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The “generations” (see Genesis 2:4) now given, though entitled those of Aaron and Moses (Aaron standing first as the older brother), are those of Aaron only. The personal dignity of Moses, though it gave him rank as at the head of his tribe, was not hereditary. He had, and desired to have Numbers 14:12; Exodus 32:10, no successor in his office but the distant prophet like unto himself Deuteronomy 18:18. Aaron was the ancestor of a regular succession of priests.
whom he consecrated - i. e. whom Moses consecrated, or literally as in the margin, whose “hand he filled,” by conferring their office upon them (Leviticus 8:1 ff).
keep his charge - i. e. so assist him that the obligations incumbent on him and on the congregation may be fulfilled.
The concluding words are better expressed thus: “Mine shall they be, Mine, the Lord’s.” On the subject of the firstborn see the notes at Numbers 3:43-51.
the cords ... the service thereof - i. e. of the tabernacle, not of the hangings of the court, for these, with their cords and other fittings, belonged to the charge of the Merarites Numbers 3:36-37. The tabernacle was under the care of the Gershonites.
Of the Levites, the Kohathites, the kinsmen of Moses and Aaron, and the most numerous, have the most important charge confided to them, namely, that of the ark, the altars, and the more especially sacred furniture generally.
twenty and two thousand - A number on which the commutation with the firstborn of the twelve tribes depends Numbers 3:43-46. The actual total of the male Levites is 22,300 (compare Numbers 3:22, Numbers 3:28, Numbers 3:34): and the extra 300 are considered by some to represent those who, being first-born themselves in the tribe of Levi, could not be available to redeem the first-born in other tribes. Others consider the difference due to an error in the Hebrew text.
The tribe of Levi is shown by this census to have been by far the smallest of the tribes.
This result, when compared with the number of male adults (603,550, compare Numbers 2:32), is small, the usual proportion of first-born sons to a total male population being about one in four: and the explanation offered is that the law of Exodus 13:1-2, prescribed a dedication of those only who should be firstborn “thenceforward”.
On the other hand, the number is very large to be born among two millions of persons in a single year; and it must be admitted, that some unusual causes must have been concerned. Such, not to mention the divine blessing, may be found in the sudden development of national energies which would immediately ensue on the Exodus. Before that event, the miserable estate of the people, and especially the inhuman order for the destruction of their first-born, would check very seriously the ratio of marriages and births; and this ratio would naturally, when the check was removed, exhibit a sudden and striking increase.
This redemption money (see the marginal references) would perhaps be exacted from the parents of the “youngest” children of the 22,273 Numbers 3:43. The cattle of the Levites was doubtless taken in the gross as an equivalent for the first-born cattle of the other tribes, which of course, no less than the first-born of men, belonged to the Lord; and in future would have to be redeemed Numbers 18:15; Deuteronomy 15:19.
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Barnes, Albert. "Commentary on Numbers 3". "Barnes' Notes on the Whole Bible". https://www.studylight.org/
the Week of Proper 15 / Ordinary 20