Dora Bas Rivka Silver O'H
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If just a regular person - not the king, High Priest or the community as a whole - committed an inadvertent sin, his chatas would consist of a defect-free female goat. He would place his hands on the goat's head, the goat would be slaughtered, and the kohein would proceed as he did for the goat of the king.
A regular person could also use a female sheep for his korban chatas. In such a case, he would have to include the fat tail among the portions burned on the altar, the same as with a korban shlamim.
Here's a new scenario. Let's say a person does one of the following things: (1) he took an oath in court to the effect that he had no information, but he lied; (2) he touched something ritually impure, then ate sanctified food or entered a holy area forgetting to first purify himself; (3) he violated an oath he forgot he made. In any of these situations, the offender must admit his wrongdoing and bring a guilt offering, or "korban asham." Unlike other sacrifices, this asham is variable in that the offender can give according to his means. (In Hebrew, it's also called a korban oleh v'yoreid, meaning that its value can go up and down.)
The basic korban oleh v'yoreid is a female sheep, but the person has the option of bringing two birds (pigeons or doves) if he can't afford the sheep. In such a case, one bird would be a chatas (sin offering) and the other would be an olah (burnt offering).