And Shemaiah - "Moses the great scribe, who is called Shemaiah, the son of Nethaneel, of the tribe of Levi, wrote them down." - T.
One principal household - for Eleazar - The family of Eleazar was the most illustrious of the sacerdotal families, because Eleazar was the first-born of Aaron, Ithamar's family was the second in order and dignity; therefore one of the principal families of Eleazar was first taken, and then one of Ithamar's, and thus alternately till the whole was finished.
Wrote them before the king - i. e., “wrote down their names as the lots were drawn forth.”
Ahimelech the son of Abiathar - A wrong reading. It should be “Abiathar, the son of Ahimelech.” See the 2 Samuel 8:17 note.