ease nature

   obsolete

   to urinate or defecate

   The allusion is to the subsequent relief.

   Also as ease yourself, ease your bladder (of urination), and ease your bowels (of defecation):

    Desecration seems to have horrified royalist commentators more than iconoclasm: soldiers stabling horses in the nave of St Paul's Cathedral, and other places, setting hounds to hunt cats in the aisles of Lichfield, resorting to other churches to 'ease nature', using stone altars as chopping blocks for meat, dressing up in priests' or bishops' vestments, and brazenly smoking, drinking and swearing inside the sacred space of churches. (Gentles, 1992 — it happened during a civil war, not a soccer tournament)

    One man I knew used to swear that he only eased his [bladder] once a month. (F. Richards, 1936)

    I had dismounted to... try to ease my wind-gripped bowels. (Fraser, 1973)

   A chapel of ease² or house² of ease was a lavatory.