Gemara

57a (Beraisa): If a Nochri measured (the depth of) wine by sticking in his hand or foot, one may sell the wine;

R. Noson says, if he stuck his hand in, one may not benefit from it. If he used his foot, one may sell it.

57a: A Nochri climbed a date tree and took a Lulav. On his way down, the end of the Lulav (our text; R. Tam - he) accidentally touched wine.

Rav: The wine may be sold to Nochrim.

Rav Kahana and R. Asi: You yourself said that a one day old Nochri makes Yayin Nesech (even though he has no intention)!

Rav: I meant only that one may not drink it. One may benefit from it.

58a (Beraisa): A case occurred in which a crazed Nochri stuck his hand in what he thought is oil, but it was really wine. Chachamim ruled that it must be sold.

59b: A Nochri's Esrog fell into a barrel of wine; he ran and stuck his hand in to retrieve it.

Rav Ashi (to Yisraelim): Hold his hand so he cannot shake it, and tilt the barrel so the wine will flow out.

60a: The spigot came off a barrel of wine. A Nochri ran and stuck his hand there to prevent the wine from spilling out.

Version #1 (Rav Papa): The wine at the level of his hand (where the spigot was) is forbidden. The rest is permitted.

Version #2 (Rav Papa): The wine at or above the level of the spigot is forbidden. The rest is permitted.

60b (Mishnah): All the following cases occurred, and Chachamim permitted selling the wine. A Nochri inserted a rod to measure the wine; he chased a wasp from the wine with a rod; he leveled off the foam on top.

R. Shimon says, it is permitted (to drink).

Rishonim

Rambam (Hilchos Ma'achalos Asuros 11:5): If a Nochri touched wine without intent, or a Nochri child touched wine, one may not drink the wine, but one may benefit from it.

Rambam (12:1): If a Nochri stuck his hand into a barrel and they grabbed his hand before he removed it or shook it, and opened the barrel from the bottom so the wine flowed out and went below his hand, it is not forbidden. The same applies if he held an open Keli of wine and shook it. Even though he did not lift the Keli or touch the wine, it is forbidden.

Ra'avad: This is only if some of the wine spilled out.

Rambam (9): In the following cases, one may only benefit from the wine. A Nochri used a reed to measure the pit holding the wine, or he chased a wasp from the wine with a rod, or he took the foam from on top of the wine, or in his anger he threw a barrel into the pit.

Ran (Reish 29a): Rashi holds that if we rule like the first Tana (of R. Noson), who says that whether one measured with the hand or foot we sell the wine, we do not distinguish touching with his body or through something else. R. Tam holds that touching through something else is mere Ko'ach, and according to the opinion that Ko'ach even with intent forbids only drinking, the same applies to touching through something else.

Rosh (4:5): Rashi's text says that the end of the Nochri's Lulav accidentally touched wine. R. Tam challenged this. How can we compare what a child himself touched to what a Nochri touched without intent, via something else?! This is not so difficult. Rashi says that these are the same. However, why did Rav Kahana and Rav Asi think to forbid Hana'ah if the Nochri himself did not touch the wine?! A Mishnah teaches that if a Nochri measured wine with a stick, it may be sold. He intended that the stick touch the wine, for the sake of measuring, and all the more so (one may benefit) when he did not intend to touch at all! Even R. Noson forbids Hana'ah only when he measured with his hand, but not if he measured with his foot. Touching through a Lulav is no worse than measuring with his foot, which does not forbid Hana'ah! Also, Rav rules like R. Shimon, who permits drinking when there was intent for Nisuch through something else. Rather, the correct text is like that of R. Chananel and the Rif, that the Nochri himself touched the wine accidentally. If he did not touch through the Lulav, why did the Gemara mention that he went up the tree to get a Lulav? Perhaps the witness reported the episode exactly, and so it was recorded. Rashi's text came about because people assumed that the Gemara mentioned that he went to get a Lulav because he touched the wine through a Lulav.

Rosh (10): When the Nochri put his hand in to get his Esrog, had they not held it still, he would have forbade Hana'ah from the wine when he removed the Esrog, even though he is distracted with retrieving his Esrog. This is like R. Noson, who forbids Hana'ah when he measured with his hand. Alternatively, it is even like Chachamim. Removing an Esrog is less distracting than measuring wine. Entering the hand did not forbid Hana'ah, because he was distracted to retrieve his Esrog. R. Tam says that when he entered his hand he thought that oil is inside, but he realized that it is wine before he would have removed his hand. The Ra'avad permits Hana'ah even if he realized that it is wine before removing his hand. It is called touching without intent because when he first touched he did not know that it is wine, and once he knew he removed his hand. This shows that he did not intend for Nisuch.

Beis Yosef (YD 124 DH u'Mah she'Chosav b'Shichshuch): The Rosh connotes that had he intended to touch wine, it would be Asur b'Hana'ah even though he did not shake.

Poskim

Shulchan Aruch (YD 124:10): There are three conditions to forbid Hana'ah from wine that a Nochri touched. One is that he intended to touch. This excludes a child who touched, for he has no intent. Another is that he knows that it is wine. The third is that he was not engaged in something else.

Gra (24): When he was engaged in measuring, the Tur and Rema (Sa'if 19) permit Hana'ah even if he touched it. The Mechaber forbids, unlike he says here. Also the case of Esrog (had they not held the Nochri's hand, he would have forbidden the wine) is unlike the Mechaber here.

Shulchan Aruch (11): A Nochri forbids Hana'ah from wine that he touched if he touched with his hand or foot or something else (Rema - in his hand) and he stirred. This forbids benefit from all the wine.

Beis Yosef (DH u'Mah she'Chosav Lo): The Mishnah teaches cases in which his actions show that he did not intend for Nisuch, rather, to measure the wine or chase a wasp from it. If not, if would be forbidden to benefit from it. The Rashba says so. From what the Poskim said about the case of of the spigot that came off and a Nochri put his hand there, it seems that they agree. The Rosh and Tosfos say similarly. The Rambam mentioned touching wine through something else only when his actions show that he did not intend for Nisuch, rather, to measure the wine or chase a wasp from it. Then, one may benefit from it. R. Avraham Shalem says that the Rashba forbids Hana'ah if a Nochri knowingly touched wine, even through something else. The rule is, when he touches through something else without a need, we are concerned lest he intended for Nisuch, and it is Asur b'Hana'ah. However, if there is a proof that he intended for something else, one may not drink the wine, but one may benefit from it. The Rambam agrees. The case of measuring and other cases brought there show that wine becomes Asur b'Hana'ah even if nothing was poured out.

Taz (6): The Beis Yosef was unsure whether we require much shaking, or even a little. Mishmeres ha'Bayis says that we do not find such a distinction. Even a small shaking forbids.

Shach (19): When he touches through something else without intent, one may even drink the wine, like in Sa'if 24 below.

Shach (20): Mere touching without shaking does not forbid Hana'ah. The Beis Yosef learns from the Rambam that putting in one's hand is mere movement; it is not called shaking. The case of the Esrog that fell into wine supports this. He derived that the Rosh holds that touching without shaking forbids Hana'ah, since he needed to say that he entered his hand without intent. (Maharshal and the Prishah accepted this.) Why should entering be different than removing?! Also, the Tur himself says that we do not forbid for entering even if he knew that it is wine, since he intends only to retrieve. Surely, the same applies to removing! This is why Tosfos, the Rosh and Tur needed to say that entering did not forbid because he intended only to retrieve, but indeed, mere touching does not forbid Hana'ah; only shaking does. After he gets the Esrog, we must be concerned lest he put his mind to shake. The Ra'avad holds like this.