This looks like a very nicely preserved example of a Ward Leonard "Vitrohm" dimmer. These guys were very widely used in theatrical stage lighting practice (and elsewhere, of course) beginning in about the mid 1920's. In smaller installations, they would be outfitted as this one is, and simply be mounted on the surface of a wall, usually with a piece of asbestos behind it - you could fry bacon on these things when they were properly loaded and had its resistance in the circuit. In larger installations, these dimmers would be mounted sideways in a steel frame, usually in one or two rows along the top of a switchboard in order to dissipate heat and protect workers from the live parts (even though early switchboards typically had dozens of exposed knife switches within too-easy reach)
. In place of the handle shown, a rack and pinion gear connected to an extension rod and a vertical pivoting handle would be used to move the contact arm to impose the proper resistance. In some installations, the smaller handles could be interlocked together and be moved in unison with one large handle (or with a worm gear and crank handle affair on very large boards). These dimmers were made typically in 250, 500, 1000, 2000, and 5000 watt varieties. Loading them below their maximum rating meant that the lamp(s) could not be dimmed completely out (unless a "phantom load" was connected somewhere to fill it out). Loading them above their rating created the risk of burning out the resistance elements in the dimmer. These dimmers were rapidly replaced when autotransformer dimmers (built in the same general physical style and capable of dimming any size load up to its maximum capacity with virtually no heat) were developed.
It's kinda interesting to note that, as late as the mid 1970's these resistance dimmers were still in use by touring production companies. The dimmers were arranged along with knife switches, fuses and receptacles in large sheet-metal lined boxes referred to as "piano boards" (owing to the size of the box which resembled a shipping crate for an upright piano). I remember having to hook three of these boards up to power sources (called "company switches" in theatrical parlance) backstage at the old Music Hall in Houston when I was working with the IATSE in 1975.
You have quite a valuable find there...