1) Mechanical device for moving water.
The OED has examples of this word from c.1440, long after pumps are known to have been in existence. They were being used at sea, for example, to pump out bilge water, and a ship in the Humber estuary in 1528 had a newe sofe for the pompe listed in its gear. They were also employed in coal-mines, and Salzmann noted that a pump worked by horse power was raising water from a pit as early as 1486. However, the first Yorkshire evidence for such a pump dates only from the seventeenth century: c.1640 All 96 yeards left to be recovered by drawing water only 14 or 15 y[ard]e: which was the length of the old Pumpe and as the Ginn was first made by my father, Barnbow. Note: 1617 a pumpe wimble that lyeth in the hall end and bitts therto belonging, Ripley.
2) A kind of light shoe.
1614 a payre of new ... stockings promised, a payre of pumpes and some ould clothes, Brandsby
1750 the pumps he had upon his feet, Wetherby
1770 Benjamin Pumps heelespecht, Meltham.