The meaning of By And By in the Bible
(From International Standard Bible Encyclopedia)

In the sense of "immediately" is the King James Version translation of exautes, of Mark 6:25 (the American Standard Revised Version "forthwith"); of euthus, Matthew 13:21 (the American Standard Revised Version "straightway"); of eutheos, Luke 17:7 (the American Standard Revised Version "straightway"); Luke 21:9 (the American Standard Revised Version "immediately"). In English literally this meaning is obsolete (compare: "After you have dyned and supte, laboure not by and by after, but make a pause—the space of an howre or more with some pastyme" (Babees Book, EETS, 247).

See more on the meaning of By And By in the Bible:
By And By {Easton's Bible Dictionary}

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