I meant to comment earlier that the assembly that sits at the right end of the bed is called the tailstock. And if it ever does show any side to-side movement, it has an adjustable gib. The gib is adjusted by tightening two slotted head screws located down in-between the ways next to the front surface of the rear way. After many years of inactivity, the gib may be stuck to the bottom of the tailstock. The gib is attached to the bottom of the tailstock base by two round head screws. To get at it, loosen the tailstock clamp and slide the tailstock off of the right end of the ways.
We don't have a manual on the 936 but the one on the Master Craftsman version is in Downloads. The two models are identical except for badges and the left and right legs. The guy at Sears responsible for the legs being different didn't retire until the early 50's. After that, both badges used the same part number legs.
Note that access to Downloads requires Donor status. )Any level)
Also, I meant to comment on the belts (the how to use them is adequately explained in the manual). The Atlas Compound Drive models have no back gears (which on the 10" and most later Atlas-built lathes are used to reduce the spindle RPM but which are more expensive and a little noisy). Back gears are so named because in the beginning, all manufacturers put them on the back of the headstock. Later lathes usually have them mounted underneath the spindle. But the name stuck.