Drunk - that is, drunk on wine.

As a bench - they would stand in their places: the non-priest next to the priest collecting [the blood]. The priest would give it to [the non-priest], and he would hold it until the one to sprinkle the blood would come and take it from his hand. The non-priest would not convey it to the side of the altar: neither by walking nor by extending his hand; rather, he would act like a bench upon which people rest a vessel.

But slaughter, etc.- this shows that the reason [that the Rabbis disqualify the offering if the conveying was done by a non-priest] does not depend on whether the rite is indispensable, and you cannot use this reason to explain the [position of the] Rabbis. If that were the case, then slaughtering, which is [also] indispensable, ought to be disqualifying if performed by a non-priest. Yet slaughtering by a non-priest is valid!

And [Rabba and Rav Yosef] answered: slaughter is not a rite - from the fact that it is valid when performed by all the disqualified people. But something comparable to an indispensable rite is disqualifying when performed by a non-priest.

And Rav said about this - to explain his ruling: why is it disqualified? Because it is written regarding its slaughter: "You shall give it to Eleazar the priest ... and it shall be slaughtered" [Numbers 19:3]. It is further written regarding the heifer: "Statute" [Numbers 19:2], and wherever the word "statute" is used it indicates the indispensability [of the rule vis-a-vis the rite it is part of].

The heifer is different - and the governing distinction there is not due to it being a [sacrificial] rite, since it does not have the sanctity of altar offerings, but rather is considered an object of mere consecrated monetary value as are objects "consecrated for Temple maintenance". You are then compelled to say that the reason [a non-priest slaughtering it] is disqualifying is not due to [slaughtering] being a [sacrificial] rite, but rather, more generally, due to a scriptural decree. However, regarding altar offerings, for which [sacrificial] rites are relevant, [slaughter] is not considered to be a rite.

Conveying the limbs ... is dispensable - because if he wanted, he could flay and cut it into pieces right next to the altar.

Where it revealed it, it revealed it - conveying the limbs, where [the verse explicitly] revealed that it requires a priest. But regarding conveying the blood, where [the verse] did not [explicitly] reveal that a priest [performs it], according to Rabbi Shimon, since it is dispensable, it does not require a priest [to perform it].

Even according to Rabbi Shimon - even though Rabbi Shimon said that thoughts during [conveying] do not disqualify [the sacrifice], because the validation of the sacrifice does not depend on [conveying] and thus we don't term it one of the things that cause it to be allowed to be eaten. Nevertheless, it is a rite as far as it being disqualifying if a non-priest performs it.

Considered conveying - and thoughts during [conveying not by foot] according to the Rabbis would be disqualifying, and if a non-priest performs it [in this way] it is disqualifying.

Or is it not considered conveying - and thoughts [during its performance in this way] do not disqualify [the sacrifice].

And likewise, if the priest is sitting - [the baraita] teaches that it disqualified if conveyed [while sitting]; but if he was standing, and does not walk with it, but rather [moves it] by extending his hand, as he would have done if he would have been sitting, it is valid. From this we see that [conveying it, not by foot] is considered conveying.

That he rubs - that he drags himself to the side of the altar. "Rubs" means that he rubs himself along the ground. "Rubs" means "drags", as in "smear him with oil" [Shabbat 10b:4] and "rubs once and strikes twice" [Menachot 76a:2]. PDYY"R and the like. Take note from this that the valid [form of conveying] while standing is when you move a little bit by shuffling the feet.

Come and hear what is taught in the Order of the Paschal Sacrifice [chapters 5-9 of Tractate Pesachim], an Israelite would slaughter - that was the usual practice.

Hand it to another - as is taught there, the priests would stand in rows.

He should return it to the fit [priest] - who had given it to him. This teaches us two things: one, that [the sacrifice] is not disqualified in that a disqualified person intervened [in the conveyance]. It [also] teaches us that the conveyance, not by foot, done by the qualified individual -- who extended [the blood] to the disqualified person who was standing next to the altar -- was not done in a valid way, and is thus not considered conveyance. As it is taught, he should return it to the one who gave it to him. If conveying not by foot were considered conveying, why should he return it in the reverse direction? Let a qualified individual come and take it from him [forward] towards the side of the altar; let [the disqualified person] not extend it out to him, but let him act like a mere table [let him be a resting place for the blood].

Say: the fit [priest] should go back - to the side of the altar and receive it -- that is, take it from the hand of the disqualified person, since the initial conveyance was valid.

Is not considered conveying - and it is not valid to convey it this way, and [likewise] thoughts during [conveying it this way] cannot render it piggul.