but it did not atone for him before Heaven, i.e., it is not accepted by God as a perfect offering.

Didn’t we learn in a mishna with regard to the purification process of a leper (Nega’im 14:10): The verse states: “And the rest of the oil that is in the priest’s hand he shall put upon the head of the one that is to be purified, to make atonement for him before the Lord” (Leviticus 14:18). This teaches that if the priest placed the oil on the leper’s head, it atoned for him, and he is purified, but if he did not place the oil on his head, it did not atone for him; this is the statement of Rabbi Akiva. Rabbi Yoḥanan ben Nuri says: Placement of the oil on the leper’s head is a non-essential mitzva. Therefore, whether the oil was placed on his head or whether it was not placed on his head, it atoned for him, but the verse ascribes the leper blame as though it did not atone for him.

The Gemara comments: What is the meaning of the phrase: As though it did not atone for him? If we say that it is necessary for the leper to bring another offering of oil, didn’t you say that whether the oil was placed on his head or whether it was not placed on his head, it atoned for him? Rather, the meaning of the statement is as follows: It atoned for the person, but did not atone for him before Heaven. Here too, with regard to one who sacrificed an offering without placing hands on its head, the baraita apparently means that the offering atoned for the owner’s transgression, even if it did not atone for him before Heaven.

The Gemara rejects this suggestion: There too, with regard to the purification process of a leper, one can explain that the oil atoned for one matter and did not atone for another: It atoned; in other words, the placement of oil on the leper’s right thumb and big toe, which was performed, effected its atonement. But it did not atone, i.e., there still needs to be an atonement effected by placement of oil on the leper’s head, and another log of oil must be brought for the performance of that act.

The Gemara returns to the matter of atonement for transgressions committed after the offering’s designation. Come and hear another proof from a baraita: Rabbi Shimon says: With regard to the communal peace offering of two lambs that accompanies the two loaves on Shavuot, for what sin are they brought?

The Gemara interrupts the citation of the baraita: The two lambs sacrificed on Shavuot are not brought for a sin; they are peace offerings brought with the annual public offering of two loaves of new wheat. Rather, the baraita should be emended as follows: For what sin are the goats sacrificed on Shavuot as a sin offering brought?

Rabbi Shimon answers: They are brought for the defiling of the Temple, by entering it while ritually impure, or for defiling its sacrificial foods, by partaking of them while ritually impure.

Rabbi Shimon continues: Once the blood of the first goat is sprinkled on the altar, thereby atoning for this defilement, for what sin is the second one sacrificed? It is sacrificed for any incident involving impurity that may have occurred between the sacrifice of that first goat and the sacrifice of this second goat. Based on this, say that the Jewish people should have had to sacrifice their offerings at all times and at every moment, as perhaps they sinned in the interim; but the verse spared them of this obligation.

The Gemara infers: And here, where an incident involving impurity occurred between the sacrifice of the two goats, is a case where the positive mitzva of distancing ritually impure people from the Temple was violated after the designation of the offering, as both goats were designated in advance. And nevertheless, the second goat atones for the violation. Evidently, an offering can atone for transgressions committed after its designation.

The Gemara rejects this inference: If both goats were designated simultaneously, this would indeed be evidence to that effect. But here we are dealing with a case where they were designated sequentially, and an incident involving impurity may have occurred between their respective designations.

The Gemara challenges this assertion: But shall we stand and say about the verse mandating these two sin offerings that when it is written, it is written specifically with regard to a case where they are designated sequentially?

Rav Pappa said the inference can be rejected for a different reason: Do you say that evidence can be adduced from communal offerings? Communal offerings are different, as the court makes a non-verbal stipulation about them, in accordance with what Rav Yehuda says that Shmuel says. As Rav Yehuda says that Shmuel says: With regard to communal offerings, the slaughtering knife, i.e., the act of slaughter, designates them for what they are. The court stipulates that the second goat be consecrated as it is sacrificed, and it therefore atones for incidents of impurity that occur beforehand. Individual offerings, by contrast, are all designated in advance.

Rav Yosef, son of Rav Shmuel, said to Rav Pappa: But does Rabbi Shimon accept the opinion that the court can make a non-verbal stipulation about communal offerings? Doesn’t Rav Idi bar Avin say that Rav Amram says that Rabbi Yitzḥak says that Rabbi Yoḥanan says: With regard to animals designated as daily offerings but which in the end were not necessary for use by the public,