Matthew 6:10 (King James Bible) thy will be done in earth as it is in heaven
In his editing of 3 Nephi 13:10 for the 1837 edition, Joseph Smith changed the preposition in to on since modern English speakers expect “on earth” rather than “in earth” for this expression. The King James text in Matthew 6:10 has the archaic “in earth”. The Book of Mormon text has a few instances of “on earth”, of which all but one refer to something being either sealed or loosed “on earth”:
The usage in Helaman 10:7 parallels the language of the King James Bible:
The only other use of “on earth” in the original Book of Mormon text is found in 2 Nephi 10:3: “and there is none other nation on earth that would crucify their God”. On the other hand, there are six other instances of “in earth” in the text, all parallel to the usage here in 3 Nephi 13:10. Five of these take the precise form “in heaven and in earth”. The sixth one, like the one in 3 Nephi 13:10, is more complicated:
Note that in Helaman 8:24 the 1830 typesetter changed “in earth” to “in the earth”. And as we might expect, “in the earth” with the meaning ‘on earth’ also occurs elsewhere in the text:
On the other hand, there are no instances in the Book of Mormon text of “on the earth”. Thus all these examples of “in (the) earth” support the original reading “in earth” here in 3 Nephi 13:10 (and this in addition to the fact that the reading of the corresponding King James passage has “in earth”).
Summary: Restore the original in in 3 Nephi 13:10 (“in earth”), the earliest reading as well as the reading in Matthew 6:10; the use of “in (the) earth” can be found throughout the Book of Mormon text, not just in this biblical quote.