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People in biblical times frequently came in the presence of dead bodies. So they must have needed a lot of the spring water mixed with red heifer ashes. But the Mishna says only 9 heifers were processed in history, with 1,000 years between the first two. So they must have highly diluted the ashes to accommodate everybody. (Halacha does not specify a density.) In fact, I read that much water was left over and used after the Second Temple was destroyed. Why didn't they keep diluting it to make it last indefinitely?

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    Assertion #1: "People in biblical times frequently came in the presence of dead bodies. " - says you. Actually, they kept far away from dead bodies so as not to have to deal with the purification process. – Danny Schoemann Jul 5 '17 at 14:38
  • Assertion #2: "Halacha does not specify a density" - says you. Actually, the Mishna explicitly says that if you can see the ashes floating on the water (when you first add them), it's sufficient. – Danny Schoemann Jul 5 '17 at 14:39
  • 1-They frequently did not have a choice. 2-The ashes will float even on the ocean. – Maurice Mizrahi Jul 5 '17 at 21:37
  • related: judaism.stackexchange.com/q/105467/170 – msh210 Jul 10 at 14:25
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Rambam Parah Adumah 9:8 says that once the water has been mixed with the ashes, no further water can be added to further dilute the mixture. Once it has been made, an additional Parah Adumah is required to make more and add to the water. Thus, if any other water accidentally drops in, the entire mixture is pasul.

When even the smallest amount of other water - even water that was drawn for the sake of the ashes of the red heifer - becomes mixed with sanctified water, it is disqualified. Similarly, if dew descends into such water, it is disqualified. If other liquids or fruit juices fall into it, the entire quantity should be poured out. The container must be dried; only afterwards can other sanctified water be placed in it.

If ink, black earth, or dark earth, or any entity that leaves a mark falls into such water, it must be poured out, but there is no need to dry the container. The rationale is that if any portion of the entity that leaves a mark will remain, it will be apparent.

The Mishna in Para (3:5) states that there were 9 para adumahs in history. The Mishna states that Moshe (really Elazar) made a Parah Aduma and that Para Adumah lasted until Ezra which is about 800 years and then Ezra made a Parah Aduma when they returned from Bavel. Then, in the period of the second Beis Hamikdash they made an additional 7 para adumahs.

This means that for the first 800 years, they were able to use the water that Moshe made and keep putting the remainder (aside from the few drops sprinkled) back in the container. This is like the anointing oil used for the Kohen gadol that Moshe made. From Ezra to the destruction of the second temple, they used 8 such cows.

It appears that either they were unable to keep the water completely pure during the second temple, or they decided to make more as they found a cow that could be used for Parah Adumah because of the fear that they might run out. Seven in 420 years is once every 60 years, so it might be once a yovel.

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    There was no limit on the amount of wood to be used to burn the poroh. And all the ashes were kosher for use. So I always thought that they kept ashes and added water as needed. Moreover, there is no limit to the initial amount of water to be used. – Avrohom Yitzchok Jul 5 '17 at 8:40
  • Thanks, @sabbahillel. Do you know the Rambam's source and/or logic in so ruling? Also, he says the 10th and last parah adumah will be in the days of Mashiach. Again, do you know his source and/or logic? Is he just saying that on his own authority? – Maurice Mizrahi Jul 5 '17 at 21:36
  • @MauriceMizrahi I would guess that once the mishna said that 9 had been brought before the destruction of the second temple, then the tenth by definition would be after the rebuilding of the temple when the mashiach comes. – sabbahillel Jul 5 '17 at 22:57
  • @sabbahillel But what about the Rambam's opinion that no new water must be added to an existing mixture of water and ashes? What was his source? – Maurice Mizrahi Jul 6 '17 at 16:02
  • @MauriceMizrahi The Rambam tends not to give sources for his rulings or citations. In fact there is a story that he said that had he rewritten it, he would have given sources. However, as we see from the writing, he normally does not give a source. – sabbahillel Jul 6 '17 at 16:36

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