Bill,
The first thing that you need to get is an intuitive understanding of the fact that when dealing with spur gear trains, if there are no compound gears in the train, the only two gears that matter are the first and last. It's easier to explain on a change gear lathe as all of the gears including the screw gear are visible. The first gear in the train on an Atlas is the 32T spindle gear. It always runs at the spindle RPM regardless of whether the lathe is in direct or back gear drive. The screw gear is the one that is actually on the lead screw. I don't know (although if I had to I could calculate them) what the ratios through the gear box are. But we do know that the slowest feed through the box yields .0042" per revolution of the spindle. In the standard setup of the gear train on all of the Atlas lathes with QCGB's, you have a 32T spindle gear driving a gear on the tumbler. On the Commercial 12" lathes, both tumbler gears are 36T. On the earlier 12" the tumbler gears were a 24T and a 20T. One or the other of the two tumbler gears drives the 32T half of a a 32T/16T compound gear. If you assume say 1 RPM spindle speed and calculate the RPM of the 32T/16T compound stud gear with the 32T gear being driven, you will find that it is also running at 1 RPM regardless of whether the intermediate gear is 36T, 24T or 20T. Stick some more gears in between and if you do the calculation properly, you will also get 1 RPM regardless of the number of gears (or their tooth count) in the train. The only thing that might be different is that for an even number of gears, the output will rotate in the opposite direction of the spindle . And for an odd number, the same direction.
Run through the calculations three or four times for different tooth counts or gear counts and you will grasp the fact that the intermediate gear tooth counts don't matter.
Now introduce the compound gear. This is two gears on the same shaft tied together. When you introduce an intermediate compound gear, you change things by the inverse ratio of the driven gear of the compound to the driving gear. The 32T is driven by one of the tumbler gears so it will run at spindle RPM since the tumbler gears are driven by a 32T spindle gear. The 16T gear of the compound will also run at spindle RPM but at half of the teeth per revolution. So the 40T gear being driven by the 16T gear will run at half of the speed that it would run at if it were driven by the 32T compound gear, or 16/40 instead of 32/40.
The overall ratio from 32T spindle gear to 48T gear in the normal OUT setting is 32/36 x 36/32 x 16/40 x 40/48, or 0.3333. Just figuring for input gear teeth over output gear teeth times compound output over compound input, 32/48 x 16/32 = 0.3333. That's the standard setup, with the gearbox further reducing it.
From your description, the 40T idler sliding gear is converted to a 40T/20T compound gear. With the 40T being driven by the 16T of the 32T/16T compound gear and the 20T driving the inner 48T, that would reduce the output (48T) gear RPM by 2:1, giving you an 0.0021" per spindle revolution carriage feed and reducing the cross-feed rate by 1/2.. You should find a keyed spacer to replace the outer 48T gear. Or another 20T gear might clear the 40T. Else the inner one will obey Murphy's Law and do its best to chew up the 40T gear. Also, the threading chart will be off by a factor of 2:1.So to get 16 TPI, you would need to set it to 8.
It's late, and I hope that I didn't make any typos. I'll check it again in the morning to be sure.
