These were a variation of the usual auction where the highest bid wins. A nail or pin was placed in the candle near to the bottom, then it was set alight. The auction continued, the person making a bid when the melted wax allowed the nail to drop out of the candle won the bid! Such events were well know in16th and 17th century England and are mentioned in the House of Lords records and in Samuel Pepys diaries.
In 1662 the Admiralty auctioned 2 ships via 'auction by 'inch of candle.'
Occasionally such auctions are still held today. On December the 13th in 2010 Aldermarston Parish Church in Berkshire auctioned the rental of a piece of land by this method.
In Lincolnshire at Old Bolingbroke the grazing rights to land known as 'Poor Folks Close' are also sold this way around the 21st of December.