the.com/brim

the edge where full becomes too much, holding its breath before the spill

means The brim is the topmost edge or rim of a container, or the projecting edge of a hat — and as a verb, to be filled right up to that edge.

from From Middle English 'brim' or 'brimme,' meaning an edge or border, especially of water — a shore or bank. Its deeper roots are uncertain, but it's likely related to a Germanic family of words for edge and rim; some link it to an old sense of 'surge' or 'roaring water,' fitting for a word that lives where the liquid reaches its limit. The hat-brim sense came later, borrowing the same idea of an edge that juts out.

hat anatomy
The brim shades eyes and sheds rain off the face
old roots
From a word meaning edge or border of water
verb mode
To brim is to fill to overflowing
liquid limit
Surface tension lets water brim above a glass rim
for instance

hat brim — the edge of a hat that projects outward, measured in inches from crown to edge

cup brim — the rim of a drinking vessel, typically filled to the brim at restaurants

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