A Commentary, Critical, Practical, and Explanatory on the Old and New Testaments, by Robert Jamieson, A.R. Fausset and David Brown  at sacred-texts.com
num 5:2THE UNCLEAN TO BE REMOVED OUT OF THE CAMP. (Num 5:1-4)
Command the children of Israel, that they put out of the camp every leper--The exclusion of leprous persons from the camp in the wilderness, as from cities and villages afterwards, was a sanitary measure taken according to prescribed rules (Lev. 13:1-14:57). This exclusion of lepers from society has been acted upon ever since; and it affords almost the only instance in which any kind of attention is paid in the East to the prevention of contagion. The usage still more or less prevails in the East among people who do not think the least precaution against the plague or cholera necessary; but judging from personal observation, we think that in Asia the leprosy has now much abated in frequency and virulence. It usually appears in a comparatively mild form in Egypt, Palestine, and other countries where the disorder is, or was, endemic. Small societies of excluded lepers live miserably in paltry huts. Many of them are beggars, going out into the roads to solicit alms, which they receive in a wooden bowl; charitable people also sometimes bring different articles of food, which they leave on the ground at a short distance from the hut of the lepers, for whom it is intended. They are generally obliged to wear a distinctive badge that people may know them at first sight and be warned to avoid them. Other means were adopted among the ancient Jews by putting their hand on their mouth and crying, "Unclean, unclean" [Lev 13:45]. But their general treatment, as to exclusion from society, was the same as now described. The association of the lepers, however, in this passage, with those who were subject only to ceremonial uncleanness, shows that one important design in the temporary exile of such persons was to remove all impurities that reflected dishonor on the character and residence of Israel's King. And this vigilant care to maintain external cleanliness in the people was typically designed to teach them the practice of moral purity, or cleansing themselves from all filthiness of the flesh and spirit. The regulations made for ensuring cleanliness in the camp suggest the adoption of similar means for maintaining purity in the church. And although, in large communities of Christians, it may be often difficult or delicate to do this, the suspension or, in flagrant cases of sin, the total excommunication of the offender from the privileges and communion of the church is an imperative duty, as necessary to the moral purity of the Christian as the exclusion of the leper from the camp was to physical health and ceremonial purity in the Jewish church.
num 5:6RESTITUTION ENJOINED. (Num 5:5-10)
When a man or a woman shall commit any sin that men commit, to do a trespass against the Lord--This is a wrong or injury done by one man to the property of another, and as it is called "a trespass against the Lord," it is implied, in the case supposed, that the offense has been aggravated by prevaricating--by a false oath, or a fraudulent lie in denying it, which is a "trespass" committed against God, who is the sole judge of what is falsely sworn or spoken (Act 5:3-4).
and that person be guilty--that is, from the obvious tenor of the passage, conscience-smitten, or brought to a sense and conviction of his evil conduct. (See on Lev 6:2). In that case, there must be: first, confession, a penitential acknowledgment of sin; secondly, restitution of the property, or the giving of an equivalent, with the additional fine of a fifth part, both as a compensation to the person defrauded, and as a penalty inflicted on the injurer, to deter others from the commission of similar trespasses. (See on Exo 22:1). The difference between the law recorded in that passage and this is that the one was enacted against flagrant and determined thieves, the other against those whose necessities might have urged them into fraud, and whose consciences were distressed by their sin. This law also supposes the injured party to be dead, in which case, the compensation due to his representatives was to be paid to the priest, who, as God's deputy, received the required satisfaction.
num 5:9every offering . . . shall be his--Whatever was given in this way, or otherwise, as by freewill offerings, irrevocably belonged to the priest.
num 5:12THE TRIAL OF JEALOUSY. (Num. 5:11-31)
if any man's wife go aside, and commit a trespass against him--This law was given both as a strong discouragement to conjugal infidelity on the part of a wife, and a sufficient protection of her from the consequences of a hasty and groundless suspicion on the part of the husband. His suspicions, however, were sufficient in the absence of witnesses (Lev 20:10) to warrant the trial described; and the course of proceeding to be followed was for the jealous husband to bring his wife unto the priest with an offering of barley meal, because none were allowed to approach the sanctuary empty handed (Exo 23:15). On other occasions, there were mingled with the offering, oil which signified joy, and frankincense which denoted acceptance (Psa 141:2). But on the occasion referred to, both these ingredients were to be excluded, partly because it was a solemn appeal to God in distressing circumstances, and partly because it was a sin offering on the part of the wife, who came before God in the character of a real or suspected offender.
num 5:17the priest shall take holy water--Water from the laver, which was to be mixed with dust--an emblem of vileness and misery (Gen 3:14; Psa 22:15).
in an earthen vessel--This fragile ware was chosen because, after being used, it was broken in pieces (Lev 6:28; Lev 11:33). All the circumstances of this awful ceremony--her being placed with her face toward the ark--her uncovered head, a sign of her being deprived of the protection of her husband (Co1 11:7) --the bitter potion being put into her hands preparatory to an appeal to God--the solemn adjuration of the priest (Num 5:19-22), all were calculated in no common degree to excite and appall the imagination of a person conscious of guilt.
num 5:21The Lord make thee a curse, &c.--a usual form of imprecation (Isa 65:15; Jer 29:22).
num 5:22the woman shall say, Amen, Amen--The Israelites were accustomed, instead of formally repeating the words of an oath merely to say, "Amen," a "so be it" to the imprecations it contained. The reduplication of the word was designed as an evidence of the woman's innocence, and a willingness that God would do to her according to her desert.
num 5:23write these curses in a book--The imprecations, along with her name, were inscribed in some kind of record--on parchment, or more probably on a wooden tablet.
blot them out with the bitter water--If she were innocent, they could be easily erased, and were perfectly harmless; but if guilty, she would experience the fatal effects of the water she had drunk.
num 5:29This is the law of jealousies--Adultery discovered and proved was punished with death. But strongly suspected cases would occur, and this law made provision for the conviction of the guilty person. It was, however, not a trial conducted according to the forms of judicial process, but an ordeal through which a suspected adulteress was made to go--the ceremony being of that terrifying nature, that, on the known principles of human nature, guilt or innocence could not fail to appear. From the earliest times, the jealousy of Eastern people has established ordeals for the detection and punishment of suspected unchastity in wives. The practice was deep-rooted as well as universal. And it has been thought, that the Israelites being strongly biassed in favor of such usages, this law of jealousies "was incorporated among the other institutions of the Mosaic economy, in order to free it from the idolatrous rites which the heathens had blended with it." Viewed in this light, its sanction by divine authority in a corrected and improved form exhibits a proof at once of the wisdom and condescension of God.