What is Ad Filum Aquae?

Legal Definition
To the thread of the water; to the central line or middle of the stream. Usque ad fllum aquae, as far as the thread of the stream. Bract, fol. 208b; 235a. A phrase of frequent occurrence in modern law; of which ad medium fllum a quae (q. v.) is another form.
-- Black's Law Dictionary
Legal Definition
To the thread or center of the stream.
-- Ballentine's Law Dictionary