What are the connotations of "Kaper le'Amcha Yisrael"?
Seforno: It is a request that Hashem should bring about the atonement by arranging the death of the murderer 1 - the one who spilled his blood. 2
Targum Yonasan: It is a request that Hashem should reveal the identity of the murderer, in order that he is sentenced to death, to which Hashem responds by causing a stream of worms to emerge from the navel of the calf 3 which walk all the way to the murderer, wherever he may be, and crawl over him, and Beis Din then judge him. 4
Hadar Zekenim (citing a Midrash): "le'Amcha Yisrael" refers to the living - and "asher Padisa", to the dead, who are redeemed from Gehinom via the Tzedakah of the living. 5
Riva (citing R"M of Kutzi): It means 'Reveal (the murderer) to your nation Yisrael, 6 because as long as the murderer is not known, the Go'el ha'Dam is liable to kill someone who is innocent. 7
Sifri: Refer to answer #3. This teaches us that the deceased require a Kaparah and that the sin of a murderer goes back to those who went out of Egypt. 8
It implies that Eglah Arufah atones like Kodshim, and is therefore compared to Kodshim inasmuch as, like Kodshim ... a. the Arifah may be performed any time during the day 9 - Megilah, 21a; b. the Eglah Arufah is Asur be'Hana'ah 10 - Avodah Zarah, 29b; c. the Eglah Arufah is Tahor 11 - Zevachim, 70b; d. an Eglah Arufah that is found to be a T'reifah or missing a limb is Pasul - Yerushalmi Sotah, 9:5.
Seforno: As the Gemara states in Kesuvos, 30b 'If someone is Chayav Misah (and there are no witnesses), he is either handed over to the ruling power (to be sentenced to death) or is attacked by robbers'.
See Bamidbar, 35:33.
See Peirush Yonasan.
And they execute him, even though there are no witnesses - See Na'ar Yonasan. Refer also to 21:4:1:1*.
Hadar Zekenim: This is the source of mentioning the Neshamos (Yizkor) on Yom-Tov and Yom Kipur and pledging Tzedakah in their name. See also answer #6.
Riva: See Targum Yonason in Yeshayah 28:18.
If no-one knows who killed him, whom would the Go'el ha'Dam kill? Perhaps he will kill based on mere suspicion without evidence - he knows that Ploni hated the victim, or he finds out that Almoni went on the road on which the body was found, shortly before it was found, and he did not tell anyone (PF).
See Torah Temimah, note 57.
As opposed to the Parah Adumah, which is Tamei.
Who declares "Kaper le'Amcha Yisrael ... "?
Why does the Torah insert the (otherwise superfluos) words "asher Padisa Hashem"?
Refer to 21:8:1:5.
Horayos, 6a: It implies that this Kaparah is fit to atone for the generation that left Egypt - To teach us that a Tzibur does not die and that one therefore brings a Chatas Tzibur even if all its owners have died. 1
Sifri #1: To teach us that Hashem took us out of Egypt on the condition that there are no murderers among us.
Sifri #2: To teach us that Hashem took us out of Egypt on the condition that if we sin, we will have a Kaparah. 2
Kerisos, 27a: Following the previous answer - bearing in mind that many Yom Kipurs have passed since Yisrael left Egypt, if an Eglah Arufah, has not had its neck broken before Yom Kipur, its neck is broken after Yom Kipur 3 - in spite of the fact that Yom Kipur atones for sins of which only Hashem is aware - and Eglah Arufah falls under that category.
What are the connotations of "Venikaper lahem ha'Dam"? Who said it?
Rashi: It means that, if they carry out the above instructions, the sin will be atoned (It is not the Kohen who said this, but the Shechinah - Sotah, 46a). 1
Seforno: With reference to 21:8:1:1, it means that, when Hashem arranges the death of the murderer, it will appear as if the death has been atoned automatically.
See Torah Temimah, citing Sotah, 46b, and note 60.
What was the result of the Kohanim's Tefilah?
Riva and Rosh: Refer to 21:9:2:3.
Targum Yonasan: No sooner had they finished Davening, than a swarm of worms emerged from the dung of the calf which led to the murderer, whom Beis-Din took into custody and sentenced to death (despite the fact that there were no witnesses). 1
Since the Kohanim declared that they did not spill the victim's blood, why is a Kaparah necessary?
Riva: To atone for the rest of Yisrael, since all of Yisrael are guarantors for one another.