The printer’s manuscript has “in behalf of ”, while the 1830 edition has “in the behalf of ”. The the was removed in the 1837 edition, with the result that this passage read like all other instances of this phrase in the Book of Mormon, including one in the very next verse (marked below with an asterisk):
We note here that the Book of Mormon has no examples of “on behalf of ”. Moreover, there is no variation in the phrase “in behalf of” anywhere else in the text. (Incidentally, the Doctrine and Covenants has four examples of “in behalf of ” and none of “on behalf of ”, thus supporting the Book of Mormon phraseology with the in —and without the the.) To be sure, the consistency of the text otherwise supports the occurrence of “in behalf of ” throughout the Book of Mormon. On the other hand, loss of the is more likely than its addition, especially since “in behalf of ” is more expected than “in the behalf of ”. Moreover, the early text omitted function words more frequently than it added them.
The King James Bible, on the other hand, always has the definite article the for “in the behalf of ” and “on the behalf of ”, although there are only three examples:
It is doubtful that the the would have been added by the 1830 typesetter in imitation of the King James style, especially since none of these phrases occur in any particularly well-known biblical passage. In terms of transmissional probabilities, the specific evidence supports the omission of the.
There are, for instance, three cases in this part of the text where scribe 2 of 𝓟 omitted the the—and without correction by himself or later by Oliver Cowdery when Oliver proofed 𝓟 against 𝓞 (see under 3 Nephi 24:13 for these three cases). There is also an example earlier in the text where scribe 2 of 𝓟 omitted a necessary the:
In this case, the 1830 typesetter supplied the the. But unlike the example here in Mormon 8:24, the text in Alma 2:22 obviously required the definite article before camp. In contrast, there would have been no motivation for the 1830 typesetter to add the definite article before behalf, especially since he did it nowhere else in the text. There are cases where the 1830 typesetter added a the, but he usually did so when it seemed necessary or expected for the context. Yet there is one case where the insertion seems unnecessary or perhaps inappropriate for the context:
(For discussion, see under that passage.) So there is some slight possibility that here in Mormon 8:24 the 1830 typesetter accidentally added the the in “in the behalf of ”. But from a statistical point of view, scribe 2 of 𝓟 was much more prone to omit the than the 1830 typesetter was to accidentally add it. Thus the more likely scenario here in Mormon 8:24 is that 𝓞 itself had the the and that scribe 2 of 𝓟 omitted it. The critical text will therefore follow the more difficult reading, “in the behalf of ”, in Mormon 8:24.
Summary: Restore in Mormon 8:24 the 1830 reading, “in the behalf of ”, instead of maintaining the reading in 𝓟, “in behalf of ”; the reading without the the is the expected reading, but the difficult reading with the the is found in the King James Bible.