We are starting the ninth and final chapter of Tractate Bechoros, and its topic is not the bechor but ma'aser beheimah - the tithe of animals in a person's possession. The topic was placed here in Tractate Bechoros because many halachos are shared between ma'aser and bechor due to them being korbanos: both are offered in the same way with a single application of blood, the eimurim are offered as usual, and both are eaten in Jerusalem as kodashim kalim. The difference between them: the bechor is the property of the kohen and is eaten by him and his household, while the ma'aser is the property of the animal's owner - the farmer, whether he is a kohen or not a kohen, brings it as a korban and eats it himself.
The procedure for separating ma'aser beheimah:
Once a year, with the years being counted from Rosh Chodesh Elul to Rosh Chodesh Elul, a person is obligated to tithe all his animals in each of his herds. A flock of tzon is all the goats and sheep together, and a herd of cattle is all the cows and bulls together. The procedure for tithing is:
He gathers all the animals of the herd into the pen. If he has, for example, fifteen cows - he brings in all fifteen.
The tenth animal that emerges from the pen is marked with a red mark, so that it will be recognizable which of them is the ma'aser.
He consecrates it verbally and designates it as ma'aser, by saying: "This is ma'aser", and thereby it becomes consecrated as ma'aser beheimah.
An unblemished animal: If it is unblemished and fit for a korban, the sanctity of the Altar takes effect upon it - an inherent sanctity of the body - and it is offered as a korban.
A blemished animal: If it develops a blemish and cannot be offered, it is eaten immediately in its place without any further restriction.
Even when he brings it as a korban, he brings it up to Jerusalem and eats it there - but he himself is the one who eats it. Ma'aser should not be viewed as a sort of tax that the person loses out on; the animal remains his, except that he brings it before Hashem as a recognition that everything in his possession comes from Him, may He be blessed.
"Ma'aser beheimah noheig ba'aretz uv'chutz la'aretz, bifnei habayis veshelo bifnei habayis" - Ma'aser beheimah applies in Eretz Yisrael and outside of Eretz Yisrael, when the Temple is standing and when the Temple is not standing:
The source of the mitzvah is in the verse: "And all the tithe of the herd and the flock, whatever passes under the rod, the tenth shall be holy to Hashem" - all the animals, the cattle and the flocks, the goats and the sheep, pass under the rod (the staff), and the tenth becomes holy. This halachah applies equally in Eretz Yisrael and outside of Eretz Yisrael, and equally during the time when the Beis HaMikdash stands and the time when it does not stand; even today there is a mitzvah to separate the tenth animal as ma'aser beheimah.
However, when the Beis HaMikdash does not exist, or when a person lives outside of Eretz Yisrael and cannot bring it up, the tenth animal is in a sort of waiting state until it can be offered as a korban. He is not permitted to do anything with it: shearing and working with it are forbidden just as with a bechor - they do not shear it, do not work with it, and do not milk it if it is a sheep - and he waits to bring it as a korban. If a permanent blemish develops in it, he is permitted to slaughter it from that moment and eat it in his location, without any further requirements of sanctity or a korban, similar to the halachah of a bechor.
Already in the Talmudic period, Chazal noted that in the absence of the Beis HaMikdash, this is a mishap waiting to happen: years might pass until a blemish develops in the animal, and it is possible that a blemish will not develop in it at all. They were therefore concerned that people would have consecrated animals roaming in the herd, and ultimately they would stumble and shear them, work with them, or milk them. Therefore, they suspended the matter for the time being, and the halachah and custom today is not to separate ma'aser beheimah, since there is no possibility of bringing it as a korban.
"Bechullin aval lo bekodashim" - the obligation applies to chullin animals only and does not include consecrated animals. An animal that was already separated for a chatas or a shelamim does not enter the pen and is not counted among the animals passing for the count of the tenth, because the verse says that the tenth shall be holy - and if it is already holy, this does not apply to it.
"Venoheig babakar uvatzoan" - in cattle, meaning cows and calves in their first year, and in flocks, meaning small livestock: specifically goats and sheep. The matter is explicit in the verse: "And if his korban is of the flocks, of the sheep or of the goats" - the flocks include the sheep and the goats. These three species, cows, goats, and sheep, are always counted as a single list, since they are the only species of animals fit for a korban.
"V'ein ma'asrin mizeh al zeh" - And we do not tithe from this for this. We have two subcategories before us: cattle on one side, and the flock - goats and sheep - on the other, and we do not tithe from one for the other. We do not bring goats and cows together into the corral and mark every tenth animal that goes out the opening, because in this way one will come to tithe goats for cows or vice versa. Rather, one brings all the cows into one corral and tithes, and all the goats and sheep into a separate corral and tithes.
It is worth noting: if he had fewer than ten animals, there is no separation of the animal tithe here, since he will not reach the count of ten. If he had nineteen cows, he brings all of them into the corral, and only one, the tenth to exit, becomes tithe. If he had twenty, he has two, the tenth and the twentieth.
As for sheep and goats, we tithe from one for the other. That is, if there are ten goats and ten sheep in the flock, he brings all of them into the corral, and those that exit at the tenth and twentieth count are both sanctified as tithe, and there is no difference if both are goats or both are sheep.
Furthermore, the tithe applies to animals born this year and those born last year: if he did not tithe his animals last year, he is obligated to tithe them this year. However, we do not tithe from one for the other - those born this year are counted as one group, and those born last year as a separate group. Therefore, if he had five from last year and five from this year, he does not bring any of them into the corral; and if he had ten this year and ten last year, he must perform two separate tithings.
The question based on a kal vachomer:
The last part of the Mishnah raises a wonder based on the rules of Talmudic logic: why do we combine the goats and the sheep together, while we do not combine those born this year with those born last year? After all, the new and the old are similar to one another - this year's cows and last year's cows, this year's sheep and last year's sheep, and what is the difference between them? But goats and sheep differ completely from a halachic standpoint: they are kilayim (a prohibited mixture) with one another, and a Torah prohibition applies to them in two separate prohibitions - we do not work with a goat and a sheep together, and we do not crossbreed them with one another. We find that goats and sheep are separate species, and it is therefore perplexing that it is permitted to tithe them as a single unit: for if he has five goats and five sheep, an obligation is created to tithe them as a single flock of ten, and he is permitted to take one of this species and one of the other species; and if he has ten of each species, he can take two goats and thereby the sheep are exempted.
And in the words of the Mishnah: "Shehayah bedin" - For it would have been logical, as logic and the rules of kal vachomer would dictate; "mah im hechadash vehayashan she'einen kilayim zeh bazeh" - if the new and the old, which are not kilayim with one another - the animals of this year and the animals of last year are not kilayim with one another, and it is permitted to crossbreed them together and to do work with them together, and nevertheless "ein ma'asrin mizeh al zeh" - we do not tithe from one for the other, as we treat them as two separate groups; "hakevasim veha'izim shehem kilayim zeh bazeh" - the sheep and the goats, which are kilayim with one another - they are halachically separate, kilayim with one another, and it is forbidden to crossbreed them together and to do work with them together, "eino din shelo ya'asru mizeh al zeh?" - is it not logical that they should not tithe from one for the other? Does reason not dictate that he would not be permitted to bring twenty animals, ten goats and ten sheep, into one corral and take out two goats that exempt the sheep?
"Talmud lomar" - The verse comes and explicitly teaches the opposite of this logic: "vechol ma'asar bakar vatzon kol asher ya'avor tachat hashavet" - And all the tithe of the cattle and the flock, whatever passes under the rod. "And the flock" includes both sheep and goats, and they all pass together under the rod upon their exit from the corral; "mashma" - meaning, from here we learn that all animals in the flock category, sheep and goats alike, are included together. And as mentioned above, this is explicit in the verse: "And if his offering is of the flock, of the sheep, or of the goats" - the sheep and the goats are included together. Consequently, the halachah is that there are only two groups here: all the cattle in one corral, and the entire flock - goats and sheep together - in another corral.
Regarding the halachah, one point should be added: the Bartenura explicitly states that the first of Elul is the new year for the animal tithe, in accordance with the first Mishnah in Tractate Rosh Hashanah. However, it makes sense that the Rambam holds in accordance with the other opinion, that the first of Tishrei, the regular Rosh Hashanah, is the beginning of the new year for the animal tithe, and it is the determining date. Thus, even though we explain the Mishnah in accordance with the Bartenura's approach, the practical halachah for the animal tithe will be in accordance with the opinion of the Rambam.