Numbers 31:3. Avenge the LORD of Midian— What is called avenging the children of Israel, in Num 31:2 is here called avenging the LORD; because the war was with idolaters, the enemies of the true religion, and for the sake of God's peculiar people. Besides, the Midianites were particularly displeasing to God for having seduced the Israelites to the worship of idols; so that to avenge the one was to avenge the other. Onkelos renders this, to avenge the people of the Lord of Midian. See Ainsworth and Poole.

Numbers 31:8. And they slew the kings— This would be more intelligible, if rendered, after Houbigant, "and in the midst of the slaughter, they slew five kings of Midian, Evi, &c."
REFLECTIONS.—The success was answerable to their wishes. Their enemies fell before them, and justly suffered for the evil they had seduced Israel to commit. Note; God will often make the tempters to sin to be tormented of those whom they deceived. They slew all the males, not all in the nation, but, probably, all they met with in that part of the country where they made their attack. Among them, five kings or princes of Midian fell; and, as an instance of especial judgment, Balaam, the author of all the mischief, was among the slain. God will take severe vengeance on those who have been the introducers of corruption among the people. If judgment overtake them not on this side the grave, it infallibly will on the other.
See commentary on Num 31:7

Numbers 31:14. And Moses was wroth with the officers— The Israelites obeyed the order in general; but, with a false pity, saved the lives of those Midianitish women whom they ought to have treated with the utmost rigour. They did not look upon them with that horror which they ought to have had for such seducers, but rather with a complacence, owing, perhaps, to a remembrance of their past criminal pleasures. This very justly provoked the spirit of Moses, by whose peremptory command sentence was immediately passed on all those women who had committed fornication with the Israelites, and all the male children which proceeded from that infamous commerce. The women children, Num 31:18 who were too young to be corrupted by unchastity or idolatry, were to be kept alive for themselves, either to be employed as servants, or, in case they turned proselytes, to marry with themselves, after the preparations required, Deuteronomy 21:11; Deuteronomy 21:23. Moses, I doubt not, followed some particular order which God had given him in this matter. But if this were not the case, the Israelites ought to have believed, that what was most odious in the sight of God in the whole country of Midian, was these impure and idolatrous women, who had seduced them to impurity and idolatry. They ought to have known, that the best use they could make of the sword which God had put into their hands, was to turn it against such notorious offenders. Thus the guilt of this people was so highly aggravated, that they were punished more severely than any other nations with whom they were at war, except those of Canaan; the like execution was, indeed, performed in after-times. See Judges 21:11. Saurin as above, and Virgil, AEn. ii. ver. 584, &c.

Numbers 31:15. Have ye saved all the women alive?— See on chap. Numbers 22:9.

Numbers 31:16. Through the counsel of Balaam— We have, in the course of the former chapters, spoken of this evil counsel. As the Moabites and Midianites, strongly infected with the ideas of local and tutelary gods, conceived Jehovah to be only the tutelary God of the Jews; we may well account, from this persuasion, for their proceedings, and for their rather choosing to entice the Israelites to their idolatry, than to embrace with them the worship of Jehovah.

Numbers 31:19. And do ye abide without the camp seven days— The whole army were to stay without the camp seven days; and such of them as had stained their hands in blood, or touched a dead body, were to purify themselves by the water of separation, ch. Numbers 19:9. For, though it was lawful to kill men in a just war; yet, because of the common affinity which subsists between all mankind, and to preserve sentiments of humanity, it was thought fit and decent to oblige all who had shed blood, as well as those who had touched the slain, to undergo a purification, before they were admitted to free conversation and public worship. It appears to have been a very ancient custom among most nations, to appoint certain purifications in all such cases; in order, no doubt, to inspire an uncommon dread and horror of bloodshed. On these occasions, it was usual, particularly, to wash their hands in water, for the purification of the defilement. Thus Homer makes Hector declare himself unfit for performing any offices of divine worship before he was purified:
Ill fits it me, with human gore distain'd, To the pure skies these horrid hands to raise, Or offer heav'n's great Sire polluted praise. POPE, Iliad. 6:
And Virgil makes AEneas say the same thing:
These hands, yet horrid with the stains of war, Refrain their touch unhallow'd, till the day When the pure stream shall wash their guilt away. PITT, AEn. 2:
It was upon this account that the man-slayer, who had involuntarily shed blood, was forced to fly his country, and repair to one of the cities of refuge, ch. 35: For the same reason David was not allowed to build the temple of God, because he had been a man of war, and had shed much blood, 1 Chronicles 28:3. See Philo, de vita Mosis; and Grotius de Jure B. & P. lib. 2: cap. 24.
It is demonstrable, says Mr. Saurin, that if Moses did not here prescribe particular rules to those who returned from any military expedition, he had already given general ones, of which he now makes the application. See Leviticus 21:1.Numbers 19:4; Numbers 19:4.Leviticus 6:28; Leviticus 6:28; Leviticus 15:12.

Numbers 31:20. Purify all your raiment, and all that is made of skins— La Roque, says the author of the Observations, mentions, as part of the common Arab's furniture, hair sacks, and trunks, and baskets covered with skin, to put up and carry their things in, which are kettles or pots, great wooden bowls, hand-mills, and pitchers; with these they content themselves, and they are all their furniture in common, or nearly so. I mention them distinctly, because this account seems to me to explain, in a clearer manner than commentators have done, (who are, indeed, in a manner silent upon the text,) the passages in Leviticus and Numbers which describe the furniture of the habitations of Israel in the wilderness. Upon whatsoever any of them, when they are dead, doth fall, it shall be unclean; (Leviticus 11:32-33.) whether it be any vessel of wood; their wooden bowls, that is, according to this representation of the utensils of those who live in tents, to which there is reason to believe those of the Israelites were like, who lived so many years like Arabs in the wilderness;—or raiment or skin, any trunks or baskets covered with skins, i.e. or sack, any hair-cloth sack used for the better carrying of goods from place to place. Whatsoever vessel it be, wherein any work is done, it must be put into water, and it shall be unclean until the evening; so it shall be cleansed. And every earthen vessel—the pitchers, used for holding liquids, and drinking out of, wherein any of them falleth, whatsoever is in it; shall be unclean, and ye shall break it. We meet with much the same account of their furniture in the present passage. La Roque's account, therefore, may serve to explain both that and the foregoing, and must be acknowledged a more natural illustration of them than that of the rabbis, who, suppose that the work of goats, (which our translators determine to mean goat's hair) implies instruments made of the horns and hoofs, and bones of goats; few or no instruments being to be found among those who now dwell in tents. See Ainsworth on these passages. There is the like agreeable simplicity in explaining the things made of wood, of their wooden bowls, instead of reckoning up all the particular things which were afterwards made of wood, in the most remote sense of the word, as Maimonides has done, who introduces the mention of vessels of bulrushes, of reed, of the shell of nuts, and the bark of trees; things, which there is reason to think were not in use in these migratory families, and consequently not immediately referred to by Moses; and, if so, not coming under the observation of a commentator, however they may, with propriety enough, have engaged the attention of a Jewish Casuist.

Numbers 31:30. Of the children of Israel's half, thou shall take one portion of fifty— The congregation, not having hazarded their lives, are enjoined to part with ten times as much as those who went to battle, and in such a proportion as the number of them that went to battle held to the whole number of warriors, which was about the fiftieth part; for that is the proportion between the twelve thousand men of war, and the whole company of warriors, which make up the number of six hundred thousand and upwards, ch. 26: See Bishop Kidder.

Numbers 31:32. And the booty, being the rest, &c.— Hence it appears, that Midian must have been an extremely populous and fertile country; for the sum total of the divided booty was as in the following table, wherein the reader will see, at one view, what portion fell to the share of the soldiers, the congregation, the Levites, and the LORD.
Sheep, 675,000 {To the soldiers, 337,500} To the Lord from the soldiers, 675
{To the people, 337,500} To the Levites from the people, 6750
Beeves, 72,000 {To the soldiers, 36,000} To the Lord from the soldiers, 72
{To the people, 36,000} To the Levites from the people, 720
Asses, 61,000 {To the soldiers, 30,500} To the Lord from the soldiers, 61
{To the people, 30,500} To the Levites from the people, 610
Persons, 32,000 {To the soldiers, 16,000} To the Lord from the soldiers, 32
{To the people, 16,000} To the Levites from the people, 320
To this must be added, what was necessarily spent for their subsistence during the war, and while they lay out of the camp, Numbers 31:19.; and from Num 31:30 it is plain, that there were other kinds of beasts taken, besides those which are enumerated; among which, most probably, were camels and dromedaries, for which this country was famous.

Numbers 31:52. Sixteen thousand seven hundred and fifty shekels— See Exodus 25:39.

Numbers 31:53. (For the men of war had taken spoil, every man for himself)— But the men of war had every one their own booty. Houbigant; or, had reserved the spoil, every man for himself: see on Numbers 31:26.
REFLECTIONS.—The piety of the officers of Israel appears here as great as their prowess. On calling their muster-roll, not a man was lost, either by disease or the sword, in this expedition. An instance of Divine protection so amazing could not but affect them: and as they loved their soldiers as brethren, and were tender of their lives, (as every good general should be,) they make the most grateful acknowledgments to God for his preservation of them. Note; 1. Great deliverances deserve particular thankfulness. (2.) Where God gives plenty, we must abound in works of piety and charity.