Before us is Mishnah 5 in Chapter 3 of Tractate Zevachim. This mishnah comes to discuss someone who offered on an altar outside the Temple bounds more than what was supposed to be done with a regular offering in its proper place in the Courtyard. The fundamental rule, as we have seen throughout the entire chapter, is that in order for liability for kares or a chatas offering to apply for offering outside, it is required that if the action had been done inside it would have been valid and effective, at least after the fact.
Offering the chalavim and eimurim together with the meat:
The first case is "hamakriv chalavim ve'eimurim bachutz" - "one who offers chalavim and eimurim outside" - when one does not offer the eimurim alone, which belong on the altar, but rather offers them together with additional meat that is attached to them. In the case of offerings that are eaten, such as a chatas and an asham, the meat has no place on the altar at all: the meat is given to the kohen to be eaten, and only in the case of an olah does it go up on the fire. The question is, therefore, what is the law for someone who took the meat and the eimurim - the part that is offered - of a chatas or an asham and offered them together. Is this a valid offering?
The Mishnah states: "chayav" - "liable" - someone who does this on an altar outside the bounds is liable for kares if he did so intentionally. From here we see that this would indeed have been effective if it had been done on the altar inside, in its proper place.
The novelty here is that since the meat has no place being there, one might have thought that if the meat intervenes between the wood of the arrangement and the eimurim being burned, it creates a separation and invalidates the offering. For the verse explicitly demands: "ve'arechu bnei Aharon hakohanim es hanetachim... al ha'etzim asher al ha'esh" - "and the sons of Aharon the kohanim shall arrange the pieces... on the wood that is on the fire" - the kohen arranges the pieces that are to be burned upon the wood itself, and here the meat separates between the wood and the parts being offered, the intestines and kidneys and the like.
To this the Mishnah answers in the negative, by virtue of the rule "min bemino eino chotzetz" - things of the same species do not constitute a separation: a separation of the same type is not considered a separation. This is also the case with holding the Four Species on Sukkos - according to Ashkenazim, the koishiklach (woven holders) made from palm branches are not considered a separation between the hand and the lulav which is also made from palm branches, even though one does not hold the Four Species directly.
Hence, even though the meat has nothing to do on the arrangement, if it separates between the eimurim - which belong on the altar - and the wood of the fire, the offering is valid on the proper altar. Therefore, one who does this on an altar not in its place, outside the bounds, becomes liable for the sin of offering outside.
A minchah from which the handful was not taken:
The Mishnah further states: "minchah shelo nikmetzah vehikrivah bachutz - patur" - "a minchah from which the handful was not taken and he offered it outside - he is exempt". Why? Because if one offers the entire minchah from the vessel without a handful having been separated from it first, it is not a valid offering. The handful is what must go up, and even though it is included within the rest of the minchah, as long as it has not been separated by taking the handful (kemitzah), the minchah is not valid. Therefore, even outside the bounds there is no liability.
Taking the handful (kemitzah) in a minchah is parallel to slaughtering an animal offering. Just as one cannot place a whole animal on the fire and say that its blood is inside it and it is on the altar, but rather slaughtering is required, so too with a minchah, kemitzah is required - separating a handful of the fine flour to go up on the fire. Therefore, one who burns a minchah without kemitzah on an invalid altar outside the Temple is not liable for kares, since this would not have been effective even inside.
He took the handful and its handful returned into it:
However, "kametzah vechazar kumtzah letochah vehikrivah bachutz - chayav" - "he took the handful and its handful returned into it and he offered it outside - he is liable": the handful was separated, and afterwards that handful of fine flour was returned to the vessel with the rest of the fine flour, until everything was mixed together, and everything was offered on an altar outside its place - he is liable for kares, and if he did this unintentionally he must bring a chatas offering. The reason is: if this had been done in the proper place, he would have fulfilled the obligation of bringing the minchah.
This is, of course, not the ideal procedure: one is supposed to burn only the handful, and the rest of the minchah is meant to be eaten, as is the law for most minchah offerings. But after the fact, if the handful was separated and then returned and mixed into the rest of the minchah, and the entire mixture was placed on the fire - it is valid. And again, this is based on the very same principle: there is no interposition here, since it is a species mixed with its own species, and it is all minchah. And just as it is valid after the fact when this is done in the proper place, so too one is liable when he does it in an invalid place.
In summary: This Mishnah applies the general rule of the chapter - liability for offering outside the Temple depends on whether such an offering would be valid inside, at least after the fact. One who offers the sacrificial parts (eimurim) together with the meat is liable, based on the principle that 'a species does not interpose with its own species', even though the verse requires them to be placed "on the wood that is on the fire". One who offers a minchah from which the handful was not taken is exempt, since taking the handful is essential and is the equivalent of slaughtering an animal offering. However, one who took the handful, returned it to the minchah, and offered the entire mixture is liable, since after the fact it is a valid offering, and a species does not interpose with its own species.