I don't have any official documents saying so but I have concluded with the 10" and 12" that each size (swing) shared the same serial number pool regardless of bed length. This makes sense for a number of reasons, not the least of which would be the significantly increased difficulty of keeping up with the various pools were it not so.
The other thing that does support it with written documentation is MMB5 on the Atlas mill. There were chronologically four models, base, A, B, and C. And as a corollary to the different length beds, there were the M1, which had manual lead screw cross feed, the MF which had power cross feed (but like the 10F, you could also run it manually, and the MH, which had lever operated cross feed and table lift. In the parts manual, it give the transition serial numbers between the base, A, B and C models. Notes at the tops of each page in the manual give the transition serial numbers for each model letter.
Plus in all of the years that I have been accumulating serial numbers for the lathes, I have never seen the same serial number used twice on the same swing lathe (6", 9", 10" or 12"). But there are two cases where different swing or size lathes have the same serial number.
And yes, I would assume that your lathe was the 516th Atlas 6" off the line. Based on the highest reported serial number, we have tentatively concluded that about 28000 612's and 618's were made. Or an average of 800 per year. We have no idea what actual [production was in any given year and don't know whether initial sales were very good or started off slow. But it is probably safe to conclude that #416 was made late in 1937 or very early in 1938.
Also, the first catalog in which the 6" appeared was probably issued in mid-1937. It shows a countershaft assembly that hung off the rear of the bed. But I would have guessed from that one photo that the countershaft hanger assembly wasn't as far away from the bed as your's is. But I could be wrong.
