Hi,All.
It's an interesting problem, and I'd like to see one of the F marked ones, which might help. One sold on Ebay, but too long ago for the pictures to still be there.
Here's some of my thoughts. To me, S for States seems unlikely. Why do that when it's just as easy to stamp 'Made in USA' or even 'USA'. The English do call the USA "The States', but that is never abbreviated as such.
For the same reason, I have my doubts that they would abbreviate "Sears Roebuck" as S, since it should be SR. Sturmey-Archer even abbreviate their own name as SA, and their's is hyphenated.
A clue could be that the typeface for the S is very different to the typeface used for the rest of the hub. Compare the S with the S in Sturmey-Archer. The S has serifs and Sturmey-Archer does not. This makes me think it is a specific reference to a company who uses a seriphed S at the start of their name. Looking at early Sears catalogues, they seem to have changed the script for their name often,.so, again, I don't think it's them. That said, here is an example of their letterhead with a similar S.
https://upload.wikimedia.org/wikipedia/commons/3/3b/Sears,_Robuck_&_Co._letterhead_1907.jpg
But then again, it's not too unusual, see this picture of a Singer sewing machine:
http://www.sewmuse.co.uk/singer 66 99.htm
Best Regards,
Adrian
PS, more on the history of King sewing machines (I tried to trace a link with Singer, but failed) here.
http://needlebar.org/main/makers/usa/histories/king/index.html