Fine focus is controlled using the large thumbscrew located on the left side of the box (arrow, Right). Turning the thumbscrew rotates horizontal shaft A. This shaft has two machined worm gears (arrows, Left) that engage with and cause the rotation of vertical shafts (B). The rotation of these two shafts causes the up or down movement of a massive crossmember, which in turn is fixed to the microscope support pillar (C). The fine thread pitch of these two shafts allows for a very fine focus movement.
This is the mechanism that Alfred Nachet described as "...rare, particularly remarkable and resembles the mechanisms used in modern microscopes. It is the only instrument to our knowledge with such a perfect fine adjustment."
Fine focus control knob