Yevamos, Chapter 8, Mishnah 4. The general rule is that a man who is incapable of fathering children is not included in the mitzvah of yibum, and therefore if his brother's widow comes before him, he is not fit to perform chalitzah or yibum. As we will learn in our Mishnah, however, this is not always the case.
The Words of Rabbi Yehoshua:
Rabbi Yehoshua testifies that he heard two rulings concerning a saris (a man incapable of fathering children, such as one whose testicles were removed). In his words: "Shamati she'saris choletz v'choltzin l'ishto, v'saris lo choletz v'lo choltzin l'ishto, v'ein li l'faresh" - "I heard that a saris performs chalitzah and chalitzah is performed for his wife, and that a saris does not perform chalitzah and chalitzah is not performed for his wife, and I cannot explain it."
"Saris choletz v'choltzin l'ishto" - there is a type of saris who is fit and obligated to perform chalitzah for his brother's widow, and if he dies, his own widow requires chalitzah. In other words, he is regarded as a man whose wife is included in the mitzvah of yibum.
"V'saris lo choletz v'lo choltzin l'ishto" - and there is a type of saris who does not perform chalitzah for his brother's widow, and if he dies, his wife does not require chalitzah, since her marriage was to a man incapable of having children.
The underlying principle: the purpose of yibum is to carry on the capacity to father children that the deceased did not merit in his lifetime, whereas a saris was never capable of fathering children at all. It emerges, then, that there is a type of saris who is included in the mitzvah of yibum and a type who is not. But Rabbi Yehoshua concludes "v'ein li l'faresh" - he was unable to explain which is which.
Rabbi Akiva's Distinction:
Rabbi Akiva said: "Ani afaresh" - "I will explain it." He had the distinction between the two types of saris:
"Saris adam" - one who became a saris in the course of his life through human intervention, and was not born that way. He performs chalitzah and chalitzah is performed for his wife, and he is included in the mitzvah of yibum, because he had a "sha'as hakosher": there was a period during which he was capable of fathering children and was included in the mitzvah, and therefore he remains included even after his condition changed.
"Saris chamah" - literally, a saris "from the sun": all his days, from the moment he emerged into the light of the sun, he was a saris, this being a congenital defect. Such a man does not perform chalitzah for his brother's widow, and if he dies his wife does not require chalitzah, since there was never a moment at which he was included in the mitzvah of yibum.
Rabbi Eliezer's View:
Rabbi Eliezer disagrees and holds precisely the opposite: a saris chamah, who was a saris all his days, performs chalitzah and chalitzah is performed for his wife, because this congenital condition has a remedy. A saris adam, however, to whom something happened in the course of his life that made him a saris, does not perform chalitzah, chalitzah is not performed for his wife, and he is not included in the mitzvah of yibum, because this case has no cure, and he is therefore considered as one who has left the mitzvah.
The Testimony of Rabbi Yehoshua ben Perachyah:
Rabbi Yehoshua ben Perachyah testified about an actual incident: there was a man in Jerusalem, ben Megusas, who was a saris adam, that is, one who became a saris in the course of his life, and when he died childless, yibum was performed with his wife. This testimony supports Rabbi Akiva's view, that one who reached his condition through human intervention, since he had a sha'as hakosher and was included in the mitzvah of yibum, remains included in it.
In summary: in this Mishnah we learned that although the rule is that one incapable of fathering children is not included in the mitzvah of yibum, this does not apply uniformly to every saris. Rabbi Yehoshua heard that there is a saris who performs chalitzah and one who does not, but could not explain which is which; Rabbi Akiva distinguished between a saris adam, who had a sha'as hakosher and therefore remains included in the mitzvah, and a saris chamah, who was never included in it; Rabbi Eliezer held the opposite, based on whether the condition has a remedy; and the testimony of Rabbi Yehoshua ben Perachyah about ben Megusas in Jerusalem supports Rabbi Akiva's view.