Before the advent of xenon lamps, the most intense electric light source was the carbon arc and these were universally used for cinema projectors, studio lights and searchlights. Carbon arcs work by vaporising carbon (and other elements) from a solid rod and passing current through the vapour to form a plasma. Although they can run on AC, the steadiest and brightest light requires DC at a roughly constant current, with typical projection arcs using between 40 and 120 amps depending on size. The voltage needs to be allowed to vary as this is dependent on the arc length which is under automatic adjustment, usually in the range of 30-60V.
Before the advent of silicon rectifiers, making DC at this range of currents and voltages from the mains was hard work. If the mains were DC, as many were before WW2, the usual solution was a motor-generator, with e.g. a 240V DC motor running from the mains, driving a 100V DC generator. The 100V was then ballasted by a tapped resistance to control the current and absorb the variations in arc voltage. The same method could be used for AC mains, but from the mid 1930s a more popular solution was the mercury-arc rectifier (see my avatar) as these are silent and maintenance-free. Metal rectifiers and oxide-cathode rectifiers were also sometimes used.
All cinemas had at least two projectors, sometimes more, plus Brenographs, followspots etc in cine-variety venues. Where there were many arcs to power, a typical setup would have two rectifiers feeding a common 110V DC bus with separate control resistances for each arc. Arc resistances were often placed outside the projection booth and remote controlled, due to the amount of heat dissipated. Alternatively, if the mains were AC and only two projectors needed supply, a more efficient method was to equip each with its own rectifier and do the ballasting with a tapped choke on the AC primary side, avoiding any resistive loss. In both the above setups, you would have an arc control of some kind next to the projector or mounted on the pedestal or lamphouse shelf. There would be current control (sometimes coarse and fine,) voltmeter and ammeter, and then on the DC main circuit a DP isolator to ensure the arc was completely isolated for re-carboning.
Your arc control panel is for the 'No.1 arc" i.e. the arc on No.1 projector, and looks like a Hewittic unit. That would confirm it to have been the remote for a mercury-arc rectifier. Very few survive now; many were broken for their mercury when it was valuable (it isn't any more) and later they were removed due to the increased concern about hazardous spillage if broken.
Operational carbon-arcs are scarce now too and carbons are hard to find. Only one or two manufacturers will still make illumination carbons (as opposed to brazing or cutting) and then only to order. I have a stock that I have hoarded so I still occasionally burn arcs for fun. Yeah, video, I know...
