It looks like you have the Model E DeVry Suitcase projector. Those were 1st made in or around 1921. A very popular projector in its time.
Here is a link to a manual for the machine, it has operating and some mechanical adjustments explained in it.
The part you show in your post does look like a rheostat of some kind... 1920s state of the art technology. Page 16 of the manual explains how these rheostats for the motor and light work. You can always check them with a VOM meter to see if the resistance is still working. You'll want to clean the contacts anyway.
A couple of things to warn you about this machine, as it was designed in the late 19teens or 1920, film speed at the time was the 'silent' speed of 16fps. There was no 24fps sound speed yet. So the normal speed would be 16fps and, possibly, the variable speed motor would run up to 24fps. Running the projector slower would give you problems with the fire shutter, if it is still working.
When you get it running, I wouldn't run any valuable or treasured film on it! Don't even think about it. Get some old faded movie trailers or expendable film to experiment with.
DeVry in their manual proudly claims: "Points of Superiority - It is the only Portable Projector -- of fireproof construction and designed on the principle of constituting its own booth." What this means, and looking at the picture of your machine, see that white stuff attached to the interior of the door, and then attached all around the interior of the projector? That is ASBESTOS! While asbestos was probably hailed as a miracle for fire retention back then, we now know the dangers of it. Do you value your lungs?
35mm film back then was the highly inflammable nitrate, so this suitcase would possibly contain any fires should the film jam and catch fire. You no longer need asbestos with the safety film of today.
No parts available. The only way to get parts is through cannibalization of other like machines.