Back gears on a "cone drive" lathe headstock work as follows:
There should be a pin or other means of locking the bull gear (large gear, immediately behind the "front" headstock bearing) to the cone pulley on the lathe spindle.
The bull gear is keyed to the lathe spindle and is the means by which the lathe spindle is driven. The bull gear turns with the spindle at all times.
On the small (tail) end of the cone pulley, there will be a smaller pinion gear. This gear is keyed to the cone pulley and turns with the cone pulley at all times.
When the locking pin is "in", it "ties" the bull gear to the cone pulley. The result is whatever speed the cone pulley is turning at, is the spindle speed. The lathe is said to be in "direct" drive.
If you were to engage the back gears with the locking pin "in", the result is the spindle of the lathe "locks up". This is actually a means of locking the lathe spindle in position for mounting/dismounting chucks if the spindle has a threaded nose rather than a "long taper" or "cam lock".
If the locking pin were pulled out (or what ever other means is on the Walcott lathe is used) so the bull gear is disconnected from the cone pulley, you will find the cone pulley spins freely on the lathe spindle and does not drive the spindle.
If you then engage the back gears with the locking pin "out", you will find that the cone pulley drives the spindle through the back gearing. The small pinion on the cone pulley (at the end with the smallest step) will engage the bull gear on the back gear shaft. The back gear shaft has a pinion at the front end, and this will engage the bull gear on the spindle simultaneously. The result is quite a deep reduction in spindle speed with a corresponding increase in spindle torque.
While the lathe may only have one back gear shaft, the actual gearing accomplishes a "double reduction" by going from the cone pulley pinion into the back gear shaft's bull gear, and from the back gear shaft's pinion into the spindle bull gear. It is a little hard to visualize sometimes, but the result is the cone pulley will be turning as fast as it ever did, whether in back gear or "direct" drive. In back gears, the cone pulley will be turning at whatever rpm the belt is set to drive it, but the spindle will be turning within the cone pulley at a much lower rpm.
Look at the cone pulley steps carefully- there may be what look like set screws tapped into the first and last steps of the cone pulley. These are actually for oiling the bronze liner bushing in the hub of the cone pulley. Similarly, if you look at the back gear shaft, it is hollow, with the pinion and bull gear either cast integrally, or keyed and shrunk onto the hollow shaft. Looking at the back gear shaft, you should find another "set screw" or some similar means of getting oil into that hollow shaft. The hollow back gear shaft turns on the stationary back gear shaft. When you go to shift the back gear in or out of engagement with the gears on the cone pulley and spindle, the stationary shaft is keyed to eccentrics at either end. These eccentrics turn in bores in the back gear shaft brackets- which are usually cast integrally with the headstock on most lathes of this type. The eccentrics are keyed to the stationary shaft, one eccentric having the back gear lever on it.
In short, you engage the back gears with the pin "in" to lock the lathe spindle. You engage the back gears with the pin "out" to put the lathe "in back gear" for running at a lower range of spindle speeds. Never attempt to engage or disengage the back gear for any reason with the spindle and cone pulley turning. Engaging the back gear with the lathe stopped, you may have to rock the spindle slightly to get the gears to go into mesh.
