Yes, the letter B means second edition; Simon and Schuster published the earliest Little Golden Books, so you know you've got a real LGB oldie! I don't know if this title is really rare; if you check findbookprices.com, they show three first editions on Amazon and/or Abebooks for sale. Findbookprices.com usually only shows what's for sale on Amazon and Abebooks; there's tons of other sites.
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I have a book BABY ANIMALS by Garth Williams says on inside cover, Copyright 1956, 1952 by Simon and Schuster. I finally found the letter "B" in the inside of the spine by the back page....is this the second edition? I am assuming it is. Of the websites i have viewed, this seems to be the oldest copy i can find on the net. Does that mean its rare???