to eat into

Webster's Dictionary (GCIDE)

1.To take food; to feed; especially, to take solid, in distinction from liquid, food; to board. [1913 Webster]

He did eat continually at the king's table.— 2 Sam. ix. 13.[1913 Webster]

2.To taste or relish; as, it eats like tender beef. [1913 Webster]

3.To make one's way slowly. [1913 Webster]

To eat, To eat in or To eat into, to make way by corrosion; to gnaw; to consume. "A sword laid by, which eats into itself." --Byron.

To eat to windward (Naut.), to keep the course when closehauled with but little steering; -- said of a vessel. [1913 Webster]