Menahot, Chapter Four, Mishnah Five
This mishnah deals with the minhah offering that the high priest offers every day (Leviticus 6:13-15). This offering had to consist of a tenth of an ephah of fine flour, half of which was offered in the morning and half in the evening. It was fried in oil on a pan, and hence they are called griddle-cakes.
1) The high priests griddle-cakes cannot be brought in [two separate] halves. Rather he must bring a whole tenth and then divide it, offering a half in the morning and a half towards evening.
2) If a [high] priest offered half in the morning and then died and they appointed another priest in his place, [the successor] may not bring a half-tenth from his house, neither [may he use] the remaining half-tenth of the first [high priest]. Rather he must bring a whole tenth and divide it, and offer one half and leaving the other half goes to waste.
a) It turns out that two halves are offered and two halves go to waste.
3) If they did not appoint another priest in his place, at whose expense was it offered?
a) Rabbi Shimon says, at the expense of the community;
b) But Rabbi Judah says: at the expense of his heirs,
c) And a whole [tenth] was offered.
Section one: The high priest is not allowed to bring the griddle-cakes in two halves, half of a tenth in the morning and half in the evening. Rather, he must bring the entire tenth in the morning and then divide it in half, offering a half in the morning and the other half in the evening.
Section two: If the high priest offers half in the morning and then dies, and the court appoints a new high priest, the new high priest must bring an entire tenth of flour, and only offer half of it. The second half of the previous high priests offering goes to waste, as does half of the new high priests offering. We should note that this is just the kind of scenario that the rabbis love to discuss.
Section three: If the court didnt appoint a new high priest, there is a debate as to who is responsible to offer the minhah. According to Rabbi Shimon, the community had to pay for the offering, whereas Rabbi Judah holds that the high priests heirs must offer it.
Furthermore, in such a situation, in both the morning and evening a full tenth would be offered.