Per Lord Esher in Nielsen v Wait (1885) 16 QBD 67 at p.72:
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"Running days" are those days, on which a ship in the ordina course is running. It is true that when they are lay days, they do not take effect under charterparty until the ship has done running; but the parties are describing the days about wh they are talking, namely, days in a port, according to the phraseology which they use with regar to a ship at sea. "Running days" therefore mean the whole of every day when a ship is running.