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you are right. my grandfather used such a small version of those as a shaving bag, although I cannot tell whether or not it was specifically sold for such a use. I will see if I can find a photo of...

This thread explains it all http://straightrazorpalace.com/srp-official-group-buys/36795-srp-june-2009-group-buy-vintage-shaving-boxes.html

Lather up and shave. If it tugs (assuming you lather work and shave technique is adequate), then it still needs more work on hones and/or strops

Keep shave testing until the razor lets those...

Inox = stainless (inoxidable)

4k/8k Norton is a great combination if you are going to use Nortons to hone your razors, inox or otherwise