In the days of sailing ships, merchant seamen were often given an advance on their first month's wages in order to purchase clothing and other essentials before a long voyage. Then for the first month they received no wages. They were said to be "working a dead horse," meaning they were working for no pay. After the month was over, a piece of canvas cut into the shape of a horse was hoisted up into the rigging to signify that from that day forward all seamen would be receiving wages. Beating a dead horse means to do something for nothing.
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