How many people can a פרה אדומה be מטהר? Part 1
How many "doses" can 1 פרה אדומה provide? How much ashes can there possibly be from 1 cow? It is not clear to me from the Mishnayos or the Rambam exactly how much ashes needs to be in each "dose" the one thing it does say is that you need to see the ashes in the water which means that you need more then a drop of ashes. I don't see how the ashes of 1 cow could provide millions of "doses" which is what it sounds like, see below.
The Mishna in Para (3:5) states that there were 9 פרה אדומה in history. However, the distribution is very puzzling. The Mishna states that Moshe (really Elazar) made a פרה אדומה in the מדבר and that פרה אדומה lasted until the time of Ezra which is about 800 years and then Ezra made a פרה אדומה when they returned from בבל. Then, in the period of the second בית המקדש they made an additional 7 פרה אדומה. How is it possible that from Moshe until Ezra one פרה אדומה was enough to be מטהר everyone while in a much shorter period from Ezra until the destruction of the second בית המקדש they needed 8? What changed between the period of the שופטים and the first בית המקדש and the second בית המקדש that required so many more פרה אדומה in the second בית המקדש? Going back to my original question how could 1 פרה אדומה possible have enough ashes to מטהר everyone for 800 years? Did people not become טהור in that time period?
[Update] It was pointed out in the comments that the ashes come not only from the cow but also from everything (wood, etc.) that was used to burn the cow which would additional ash. However, I don't think that it dramatically changes things, even adding in the wood that was burned teh questions above still remain.