Kilayim, Chapter 2, Mishnah 1. Our Mishnah deals with a mixture of seeds: there is a measure and quantity in which there is a problem of kilayim, and there is a measure in which there is no problem at all. And this is the rule: if one twenty-fourth of the quantity of seed set aside for planting consists of another type of seed, that is a problem of kilayim; but if another species became mixed in at less than one twenty-fourth, it is permitted.
The reasons for the leniency in a minimal measure:
The approach of the Tosafos Yom Tov: The Torah forbade sowing kilayim by Torah law only when a person wants there to be kilayim here. But when he has no interest in it, and the mixture came about in a way that he never actually asked for, there is no Torah prohibition. The Sages forbade it because of appearances - because it looks like kilayim that were made intentionally - and therefore they gave a measure: from when is the matter considered a question of appearances. Below that measure the Sages did not forbid it.
The approach of the Rashba: When we are speaking of a very small percentage, it is extremely difficult to separate it out, and as the well known expression puts it, "the Torah was not given to the ministering angels" - therefore the Sages did not forbid it at such a minimal percentage.
An additional explanation: Since people are not particular about a mixture containing a tiny quantity, we view the entire mixture as though it were of one species only, and we do not count the second species as being present there at all.
The wording of the Mishnah:
"Kol se'ah sheyesh bo rova mimin acher" - any measure of a se'ah that contains a quarter of a kav of another species. This measure is one twenty-fourth, since there are six kabin in a se'ah, and a quarter kav is one out of four - four times six gives one twenty-fourth. Once the other species reaches this measure within the majority species, one must reduce it and make sure that the percentage will be less than one twenty-fourth. There are two ways to do this, and this is the view of the first Tanna:
Adding: to add more of the majority seed.
Removing: to take away from the minority seed, until it is less than one twenty-fourth.
Rabbi Yosi disagrees and says that one must sort it out entirely: once a person has begun the process of separating out the minority seeds, he is obligated to get rid of all of them, so that he should not appear to be maintaining kilayim. However, if from the outset the mixture was brought and it contained less than one twenty-fourth, there is no concern for this even according to Rabbi Yosi; but if it contains more than the measure and he began removing from it, he must finish the job until none of it is left.
One species or two species:
The Mishnah adds that the minority seeds that can create a problem at the measure of one twenty-fourth are "bein mimin echad bein mishnei minin" - whether they are one minority seed or two minority seeds. For example, the majority species is wheat, and both barley and spelt are mixed into it: the barley and the spelt combine together, and if together they make up one twenty-fourth, that is a problem.
Rabbi Shimon disagrees and says: "Lo amru ela mimin echad" - it is a problem only when the minority consists of one species of seed, but two species of seed in the minority do not combine to create a problem.
"VeHachachamim omrim: kol shehu kilayim ba'se'ah mitztaref larova" - any species of minority seed that is considered kilayim with the majority seed in the se'ah combines to make up the quarter, the quarter kav that is one twenty-fourth. That is, if there are two types of seed that we know are kilayim with the majority species, that is a problem.
What, then, is the novelty in the words of the Sages?
Seemingly their words are identical to those of the first Tanna, with whom Rabbi Shimon disagreed, but the commentators explain the difference: according to the first Tanna, even if one of the two minority seeds is not of the type that is considered kilayim with the majority seed, it still combines with the other minority seed to create a problem. For example, the halachah is that oats are not considered kilayim with barley. If the majority seed in the se'ah is barley, and mixed into it are spelt - which is considered kilayim with barley - and also oats: according to the first Tanna the spelt and the oats combine and are considered kilayim if together they reached the measure of one twenty-fourth, even though oats on their own are not kilayim with barley; the very fact that it is another species, when it joins another species that is kilayim, is considered a problem. But according to the Sages, there is no combining unless both minority species are kilayim with the majority species.
In summary: In this Mishnah we learned the measure of a mixture in seeds - a quarter kav in a se'ah, which is one twenty-fourth. Below that there is no problem, since the matter was forbidden only because of appearances, given that people are not particular about it and it is also difficult to separate out a minimal mixture. If the mixture reached the measure, he should reduce it, either by adding majority seed or by removing minority seed, and according to Rabbi Yosi, once he has begun sorting he must sort out all of it. And the Tannaim disagreed about combining two minority species: the first Tanna combines even a species that is not kilayim with the majority, Rabbi Shimon does not combine two species at all, and the Sages combine only species that are themselves kilayim with the majority species.