Explanation: breast (1), chimney breast . A projection of a wall into a room containing the flue ...
(2) The wall under a window sill, down to the floor
[Scott/Penguin Dict. of Building]
breast. 1. A projecting part of a wall, as at a chimney. 2. That portion of wall between the floor and the window above ...
[Dict. of Architecture & Constrution, ed. Cyril M Harris, McGHill]
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I allege it should be aLLège.
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Both dictionaries quoted concur that an apron wall, aka spandrel wall, is the portion of wall between the top of one window and the bottom of the window above, i.e. potentially rather deeper than a breast wall.