and in this manner all forty se’a are ritually pure. The reason is that drawn water is purified by a majority of fit water that was already present in the ritual bath and by the drawn water flowing into the ritual bath. This is the meaning of the mishna’s statement that drawn water invalidates the ritual bath only according to calculation: One calculates the amount of drawn water that flowed into the ritual bath, as the ritual bath is invalid only if most of the forty se’a is of that drawn water.

The Gemara asks: If this is the opinion of Rabbi Eliezer ben Ya’akov alone, one must conclude by inference that the Rabbis hold that the ritual bath is not fit even by a majority of fit water and by the flowing of the drawn water. But if so, consider that which Ravin said when he came from Eretz Yisrael to Babylonia, namely, that Rabbi Yoḥanan said: A ritual bath that consists in its entirety of drawn water that one made flow into it is pure. In accordance with whose opinion is this? It is not in accordance with the opinion of the Rabbis, who maintain that drawn water invalidates the ritual bath even if it flowed into it, and it is not in accordance with the opinion of Rabbi Eliezer ben Ya’akov, who holds that drawn water invalidates the ritual bath if it constitutes a majority of the forty se’a.

Rather, Rabba says: The mishna’s ruling, that drawn water invalidates the ritual bath only according to calculation, is not referring to drawn water that flowed. Instead, it means according to the calculation of the number of vessels from which the drawn water was directly poured into the ritual bath, and this is in accordance with the opinion of Yosef ben Ḥoni.

As it is taught in a baraita: If three log of drawn water fell into the water of a ritual bath that lacked the requisite measure, from two or three vessels, with each containing at least one log of drawn water, or even from four or five vessels, where no whole log fell in at once, it invalidates the ritual bath. Yosef ben Ḥoni says: It is only if the drawn water was in two or three vessels that the water invalidates the ritual bath. But if the drawn water was in four or five vessels, the water does not invalidate the ritual bath. This is what the mishna means.

§ The mishna teaches: And the water of purification of the red heifer becomes water of purification only with the placement of the ashes into the water, but not by the placement of water onto the ashes. The Gemara asks: Who is the tanna whose opinion is reflected in this ruling? Rabbi Ḥiyya bar Abba said that Rabbi Yoḥanan said that it is not in accordance with the opinion of Rabbi Shimon.

As it is taught in a baraita: A sota, a woman suspected of unfaithfulness by her husband, must drink bitter waters prepared in the Temple. The verse states: “And the priest shall take holy water in an earthen vessel; and of the dust that is on the floor of the Tabernacle the priest shall take and put it into the water” (Numbers 5:17). This verse teaches that the water must be placed in the vessel first, and the dust is placed on top of it. If one places the dust in the vessel before the water, the mixture is unfit, but Rabbi Shimon deems it fit.

The Gemara explains: What is the reasoning of Rabbi Shimon? As it is written with regard to the red heifer: “And for the impure they shall take of the dust of the burning of the purification from sin, and place on it flowing water in a vessel” (Numbers 19:17). And it is taught in a baraita that Rabbi Shimon said: But is it dust [afar] that is taken? Isn’t it really ashes [efer]?

Evidently the verse altered its standard usage and referred to ashes as dust in order to derive a verbal analogy from it: “Dust” is stated in the verse here, and “dust” is stated there, with regard to the sota. Just as there, in the case of the sota, the verse teaches that the dust must be placed on top of the water, so too here, with regard to the red heifer, the dust, i.e., ashes, must be placed on top of the water. And likewise, just as here, with regard to the red heifer, if one places the dust in the vessel before the water, it is fit after the fact, so too there, in the case of the sota, if one places the dust in the vessel before the water, it is fit after the fact.

The Gemara asks: And here, with regard to the red heifer, from where do we derive that the mixture is fit even if the dust is placed first? Two phrases are written. First it is written: “They shall take of the dust of the burning of the purification from sin and place on it.” Apparently, the ashes should be placed in the vessel first and the water afterward. And then it is written: “Running water in a vessel,” indicating that the water should be placed in the vessel first, while it is still empty. How can these texts be reconciled? They can be reconciled by concluding that if he desires to place the dust, i.e., the ashes of the red heifer, below, and put water on top, he may do so; and if he desires he may place the water first and then place the dust above the water.

And the tanna of our mishna, who deems the mixture unfit if the ashes are placed first, what is his reasoning? He could say to you that the last clause of the verse: “Running water in a vessel,” is meant specifically, i.e., the water must be placed first. And when the verse states beforehand: “They shall take of the dust of the burning of the purification from sin and place on it,” this teaches only that after placing the ashes upon the water one is required to mix the ashes with the water, so that the water covers the ashes.

The Gemara objects: But one could just as easily say the opposite. What did you see that led you to say that the last clause of the verse is meant specifically? Perhaps the first clause of the verse is meant specifically. The Gemara answers: You cannot say so, as just as we find in every instance that the facilitating item goes above, e.g., in the case of a sota the dust, which enables the water to be used, goes on top of the water, so too here, in the case of the red heifer, the facilitating item must go above. The water must be placed first, and only then the ashes.

§ The mishna further teaches: And one beit haperas does not create another beit haperas. The Gemara comments: The mishna is not in accordance with the opinion of Rabbi Eliezer, as we learned in a mishna (Oholot 17:2) that Rabbi Eliezer says: One beit haperas creates another beit haperas. If one plowed from a beit haperas into another field, that field is also ritually impure.

The Gemara asks: And according to the Rabbis, who disagree with Rabbi Eliezer, how far does a beit haperas extend? When Rav Dimi came from Eretz Yisrael to Babylonia, he said that Reish Lakish said that Rabbi Shimon bar Abba said: