In Old England, the naval recruiters used to buy men booze in bars. When the poor man finished his drink he would see a shilling (or some coin). This was seen by the government as payment from the navy to the man and the man would be automatically enlisted in the navy. British Naval service was absolute hell for most people, and the defection rate was high (even though the penalty for running was death for treason). Because of this, people started making mugs with glass bottoms so that one could check the bottom of his glass to be sure they were not being duped into naval service. This tradition has stuck - When I graduated from high-school I received a glass bottomed mug.
Thats where the glass bottomed mug came from.