Adventist Miller calculated 1844 as the year of Christ's return. It didn't happen, of course, and the non-event became known as the Great Disappointment.
Russell (Barbour?) built on this failed date by using more 'prophetic parallels' which went something like this:
1844, the Bridegroom (Matt. 25) was expected to make an appearance. He didn't. He 'tarried' or delayed for 30 years which was akin to the 30 years from his birth to his baptism and the start of his ministry or 'harvest work.' Thus the Bridegroom 'came' in 1874 and divided the wise virgins from the foolish ones (this will be where the ideas about 1878 fit in).
Just as it took 40 years from the beginning of Jesus' ministry and the institution of Christianity (the 'Gospel Age' - c. 30 CE onwards) to the overthrow of the Jewish system (70 CE), so it would take 40 years from Jesus' return in 1874 to the overthrow of Gentile rulership in 1914 and the inauguration of the Millennial Age.
Oh, and as already mentioned, there were the Jubilee cycles and other prophetic numbers that were slotted in too.
It was a nice idea at the time and appeared to all hang together neatly on the face of it. I can understand why it hooked some people in.