^ That's curious, because I just noticed that box is different than the one in the post above it (the set.)
Only in the 1936 ad is the divider at the top of the box - the earlier ads all show the divider more toward the middle.
That is curious, BK. Curious enough for me to go back and do some double-checking.
EDIT: In Catalog No. 231 (1931), there is only an 11-ND set, and the case has the socket tray in the middle.
Both versions of the "N" case are shown in Catalogs No. 235 (1935) and No. 239 (1939). In both catalogs, the smaller midget sets (11-ND, and later 10-ND - no obstruction offset bar) are shown in an "N" case with the socket tray in the middle, and the bigger midget sets (16-ND - offset bar + five (5) DOE wrenches) are shown in an "N" case with the socket tray in the back.
Your ads imply that it was less consistent than the catalogs indicate, though, showing an 11-ND set in each style of the same case "N".
What I find curious are the decals on that eBay box (the first link, with the "set"). The brand decal is from the 1920's up through c. 1938. The set number decal is not. It's rectangular. From the late 1920's to c. 1938, that decal was always a ribbon. In the 1939 catalog they started going to a new decal that incorporated the branding and the set number in a single decal (some boxes still shown with old decals). By 1943, all boxes are shown with the new decal.
My guess is it's late 1938 transitional.