E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
Rum and water, cold without. Admiral Vernon was called Old Grog by his sailors because he was accustomed to walk the deck in rough weather in a grogram cloak. As he was the first to serve water in the rum on board ship, the mixture went by the name of grog. Six-water grog is one part rum to six parts of water. Grog, in common parlance, is any mixture of spirits and water, either hot or cold.