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Filling a Mikvah from the Faucet

I read a book by Rabbi David Miller (1869 – 1939) ( he had semicha from Rabbi Isaac Elchanan of Kovno ) , The Secret of the Jew, which says you can fill an empty mikveh straight from a faucet (see pages 366 and 428). There is a copy of the book on Hebrew Books.

Are there opinions that argue on Rabbi Miller? Who are they, and what is the basis of their disagreement?