Today's passage covers a few laws for the purity of the camp; some laws for the restitution of wrongs; a ritual designed to uncover adulterous wives; regulations for Nazarites; and a priestly blessing.
Your wife has been acting strange lately. She says she's working late at the office, but she's not making any extra income. She says she's at her friends' house, but her friend is out of town. She buys little gifts, but never gives them to you. In short, you're beginning to feel that there's some funny business going on. Unfortunately, you can't prove it, and your wife claims she's the soul of innocence. What do you do?
People have been trying to prove cases of adultery for as long as there has been adultery, which is probably as long as there have been monogamous relationships. Today, these issues are dealt with by the courts. In ancient Israel they were dealt with by the priesthood.
Numbers 5:11-31 is an extended instruction manual for what to do when a husband suspects, but cannot prove, that his wife is being unfaithful. Here's a short version:
The jealous husband takes his wife and a barley offering to the tabernacle. The priest then takes the woman, uncovers her hair, and has her hold the offering. Meanwhile, he mixes some holy water with dust from the tabernacle floor. He then tells the woman that if she has been faithful, the bitter water won't hurt her, but if she has, it will "make thy belly to swell, and thy thigh to rot" (Num. 5:22, KJV). She says, "amen." The priest writes down these words on a scroll and then washes them into the water. He offers the barley on the altar, then the woman drinks the water. Assuming she's pure, she'll be fine. If she's guilty, she receives the effects of the curse.
One thing we realize about this ritual is that it has absolutely no physical relationship to the act of adultery, other than the consequence of the curse. Today, when we want to find evidence of a crime, we look for evidence, even circumstantial evidence. We want to convince other people by force of reason, or at least by force of emotion, that the woman was up to no good. The ancient Israelites did not do this. Their ultimate test was not the strength of evidence, but the revealing power of God. God knows everything, and is capable of everything. Therefore, if there was any wrongdoing here, and the wife agreed to suffer the consequences if she's guilty, God would certainly reveal any sin.
This is, incidentally, very similar to the medieval idea of "trial by combat." The theory behind trial by combat was that God would cause the person in the right to gain victory in single combat. The winner was, by definition, chosen by God and therefore deserved to win the court case.
The flip-side to this "divine revelation" method of justice, of course, is that it doesn't work if you don't believe in the system. As outsiders looking in, we can imagine all sorts of scenarios where the water-dust-and-ink mixture would cause problems, none of which involve a woman actually being unfaithful. In fact, we would probably say that any effect would be dependent on the woman's constitution, the presence or lack of poisons in the dust and ink, and the quantity of contaminants in the water. If the ink were made with gall nuts, copper sulfate, and gum arabic (reference here), we can expect that ingesting it would create some physical symptoms in the woman. Though I am no doctor, I suspect that some of these materials might very well cause stomach problems, if not infertility. This site mentions some harmful effects of ingesting copper sulfate, for example.
Undoubtedly the ancient Israelites knew about these potential health problems. Even if they did not have chemical analysis, surely someone must have discovered, early in the Israelites' history, "drinking bits of metal mixed in water isn't good for you." Given the six-hundred-thousand men in the Israelite camp, there were surely a good number of them who understood some basic medical principals like, "don't eat the dirt on the floor."
Why, then, did the women agree to perform the task of drinking potentially-harmful materials? One reason might be that they assumed God would save them if they were actually innocent. After all, the priest assured them that if they were guiltless, the bitter water wouldn't have any effect. In a faithful, religious society -- which the ancient Israelite camp probably was -- this would likely have been enough assurance for most women.
Another reason might have been more social. Couples who need to deal with accusations of adultery are full of conflict and stress. It might have simply been easier for the woman to subject herself to the bitter water than to continually listen to her husband accuse her. Or, in a particularly dominant relationship, the husband may have forced his wife to undergo the ritual.
At least one benefit may have derived from this ritual. Unlike, for example, the medieval and Renaissance witch-hunts, if a woman didn't react to the bitter water, she was declared innocent. In many ancient, medieval, and even modern institutions, it is sometimes difficult to be proven innocent; there are only degrees of guilt. At least in ancient Israel, if the woman survived drinking water with ink and dust in it, she could point and laugh at her husband's unfounded jealousy. Of course, if the result was a false negative, she'd probably be a lot more careful with her lover in the future, which is just as good.