The issue at stake in the translation of Luke 24:21 is whether the text identifies the day on which the words were uttered as the "third day" or on the other hand whether the text says that the third day had just passed. If the text identifies the day on which the words were spoken as "this third day," then then it will agree perfectly with the Friday to Sunday Chronology, and it will contradict all other chronologies.    

    But if the words are spoken when the third day has just passed a Friday to Sunday Chronology will be contradicted, and not only a Friday chronology will be contradicted by this second case.  Also any chronology placing the crucifixion on a Wednesday and the resurrection late on the Sabbath will be contradicted. The only chronologies that can survive in this case are Wednesday to Sabbath dawn, and Thursday to Sunday dawn chronologies. We already know that the resurrection was on the "Later of the Sabbaths" (Mat. 28:1), and therefore the Thursday to Sunday view is refuted.
    The current critical text of the NT says "this day." The Byzantine text says "this day" and then adds the word "today." Codex Bezae, the Syriac (Aramaic), and other witnesses contradict both the current critical text and the Byzantine text.
    Codex Bezae reads "a third day passes by" which is to say a third day has just passed by at dawn on the Sabbath. Codex Bezae is also correct in its reading of Luke 23:54, where it omitts the impossible word "dawning." Here too Codex Bezae (D 05) is correct.  It makes no sense to complain about the third day being gone unless the third day actually is completely gone. If the day they were speaking on was "this third day", then they would have to wait to the end of it before claiming that the prophecy was unfulfilled. Luke 24:21 begins, "we had hoped..." and then the remark about the third day passing by is made because it was evidence to them that their hope was dashed.  In otherwords, the prophecy they thought was unfulfilled!
    Whenever someone makes an eschatological prediction that something will happen on a given day, then the followers of the prophet always wait to the end of that day before they give up hope.  They don't give up hope while the predicted day is still ongoing.
    So we have internal contextual evidence as to which reading is right. Further, we have the external consideration that Catholic Friday to Sunday teachers would be highly motivated to corrupt Luke 24:21 to say "this third day." For if it doesn't read that way then their chronology is in ruins. Thankfully they were not able to get their hands on every manuscript to destroy them or to copy them wrongly and then destroy them. Codex Bezae, some old Latin MSS, and the Aramaic escaped from the almost sucessful attempt to add the word "this" in front of "day" in all the texts.