Jamieson-Fausset-Brown on Numbers 31:19
abide without the camp seven days: whosoever hath killed any person . . . purify both yourselves and your captives--Though the Israelites had taken the field in obedience to the command of God, they had become defiled by contact with the dead. A process of purification was to be undergone, as the law required (Lev 15:13; Num 19:9-12), and this purifying ceremony was extended to dress, houses, tents, to everything on which a dead body had lain, which had been touched by the blood-stained hands of the Israelitish warriors, or which had been the property of idolaters. This became a standing ordinance in all time coming (Lev 6:28; Lev 11:33; Lev 15:12).
John Gill on Numbers 31:22
Only the gold, and the silver, the brass, the iron, the tin, and the lead. These are excepted, and, though unclean, are not to be purified by washing, but in another way, by fire, as follows; all these metals were well known in those early times, and were made use of for instruments and vessels of various sorts.
John Calvin on Numbers 31:19-24
And do ye abide without the camp seven days. We have elsewhere seen, [209] that, if any one had touched a dead body, he was accounted unclean. Moses, by now extending the ceremony of expiation to lawful homicide, intimates how carefully we ought to abstain from shedding human blood. It was required of the Israelites that they should strenuously advance through the midst of carnage; but, inasmuch as it is in a manner contrary to the order of nature that men should be killed by men, as if they were raging against their own bowels, God would have some vestiges of humanity preserved even in just punishments, so as to put a restraint upon all cruelty in the abstract. Nor is it without cause that…
Read the whole note in the consoleKeil & Delitzsch on Numbers 31:21-24
To this end Eleazar, whose duty it was as high priest to see that the laws of purification were properly observed, issued fuller instructions with reference to the purification of the different articles, in accordance with the law in ch. 19. למּלחמה הבּאים, those who came to the war, i.e., who went into the battle (see at Num 10:9). "The ordinance of the law:" as in Num 19:2. The metal (gold, silver, copper, tin, lead), all that usually comes into the fire, i.e., that will bear the fire, was to be drawn through the fire, that it might become clean, and was then to be sprinkled with water of purification (Num 19:9); but everything that would not bear the fire was to be drawn through water. -…