Russell and Barbour (1875+)
Charles Taze Russell was the founder of the Watch Tower Society and Bible Student movement. His interpretation of Daniel 4's 'seven times' as a 2520-year prophecy spanning 606 BC to 1914 AD was taken from the Adventist writer Nelson Barbour.
In the September 1875 edition of Herald of the Morning Barbour wrote [1, p. 52]:
I believe that though the gospel dispensation will end in 1878, the Jews will not be restored to Palestine, until 1881; and that the “times of the Gentiles,” viz. their seven prophetic times of 2520, or twice 1260 years, which began where God gave all, into the hands of Nebuchadnezzar, 606 B.C.; do not end until A.D. 1914; or 40 years from this.
In 1876 Russell read this, and spent time discussing it with Barbour [2, p. 46]. Russell adopted the same views and in the October 1876 edition of Bible Examiner he wrote [3, p. 27]:
if three and one-half times are 1260 years, seven times would be twice as much, i.e. 2520 years. At the commencement of our Christian era. 606 years of time had passed, (70 years captivity, and 536 from Cyrus to Christ) which deducted from 2520, would show that the seven times will end in A.D. 1914
Together in 1877 Barbour and Russell published the book Three Worlds, and The Harvest of This World in which they reiterated the same interpretations of the prophecy along with an explanation of the chronology that it was based on [4, pp. 83, 194]:
The seventy years captivity ended in the first year of Cyrus, which was B.C. 536. They therefore commenced seventy years before, or B.C. 606. Hence, it was in B.C. 606, that God’s kingdom ended, the diadem was removed, and all the earth given up to the Gentiles. 2520 years from B.C. 606, will end in A.D. 1914, or forty years from 1874.
The fact that the first year of Cyrus was B.C. 536, is based on Ptolemy’s canon, supported by the eclipses by which the dates of the Grecian and Persian era have been regulated. And the accuracy of Ptolemy’s canon is now accepted by all the scientific and literary world, Hence, from the days of Nebuchadnezzar to the Christian era, there is but one chronology.
Russell later dedicated an entire chapter of Millennial Dawn (later published as Studies in the Scriptures) Volume II (first edition in 1889) to the ‘Gentile times’, he explains [5, p. 79]:
The Bible evidence is clear and strong that the “Times of the Gentiles” is a period of 2520 years, from the year B.C. 606 to and including A.D. 1914. This lease of universal dominion to Gentile governments, as we have already seen, began with Nebuchadnezzar—not when his reign began, but when the typical kingdom of the Lord passed away, and the dominion of the whole world was left in the hands of the Gentiles. The date for the beginning of the Gentile Times is, therefore, definitely marked as at the time of the removal of the crown of God’s typical kingdom, from Zedekiah, their last king.
According to the words of the prophet (Ezek. 21:25-27), the crown was taken from Zedekiah; and Jerusalem was besieged by Nebuchadnezzar's army and laid in ruins, and so remained for seventy years—until the restoration in the first year of Cyrus. (2 Chron. 36:21-23.) Though Jerusalem was then rebuilt, and the captives returned, Israel has, never had another king from that to the present day. Though restored to their land and to personal liberty by Cyrus, they, as a nation, were subject successively to the Persians, Grecians and Romans. Under the yoke of the latter they were living when our Lord's first advent occurred, Pilate and Herod being deputies of Cæsar.
With these facts before us, we readily find the date for the beginning of the Gentile Times of dominion; for the first year of the reign of Cyrus is a very clearly fixed date — both secular and religious histories with marked unanimity agreeing with Ptolemy’s Canon, which places it B.C. 536. And if B.C. 536 was the year in which the seventy years of Jerusalem’s desolation ended and the restoration of the Jews began, it follows that their kingdom was overthrown just seventy years before B.C. 536, i.e., 536 plus 70, or B.C. 606. This gives us the date of the beginning of the Times of the Gentiles—B.C. 606.
Issues
Ptolemy’s canon
As we saw in the Ptolemy’s canon section, the canon in fact dates the first year of Cyrus II to 538 BC and not 536 BC as incorrectly claimed by Russell.
It is quite probable that Russell actually took the 536 BC date from Volume II of William Hales' New Analysis of Chronology [6, p. 448] which he cited in the previous chapter of Millennial Dawn in relation to the chronology of Nehemiah [5, p. 67].
However, in the first volume, Hales explains that he has modified the Canon's date from 538 BC to 536 BC in order to fit his own interpretation of Jeremiah's prophecy [7, pp. 166, 167]:
It must, however, be acknowledged, that accurate as these authentic copies of the Canon unquestionably are every where else, in this single period a small correction is necessary, to accommodate it to Scripture; for, according to the Canon, from the first of Nabokolassar, or Nebuchadnezzar, B.C. 604, to the first of Cyrus, B.C. 538, is an interval of only 66 years; and therefore, if the Captivity began in the end of the third, or commencement of the fourth year of Jehoiakim, B.C. 605, Dan. i. 1; 2 Kings xxiv. 1; Jer. xxv. 1; from thence, to the accession of Cyrus, was only 67 years complete, or 68 current.
...
Scaliger, Petavius, Usher, Prideaux, Jackson, &c. have adopted this interpolation as indispensably necessary to reconcile the Canon to Holy Writ, which is effectually done thereby; for from the commencement of the Captivity, B.C. 605, to the corrected first of Cyrus, B.C. 536, is 69 years complete, or 70 years current,
Year Zero
Russell made an error in his calculation counting 2520 years from 606 BC, since there was no year zero, he should actually have arrived at 1915 AD, not 1914.
An article in The Watchtower 1912 [8] discusses this issue in detail, it starts with the statement that 'we may not be sure' if there was a year zero or not:
So matters continued with little effort to arrange an exact chronology of human history, until the Sixth Century A.D. when Dionysius, a Roman abbot, set forth our present method of counting, styled the Christian Calendar. It undertook to mark the beginning of the Christian era with the birth of Christ, reckoned as January 1st. Previous history was reckoned and styled Before Christ (B.C.) and subsequent history was styled Anne Domini (A.D.)—in the year of our Lord.
Whether Dionysius began his A.D. period January 1st, A.D. 1, or whether he began it January 1st, A.D. 0, we may not be sure; neither may we feel too certain whether he began the B.C. dates December 31st, B.C. 0, or December 31st, B.C. 1. For all ordinary purposes this question would be rather immaterial. But it has a very important bearing on our calculation of Gentile Times.
Again this is still incorrect - it is a certain fact there was no year 0; Dionysius began his calendar from 1 BC. The article ends with an extract from a sermon given by Russell in 1904 [8]:
Many of our readers will recall our reference to this subject in a sermon preached at Allegheny, Pa., January 11, 1904. and published in the Pittsburgh Gazette. We make an extract from that sermon as follows:—
"We find, then, that the Seven Times of Israel’s punishment and the Seven Times of Gentile dominion are the same; and that they began with the captivity of Zedekiah, and, as will be seen from the Chart, they terminate with the year 1915. According to the best obtainable evidences on the subject, synchronized with the Scriptural testimony, Zedekiah’s captivity took place in October, 605¾ years before A.D. 1. If we will add to this 1914¾ years, we will have the year, October, 1915, as the date for the end of Gentile supremacy in the world—the end of the lease of 2,520 years, which will not be renewed. Instead, he whose right the kingdom is, shall take possession of it. This, therefore, marks when the Lord himself shall assume control of the world’s affairs, to end its reign of sin and death, and to bring in the True Light."
There surely is room for slight differences of opinion on this subject and it behooves us to grant each other the widest latitude. The lease of power to the Gentiles may end in October, 1914, or in October, 1915. And the period of intense strife and anarchy "such as never was since there was a nation" may be the final ending of the Gentile Times or the beginning of Messiah’s reign. [See Vol. 2, SCRIPTURE STUDIES.]
In the March 1915 Watchtower changes to the Studies in the Scriptures series were listed, including some replacements of '1914' with '1915' [9] [10], indicating Russell had recognized his error, but also that the year 1914 had not met his prophetic expectations:
We call attention to a few slight changes which have been made in four pages of Vol. II. and six pages of Vol. III., “Studies in the Scriptures.” These are all trivial and do not alter the real sense and lesson, but conform to the facts as we have them today...
Vol II., page 77, lines 16, 17, "end of A.D. 1914," reads "end of the overthrow."
Vol II., page 81, line 9, "can date only from A.D. 1914," reads "could not precede A.D. 1915."
Vol II., page 221, line 25, "full favour until A.D. 1914" reads "full favour until after 1915."
References
[1] N. H. Barbour, Herald of the Morning, vol. 3, no. 4, pp. 49–64, Sep. 1875, [Online]. Available: https://archive.org/details/1875-1880HeraldOfTheMorningAssortedIssues/1875-1880_Herald_of_the_Morning_Assorted.
[2] Jehovah’s Witnesses: Proclaimers of God’s Kingdom. Watch Tower Bible and Tract Society, 1993, [Online]. Available: https://wol.jw.org/en/wol/publication/r1/lp-e/jv.
[3] C. T. Russell, “Gentile Times: When Do They End?” Bible Examiner, pp. 27–28, Oct. 1876, [Online]. Available: https://archive.org/details/1876BibleExaminer.
[4] N. H. Barbour and C. T. Russell, Three Worlds, and the Harvest of this World: A Brief Review of the Bible Plan of Redemption, which Spans Three Worlds: "the World that Was", "the World that Now Is" and "the World to Come"; with the Evidences that We are Now in the "time of Harvest" Or Closing Work of the Gospel Age. N. H. Barbour. C. T. Russell, 1877, [Online]. Available: https://archive.org/details/N.H.BarbourThreeWorldsAndHarvestOfThisWorld.ABriefReviewOfThe.
[5] C. T. Russell, Millennial Dawn: The time is at hand, 86th Thousand Edition., vol. 2. International Bible Students Association, 1889, [Online]. Available: https://archive.org/details/millennial-dawn-vol.2-the-time-is-at-hand-premiere-edition-1889.
[6] W. Hales, A New Analysis of Chronology and Geography, History and Prophecy: In which Their Elements are Attempted to be Explained, Harmonized and Vindicated, Upon Scriptural and Scientific Principles, 2nd ed., vol. 2. C.J.G. & F. Rivington, 1830, [Online]. Available: https://archive.org/details/newanalysisofchr02hale/.
[7] W. Hales, A New Analysis of Chronology and Geography, History and Prophecy: In which Their Elements are Attempted to be Explained, Harmonized and Vindicated, Upon Scriptural and Scientific Principles, 2nd ed., vol. 1. C.J.G. & F. Rivington, 1830, [Online]. Available: https://archive.org/details/newanalysisofchr01hale/.
[8] “The Ending of the Gentile Times,” The Watch Tower and Herald of Christ’s Presence, vol. 33, no. 23, Dec. 1912, [Online]. Available: https://archive.org/details/WatchTowerAndHeraldOfChristsPresence1910-1919.
[9] “Changes in "Scripture Studies",” The Watch Tower and Herald of Christ’s Presence, vol. 36, no. 5, Mar. 1915, [Online]. Available: https://archive.org/details/WatchTowerAndHeraldOfChristsPresence1910-1919.
[10] C. T. Russell, Studies in the Scriptures: The time is at hand, 1,582,000 Edition., vol. 2. International Bible Students Association, 1915, [Online]. Available: https://archive.org/details/studiesinscriptu02russ.