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The preparation of the mei chatat (the water used to purify a person that was tameh met) involved placing the ashes from the para aduma on natural spring water. This act is referred to as kidush mei chatat. The Mishnah (6:1) teaches that the water had to placed directly and intentionally. If the ashes fell into the water, it would not have been valid. Furthermore, if he intended to place the ashes directly in the water, but it landed and rested on the wall of the vessel before falling in the water it would also be invalid.
The Mishnah Achrona understands that in this case the ashes that fell could be recovered and used again for preparing the mei chatat. He reasons that nothing occurred to the water or ashes that would have rendered them invalid per se; the issue was the placement of the ashes. Recall that if one engaged in another activity between filling the water and placing the ashes, the water will be invalid. The Mishnah Achrona explains that even though the placement of the ashes in this case was invalid, it is not considered an intervening activity, since when the individual placed the ashes, he was intending to do so properly.
The Mishnah Achrona cites the Tosefta as a support for this conclusion. The Tosefta teaches that if wind blew the ashes into the water, one can dry the ashes and still use them for kiddush. If however the ashes had already been used for a valid kiddush, then R' Shimon and R' Meir maintain that it could still be dried and reused while the Chachamim disagree. Since the debate seems to only be when the ashes were used properly, it appears that everyone agrees that if they fell in, they can be reused. The Chasdei David explains that this is how the Rash understands the Tosefta.
What would be the reason to differentiate between the two cases? When explaining the position of the Chacahmim that the ashes cannot be reused, the Tifferet Yisrael explains that they cannot be used for kiddush of other water. He explains that this is because the mitzvah was already performed with these ashes. He continues that this is no different to the mei chatat. Once some of that water was used to purify someone, it cannot be collected and reused to purify someone else. It would follow that in our case, since the mitzvah of kidush was not fulfilled with the ashes, nothing should prevent them from being reused.
The Rambam (hilchot Para Aduma 9:3) however rules that in our case the ashes cannot be dried and reused. The Mishnah Achrona suggest that the Rambam simply had a different version of the Tosefta on which he based his ruling.
The Chasdei David maintains that the Rambam disagreed with the Rash's understanding of the Tosfeta. In other words, when the Tosfeta presents the position of the Chachamim, they argue in both cases. He explains that even though the ashes were not able to affect a valid kiddush, there landing in the water is considered enough of an act of kiddush to prevent them for being dried and reused.
The Aruch HaShulchan (Parah 68:11) presents another explanation. The next Mishnah (6:2) records the debate between R' Meir, R'Shimon and the Chachamim differently. The Mishnah opens and present the case as follows: "if the kiddush (i.e. the ashes) where floating on the surface of the water...". The Aruch HaShulchan notes that the Mishnah does not differentiate whether the ashes were placed there intentionally, or blown in. The Chachamim argue there that any of the ashes that got wet cannot be reused. The Aruch HaShulchan therefore suggests that the Rambam ruled according to the Mishnah in favour of the Tosefta.
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