Several people witnessed the “translation” of the Book of Mormon, and some of these witnesses provided accounts of what they saw.
Elizabeth Ann Whitmer, at whose home the Book of Mormon was translated, and who later married Oliver Cowdery, recorded in 1870:
I cheerfully certify that I was familiar with the manner of Joseph Smith’s translating the Book of Mormon. He translated the most of it at my Father’s house. And I often sat by and saw and heard them translate and write for hours together. Joseph never had a curtain drawn between him and his scribe while he was translating. He would place the director [stone] in his hat, and then place his face in his hat, so as to exclude the light.
Her brother, David Whitmer, described the process this way:
I will now give you a description of the manner in which the Book of Mormon was translated. Joseph Smith would put the seer stone into a hat, and put his face in the hat, drawing it closely around his face to exclude the light; and in the darkness the spiritual light would shine. A piece of something resembling parchment would appear, and on that appeared the writing. One character at a time would appear, and under it was the interpretation in English. Brother Joseph would read off the English to Oliver Cowdery , who was his principal scribe, and when it was written down and repeated by Brother Joseph to see if it was correct, then it would disappear, and another character with the interpretation would appear. Thus the Book of Mormon was translated by the gift and power of God, and not by any power of man.
The witness accounts agree on the basics. After the original 116 manuscript pages were lost, Joseph Smith translated the remainder of the Book of Mormon in plain view of others. He would place a seer stone into a hat, put his face in the hat to block the ambient light, and read to his scribe the text he saw. He didn’t look at the gold plates or any other book during this process. He would dictate for hours at a time. Upon starting on a new day, he didn’t have to be reminded where he had left off the day before. When he came to an unfamiliar word, such as a person’s name, he would spell it out.
This is not the way that many of us, including leaders and teachers in the church, have assumed that it happened. It is, however, just as amazing. Skeptics would say that Joseph Smith must have been reading from a slip of paper hidden in his hat, or that he had the text memorized. But both the short focal distance required and the darkness inside his hat would have prevented reading from a hidden slip of paper. And how much text could he have fit on one piece of paper? The idea that Joseph Smith could have memorized a previously written manuscript or entire chapters of the Bible and then dictated them to his scribe is similarly implausible. Neither could he have composed such a coherent book on the fly. No one could have. On the other hand, those who don’t accept the possibility of modern revelation would probably not consider it plausible that Joseph Smith was seeing words in a hat. Ultimately no story of the origin of the Book of Mormon can be proven beyond all doubt with historical and textual evidence. For whatever story you believe, you will always need a bit of faith. And ultimately, no historical analysis will substitute for actually reading the book in question.
For a closer look at the witness accounts, see Book of Mormon Translation–The Most Credible Accounts