhibit !
In simple terms it checks eye-muscle balance. Very few people have two eyes aimed in EXACTLY the same direction at all times. But once the brain realises that the image reaching each eye is nearly the same it can automatically compensate by adjusting the aim so that the two images are fused. Otherwise there would be double-vision (diplopia). If the misalignment of the eyes is severe, then it's visible to others, and is known as a squint (strabismus). This device is intended to pick up degrees of misalignment much less than the obviously visible squint. Misalignment is the horizontal plane is known as exophoria or esophoria, and in the vertical plane is known as hyperphoria.
The way it works is simplicity itself. As explained above, if the images reaching each eye are similar then the brain can fuse them. This device, by the use of the screens between the eyepieces and the far end plate, just gives each eye something completely different to see.
Then the brain will not attempt to fuse them. Thus, if the white arrow is seen to be pointing at the white zero, then the person is orthophoric. If the white arrow is seen to point at the white six, then the person is mildly exophoric.
Very old technology, really !
Hope that helps ! Best wishes.