Rambam - 1 Chapter a Day

This expression implies that the red heifer should be burnt outside, not only of the Temple Mount (which is equivalent to the Camp of the Levites), but outside the city of Jerusalem (which is equivalent to the Camp of the Israelites). And indeed, the Mount of Olives was outside the entire city. In contrast, there were sacrifices that were disqualified which were — as stated in Hilchot Ma’aseh HaKorbanot 7:4 — burnt on the Temple Mount (Rambam LeAm).

The Mount of Olives is positioned directly behind the Temple Mount, but the Kidron Valley is interposed between them. The ramp would run from one mountain to the other.

In his Commentary to the Mishnah (Parah 3:5), the Rambam explains that if there is impurity under the sides of one arch, there will be hollow space above it, covered by a second arch. Thus a person standing above will not contract impurity.

See Chapter 2, Halachah 6. With regard to the Mount of Olives, such a ramp was a necessity for it was — according to tradition, even in the era of the First Temple - used for burial.

See Chapter 1, Halachah 14.

I.e., this is the way they imparted impurity to him when they did not have the carcass of a crawling animal or an object that imparts ritual impurity. Since the elders had not immersed with the intent of offering the red heifer, they are considered impure with regard to it. And by touching the priest, they make him impure as well.

As, in fact, all the red heifers brought during the Second Temple were.

This stipulation is made only with regard to the fig wood, because other species of wood are naturally smooth [the Rambam’s Commentary to the Mishnah (loc. cit. 3:7)]. Diagram

In the above source, the Rambam emphasizes that the intent is that its base is wider than its upper surface.

I.e., open places to allow air to enter and enable the fire to catch quickly. (ibid.).

Our translation quotes Rav Kappach’s translation of the Arabic term used by the Rambam in his Commentary to the Mishnah (loc. cit.:8). The Kessef Mishneh emphasizes that such a rope is not susceptible to ritual impurity.

I.e., facing the Holy of Holies.

In the palm of his hand; he would not use a container (Sifri). Although the blood of sacrificial animals had to be received in a container held in one’s right hand, there were no such requirements for receiving the blood of the red heifer.
The Ra’avad states that although the priest would receive the blood in his hand, the heifer is not disqualified if he receives it in a container.

The finger that is next to the thumb.

See Chapter 4, Halachah 5.

In his Commentary to the Mishnah (loc. cit.:8), the Rambam. states that this is derived from the wording of the prooftext “And he shall dip his finger... and sprinkle.” Implied is that there should be a dipping for each sprinkling.

Plural, i.e., the right hand which he had used for sprinkling and the left hand in which the blood was held.

In his Commentary to the Mishnah (loc. cit. 3:9), the Rambam. writes that he could not find a figure for the minimum required length for the branch of cedar wood.

A sela was a coin used in the Talmudic era. Shiurei Torah states that five selaim are equivalent to 101 or 96 grams.

In addition to this rationale, some have pointed out that — just as was done with regard to the harvesting of the Omer (Hilchot Temidim UMusafim 7:11) — the process of questions and answers drew attention to the offering and thus reinforced the Rabbinic tradition with regard to a matter concerning which the Sadducees had raised issues.

A herbaceous climbing plant.

Rav Kappach identifies this dye with the color argaman, usually translated as “purple.”

The type of dye required by the Torah, Numbers 19:6.

Our translation is based on the Rambam’s Commentary to the Mishnah (Keilim 26:3). The term refers to a shrub of the rhus genus that has clusters of green flowers, red hairy berries, and feathery leaves.

For in neither instance would the term “conflagration of the heifer” be appropriate (Sifri).

I.e., the procedure outlined by the Rambam above in which the three are bound together and cast into the belly of the heifer is the optimum way of performing the mitzvah, but it is not an absolute requirement.

To reduce them to small pieces.

As the Rambam emphasizes in his Commentary to the Mishnah (Parah 3:10), the fundamental concept gleaned from this halachah is that “the ashes of the red heifer” that are preserved included, not only the ashes of the red heifer itself, but also the ashes of all the wood used to burn it. See also Chapter 4, Halachah 16.

Here the term “camp” refers to the camp of the Divine presence.

A rampart that surrounded the wall of the Temple Courtyard (Hilchot Beit HaBechirah 5:3).

In his Commentary to the Mishnah (Parah 3:10), the Rambam states that this refers to the 24 guardposts at which the priests and Levites would stand watch over the Temple. See Hilchot Beit HaBechira 8:4-5.

Seemingly, this refers to the ashes mentioned in Chapter 2, Halachah 6.

And its ashes were used throughout the forty years in the desert, the 440 years before the First Temple was built, and the 410 years that the First Temple stood.

After the return to Zion following the Babylonian exile, when the Second Temple was built.

Parah 3:4 relates that two were offered by both Shimon the Just and Yochanan the High Priest, and one each were offered by Eliyahu Eini ben Hakaf, Chanamael the Egyptian, and Yishmael ben Piabi.

Likkutei Sichos, Vol. 28, questions the rationale for the inclusion of this halachah. After all, the Mishneh Torah is not a book of history, but a text of halachah, Jewish Law. It mentions points of history only inasmuch as they affect Jewish Law. Why then are the different red heifers brought previously recounted? And why is a prayer for Mashiach’s coming mentioned?
Likkutei Sichot answers by pointing to a difference between the Rambam’s treatment of the subject here and its treatment in his source, the Mishnah, Parah, loc. cit. The Mishnah mentions the heifers brought in previous generations as part of its description of the process of preparing the priest to offer the red heifer (as mentioned inch. 2 above). The Rambam, by contrast, mentions it as part of the commandment to set aside a certain portion of the ashes for safekeeping without any consideration of the function that they would play.
For this reason, as an illustration of the latter point, the Rambam emphasizes that our people always had a portion of the ashes of the red heifer put away for safekeeping. After the destruction of the Temple, that ceased, but with the coming of Mashiach, that will change and the mitzvah will be fulfilled as before.
Immediately after mentioning Mashiach, the Rambam then adds a prayer for his immediate coming. That is also a halachah: that a person should always be anticipating Mashiach’s coming, hoping and yearning for it at all times, as implied by the Rambam’s words in Hilchot Melachim 11:1, it is not sufficient to believe in Mashiach, one must “await his coming.” For this reason, the Rambam mentions this prayer here, in the laws of the red heifer, and not when speaking about subject matter that concerns Mashiach directly. For, at all times, even when we are not focused immediately on Mashiach, one must anticipate his coming.