Temurah, Chapter 1, Mishnayos 1-5. The Mishnah brings here a series of cases that have no connection to one another in terms of their subject matter, but that all resemble the law of "a temurah cannot create another temurah": something upon which sanctity has taken effect, and yet it lacks the power to transfer that sanctity onward.
The first case - the waters of the chatas:
The preparation of the purifying waters has two basic components:
Living water - water from a spring.
The ashes of the parah adumah - the ashes of the red heifer that was burned.
The main novelty of the Mishnah lies in the order in which they are placed: first the water is put into the vessel, and afterward the ashes are placed on top of it. In this order the waters of the chatas are created - purifying waters that are effective in purifying someone who contracted tumah from a corpse, while they themselves convey tumah to those who handle them. But if it was done in the reverse order, the mixture has no status at all: it is neither a source of purity nor a source of tumah.
And why is this law taught here? Because the ashes too are holy and designated for the chatas, fit and consecrated for this purpose; and nevertheless, if the technical details were not observed, the ashes do not transfer their sanctity so as to create something of greater effectiveness - the waters of the chatas. This is similar to a temurah, which, although it is sanctified, does not transfer its sanctity onward. That is the connection, loose as it may be, between these laws.
The language of the Mishnah: "Ein mei chatas na'asin mei chatas ela im matan efer" - the water does not become the waters of the chatas until the ashes are placed into it, meaning that the water comes first from the spring, and the ashes are placed on top of it. The reverse order is ineffective.
At first glance one could raise an objection from the verse in Parashas Chukas: "And they shall take for the impure person from the ashes of the burning of the chatas, and he shall put upon it living water" - it emerges that the ashes come first and the water is placed on top of them, so how could the Mishnah rule the opposite? The answer is found in the continuation of the verse: "living water into a vessel" - the spring water must be placed into an empty vessel, and from here we learn that the water comes first and the ashes come on top of it. If so, what does "and he shall put upon it living water" come to teach us? An additional law: after the ashes are placed in, one must mix the mixture with a finger, so that the water at the bottom rises up over the ashes. Thus this law too is derived from the verse itself.
The second case - beis haperas:
A beis haperas is a questionable cemetery, a field suspected of tumah. The case under discussion: a grave or a known cemetery that was plowed over. When a cemetery is plowed, the blade of the plow - the large metal blade that enters the ground - is liable to catch the corpse itself and drag the bones from their place. And even a bone the size of a barleycorn, a bone the size of a grain of barley, is a source of tumah, and one who touches it becomes tamei. Because of this concern, a kohen may not enter there - not because it is a definite cemetery, but because it is a suspected cemetery, it is a beis haperas.
How far does the beis haperas extend? How do we know that the bones were not dragged an enormous distance from their place? The Sages established that we must be concerned about the bones having been scattered up to one hundred amos from the known grave, and of course in the direction in which the plowing was done. Thus, if a grave is located at the eastern end of the field, and the field was plowed from the grave westward, we must be concerned for up to one hundred amos from that grave, and a kohen may not enter this area, lest he step on fragments of bone dragged along by the plow or come into contact with them.
So we have two levels before us: the grave or the definite cemetery, and the beis haperas - the suspected cemetery. And what is the law if the following year the farmer plows the beis haperas itself, and this time from south to north? Should we be concerned that in the first year the bones were dragged westward, and in the second year northward, and that over time the beis haperas will keep spreading further and further? The answer is no. The maximum we are concerned about is one hundred amos from the grave and no more. Even though you plowed the beis haperas and there may well be bones in it, we do not suspect that the bones of the first beis haperas were dragged more than one hundred amos from the original grave and created a second beis haperas.
This principle - that the first beis haperas does not create a second beis haperas - parallels beautifully the law that a first substitute does not create a second substitute, and that is why it is taught here. And this is the language of the Mishnah: "ein beis haperas oseh beis haperas" - a beis haperas does not create another beis haperas.
The third case - "v'lo Terumah achar Terumah" (nor Terumah after Terumah):
The simple meaning is that one may not separate Terumah after Terumah has already been separated, but the Bartenura explains it in an entirely different way. There is a rule that first one separates from the produce the first portion given to the kohen, and that is called Terumah, ideally about two percent - that is the general estimate of the measure of Terumah. And only the owner of the produce may separate Terumah from it; if I separate Terumah from my friend's produce, that separation has no validity whatsoever, and it has no status of Terumah, but rather it may still be eaten even by someone who is not a kohen.
When the produce belongs to two partners, both of them are its owners, and neither one may separate without his partner's consent. Therefore, if Reuven separated Terumah from the produce, and afterward his partner Shimon separated Terumah from that very same produce, it is clearly evident that they did not consult one another - for if they had, why would Shimon separate after Reuven had already separated? And since this is so, not only did Shimon not give Reuven permission to separate, but Reuven likewise did not give Shimon permission to separate, and it turns out that both of them are separating from what is not fully in their control, and their separation is not valid, and both of them have to start over.
This is the intent of the Mishnah, "v'lo Terumah achar Terumah": when a second Terumah was taken after the first, the second is not Terumah, and the first is not Terumah either, since the very fact that the second partner separated shows that the first was not authorized to separate in the first place, and vice versa.
"V'lo temurah osah temurah" - nor does a substitute create a substitute:
From here the Mishnah returns to our subject. If you have animal A, which is consecrated as an olah, and you said that you want animal B to be its substitute - this is a valid temurah, and it takes effect: animal B becomes consecrated and the sanctity of an olah rests upon it. But if you said that you want animal C to be the substitute of animal B - this does not take effect, and animal C remains chullin. It turns out that the substitute animal does not create a substitute.
"V'lo havlad oseh temurah" - nor does the offspring create a substitute:
The same applies to the animal's offspring. I consecrated a cow as shelamim, and it gave birth to a calf - the offspring too has the status of shelamim, but it is not the source of the consecration. If I substitute a cow, a goat or a sheep for the original shelamim cow, the second animal becomes a temurah and becomes consecrated; but if I try to substitute an animal for a calf just born from the shelamim cow, the substitution is not valid, since the calf is not the source of the consecration. And the basis for this is in the verse: "hu u'temuraso yihyeh kodesh" - "it and its substitute shall be holy": the verse uses the singular, its substitute and no more than that.
The dispute between Rabbi Yehudah and the Sages:
Rabbi Yehudah says: the offspring does create a substitute - the offspring born from the mother can indeed create a temurah. He too agrees that the verse says "temuraso" in the singular, but the word "yihyeh" is also stated, and it comes to teach that even the offspring makes the second animal a substitute.
And the Sages disagree - they do not accept this derivation, since in their view "yihyeh" comes to teach a different law: one who makes a substitution unintentionally, such as where he meant to say that the white cow should be the substitute and in the end said that the black cow should be the substitute - the black cow is the one that becomes the substitute. And this is an exceptional matter, since generally with sacrifices and consecrations a person is required to say what is in his heart and to intend what he said, whereas regarding temurah this leniency, or this stringency, whichever way you want to call it, was stated.
Their words are as follows: "Amru lo: hekdesh oseh temurah, velo ha'vlad velo temurah oseh temurah" - only the original consecrated animal can create a temurah, whereas the temurah and the offspring cannot create a temurah. And the halachah follows the Chachamim.
The Bartenura is quick to add that although the offspring and the temurah cannot create a temurah, the original animal can create many temurah animals. If a person brought ten new animals one after another to exchange for the original animal, each one of those ten animals becomes a temurah, and each one is a separate prohibition for which he receives lashes on its own - whether he did so one after another or all at once.