Parah, Chapter 3, Mishnah 11. This chapter traces the preparation and burning of the parah adumah from beginning to end. Our mishnah brings the process to its conclusion: the cedar wood, hyssop and crimson wool are thrown into the fire, the burned remains are processed into ashes, and those ashes are then divided into three portions, each with its own purpose.
The bundle
"Krachan bishiyarei halashon": the kohen took the three items, the stick of cedar, the eizov and the wool dyed crimson, and fastened them into a single bundle using the strip of crimson thread left over from the tongue that had been used earlier. Why tie them together at all? The reason is practical: a bound package carries enough weight to be aimed properly, and none of the three will drift off to the side instead of reaching the flames. "Vehishlich lesoch sereifasa": he then flung that bundle into the fire that was consuming the cow.
Reducing the remains to ashes
"Nisrefah": once the cow had burned completely. "Chovtin osah bemaklos": the remains were struck with rods to break them apart, "vekoverin osah bikevaros": and afterward passed through sieves. There is a second view on the tools employed. "Rabbi Yishmael omer", and his opinion is that the implements themselves were made of stone: "bemakavos shel even", mallets hewn from stone, "uvkivaros shel even hayesa na'aseis", and stone sieves as well, were what this work was carried out with.
A charred fragment that still held ash within it, "shachor sheyesh bo eifer", was pounded down further, "kotshin oso", so that the ash inside it would not go to waste. One that no longer held any ash, "ve'she'ein bo", was left untouched, "manichin oso". A bone, though, "ha'etzem bein kach uvein kach", was treated the same way in either case, whether ash appeared to be in it or not: "haya niktash", it was ground up.
Three portions
"Vecholkim oso lishloshah chalakim": the ash that resulted was separated into three shares. The first, "echad nitan bachel", was deposited in the chel, the rampart that surrounded the Har Habayis. The second, "ve'echad nitan behar hamishchah", was placed on Har Hamishchah, the Mount of Anointing, which is Har Hazeisim. The third, "ve'echad haya mischalek lechol hamishmaros", was apportioned out among the mishmaros, the rotating watches of kohanim.
Each portion served a different function. The share kept in the chel was stored there as a safeguard for the generations to come. The share on Har Hamishchah was drawn upon by the kohanim when they needed to prepare the mixture of ashes and water. And the share divided among the mishmaros was the working supply, used for sprinkling upon those who required purification.