As joiner and lecturer:
You have never taught English, it is sill and sill is not American at all. In many other countries also making the use of English it would be called a window ledge. My God call yourself English and cannot even speak or spell your own language. The well spoken American will have a high command of the English language contrary to what we might believe here.
Foolish comment, Smithie; and where is the punctuation point after "My God"? Also, after "lecturer" it should be a semi-colon. The whole post should be revised for grammar too.
British English - can be cill or sill.
American English - sill.
I believe that the earliest use of the word predates the Norman conquest with "sylle" - this became "sill" but in the 1800's "cill" began to appear as an alternative - now both are acceptable but by far the most used, especially since Worldwide (i.e. non-British) English has gained in popularity is sill.
Bit like Waggon or Wagon - both acceptable.