Why was the section of Miriam adjoined to the section of the heifer ? To teach you that just as the heifer effects atonement..."

Now it needs to be understood why it was adjoined precisely to the "red heifer" ( which was prepared outside the three camps; it is just that the Torah calls it a sin-offering ), and it was not adjoined to the section of the sin-offering that was prepared within, on the actual altar of atonement.

However, it is known from the sacred Zohar, and from R. Isaac Luria, of blessed memory, that the principium of the sacrifices brought on the altar is that they are an aspect of the elevation of tnayin nukvin: from the animal soul, which is in (the class of) nogah, to their root and source, i.e. the forms of the four Animals of the Chariot bearing the Throne: the Face of the Ox, and the Face of the Eagle.... Thereby the mayin duchrin are elicited and descend from the aspect of the "Man upon the Throne," referred to as malka, and zeyr anpin. As for the burning of the red heifer, however, by throwing in the cedar-wood, and the hyssop .... and the placing of running waters into the ashes, the Mishnah refers to this as the sanctification (kidush) of the waters of lustration. This is the aspect of kodesh haelyon referred to as tala dibedulcha, as mentioned in the sacred Zohar the aspect of the supreme chochmah and the mocha setimaah of arich anpin Of it is said in many places in the sacred Zohar that through chochmah they are disencumbered and darkness is converted to light. That is, by means of the mocha setimaah of arich anpin the world of tikun is disencumbered and corrected from the world of tohu and the breaking of the vessels that fell into Beriah, Yetzirah and Asiyah.... as known. That is why (the red heifer) purifies from, the defilement by a corpse, even though such is the highest degree of impurity, and much lower than nogah.

Now, it is known that abba draws from the eighth mazal.. .. the tuft of notzer chesed Notzer is (composed of the same) letters (as) ratzon It is the et ratzon that becomes revealed and radiates in a manifest way, from above downwards, at the time of the passing of the great tzadikim who serve the Lord out of love, surrendering their soul to the Lord during their life-time every evening and morning when reading the Shema For thereby they elevate the mayin nukvin to abba and imma, as known. ( The same applies to (their) study of the Torah which derives from chochmah. ) Thus, the aspects of the mayin duchrin were elicited thereby and descended from the tuft of notzer chesed; and they, indeed, radiate in a manifest way at the time of their passing. For as known, ail the effort of man, which his soul toiled during his life-time, is above in a hidden and concealed state. It becomes revealed and radiates in a manifest way from above downwards at the time of his passing.

Now, by the manifestation of the illumination of the tuft of notzer chesed at the time of their passing, the chesed of the Lord radiates from world to world, over those who fear Him, and effects salvations in the midst of the earth to atone for the sin of the generation, even for the deliberate sins which are of the three impure kelipot [which are inferior to nogah]. For the mazal of notzer is of the mochin setimin of arich anpin, the source of the extractions (birurim). Thus the darkness of the shevirat hakelim is converted into the light of the world of tikun. This is not the case, though, with the sacrifices that are upon the altar. They atone only for inadvertent sins which come about because of the strengthening of the animal soul which is of nogah, as mentioned in Likutei Torah, section of Vayikra.

That is why (the section of Miriam) was adjoined expressly to the section of the heifer: "just as the heifer..." Indeed, in the Yalkut, section of Shemini, the version is "the waters of lustration ..."