Gemara

(R. Avahu citing Reish Lakish): (To get water) for washing before eating, one must walk four Mil.

(R. Yosi bar Chanina): Four Mil is the Shi'ur in the direction one was going. One need not backtrack even one Mil.

Inference (Rav Acha bar Yakov): If he can go back less than one Mil and find water, he must do so.

107a - Question: May one eat with a cloth on his hands, without washing?

Are we concerned lest he come to touch the food?

Answer #1 (Beraisa): R. Tzadok was given less than k'Beitzah (the volume of an egg) to eat. He took it in a cloth and ate it outside the Sukah. He did not bless afterwards.

Inference: Had it been k'Beitzah, he would have washed!

Rejection: Perhaps, had it been k'Beitzah, he would have eaten it in the Sukah and blessed afterwards, but still he would not have washed!

Answer #2: Shmuel found Rav eating with a cloth.

Shmuel: Is this permitted?

Rav: I eat with a cloth because I am particular not to touch the food.

R. Zeira found R. Ami and R. Asi eating with cloths.

R. Zeira: DId you err about the episode with Rav? Rav had washed. He ate with a cloth because he is particular!

R. Zeira did not know Rav Tachlifa's teaching, that Chachamim permitted those who eat Terumah to may eat with a cloth, but not those who eat Tahoros (Chulin as if it were Kodesh. R. Ami and R. Asi were Kohanim.)

Rishonim

Rambam (Hilchos Berachos 6:18): One may wrap his hands in a cloth and eat bread or a food dipped in a liquid, even though he did not wash. One who eats with a fork must wash his hands.

Rebuttal (Ra'avad): Chachamim permitted only those who eat Terumah to eat with a cloth!

Rosh (8:18): One who has a wound and bandage on his hand, he washes the rest of his hands not where the bandage is. This is like one whose finger was cut off. Chachamim did not allow people who eat Chulin in Taharah to eat Chulin with a cloth, and all the more so one may not eat Stam Chulin with a cloth, for they are not careful and they will come to touch. Here is different. We are not concerned lest he touch food with his skin under the bandage, for he will not remove the bandage, due to pain of the wound.

R. Yonah (Berachos 8a DH Layit): Rashi explains that one who eats Chulin b'Taharah must go four Mil to find one who can knead for him in Taharah. This is also the Shi'ur to delay praying until one will reach a place with a Minyan, and to delay eating (bread) until he will find water to wash. I checked accurate texts, and found that they say that Rav Chisda cursed one who delays Kri'as Shma, after the time came, for the sake of washing. The same applies once the time for Tefilah came. The Rishonim say that one delays for water for Tefilah, but not for Kri'as Shma. They were more stringent about Tefilah, for it is only mid'Rabanan. I disagree.

Rashi (107b DH Hitiru): Kohanim who eat Terumah may eat with a cloth, for they are careful not to touch. Chachamim did not permit those who eat Chulin in Taharah, for they are not as careful as Kohanim.

Tosfos (Yoma 79b DH Ha): R. Tzadok was a Kohen. In Chulin, we say that one who eats Terumah may eat with a cloth, but not one who eats Tahoros. We can say that we permit one who eats Terumah to eat only Terumah with a cloth, for he is very careful about it, but not those who eat (Chulin) Taharos, even a Kohen who eats Al Taharas ha'Kodesh.

Tosfos (Sukah 26b DH Natlo): Rashi explains that R. Tzadok took the food in a cloth for cleanliness. There was no need to say so. He was a Kohen, and he used to eat Al Taharas ha'Kodesh. He needed a cloth, for otherwise Stam (unwashed) hands are a Sheni l'Tum'ah and they would be Metamei the food!

Poskim

Shulchan Aruch (OC 163:1): If one does not have water in front of him more than four Mil, or one Mil in back, he wraps his hand in a cloth to eat bread or a food dipped in a liquid.

Beis Yosef (DH Asur): We conclude that those who eat Terumah may eat with a cloth (without washing), but those who eat Taharos may not. Rashi explains that Kohanim are zealous not to touch. We are not lenient for people who eat Chulin in Taharah, for they are not trained to be careful like Kohanim are. The Rosh, R. Yonah, Semag and Semak say that Chachamim did not permit people to eat Chulin with a cloth.

Beis Yosef (DH Aval): The Rambam permits eating bread with a cloth. He holds that the Gemara forbids only people who eat Chulin Al Taharas ha'Kodesh, but not for Stam Chulin. Since Netilas Yadayim was enacted only due to Terumah (so people will be used to guarding it in Taharah), Chachamim did not decree more than for Terumah itself. This is why the Rambam was lenient in Hilchos Berachos. In Hilchos She'ar Avos ha'Tum'ah (8:9), he permits eating Terumah in a cloth, but forbids this for Chulin Al Taharas ha'Kodesh or Al Taharas Terumah, lest he touch, since he is not particular about them. The Ra'avad argued, for he holds like R. Yonah and the Rosh. Rashi holds like the Rambam.

Beis Yosef (DH veha'Aruch): The Aruch says that one may not eat without Netilas Yadayim if there is water four Mil in front of him, but he need not go back even a Mil. Rather, he eats with a worn pouch. I.e. he wraps his hands in a cloth. The Roke'ach (328) connotes that when there is no water within this distance, he may eat without washing at all. This is like soldiers in an encampment, who are exempt. I say that we do not permit eating through a cloth because many argue with the Rambam. However, if water is not available four Mil in front or one Mil in back, he may eat with a cloth.

Bach (1): One might have thought that since the enactment was only due to Terumah, it is only l'Chatchilah when one can wash without toil, but if not, one may eat without washing. The Tur teaches unlike this. One may not even wrap his hands in a cloth. Since people are not careful, perhaps he will touch. Therefore, even if he has no water, he may not eat without washing, even through a cloth. The Tur holds like the Rosh, Semag and Semak, based on the conclusion in Chulin. Chachamim did not permit those who eat Taharos, and all the more so not for regular Chulin. This is unlike the Rambam, who permits using a cloth for regular Chulin. However, if water is not found within four Mil in front, he may wrap his hands in a cloth and eat without washing.

Magen Avraham (1): If it is a Safek whether he will find water within four Mil, perhaps one may rely on the Rambam who permits eating with a cloth even if one has water. The Yerushalmi says that one who guards a garden or orchard is like one who must go back. (He need go only until a Mil.) This implies that one who is in his house must go four Mil. This requires investigation.

Kaf ha'Chayim (3): Rabbeinu Zalman says that one who is in his house must go four Mil for water. Chayei Adam and others says that he must go only one Mil. Pesach ha'Dvir says that one may be lenient like them, since Netilas Yadayim is mid'Rabanan.

Bi'ur Halachah (DH Im): Chayei Adam says that the Heter if he is in Safek is only if he is very hungry. The Ritva (Pesachim 46) connotes that even if surely he will not find water, one should be lenient only for a great need, e.g. he is weak due to traveling.

Gra (DH Im): The Gemara and all the Poskim connote that when he will not find water within four Mil, he is totally permitted without Netilas Yadayim. However, the Aruch permits (in this case) only with a cloth.

Mishnah Berurah (6): Eliyahu Rabah says that when Chachamim required a cloth, if one does not have a cloth, he is permitted without a cloth. This is very rare that he is naked and has nothing to wrap his hands in. If he can, he must, for not only the Aruch requires a cloth. Also R. Chananel (Pesachim 47) says so.

Kaf ha'Chayim (5): If one has only water Pasul for Netilas Yadayim, he washes with it without a Berachah, and also eats with a cloth.

Kaf ha'Chayim (6): Eating with gloves is like eating with a cloth (Kitzur Shulchan Aruch).

Gra (DH Aval): Tosfos says that Chachamim were not lenient for people who eat Chulin Al Taharas ha'Kodesh. It seems that Rashi explains that R. Tzadok ate Chulin with a cloth. (If the leniency were only for eating Terumah, Rashi would not have needed to say that Kohanim are more careful than others - PF.)

Mishnah Berurah (3): If one is traveling and wants to eat, if he estimates that water will be available right after four Mil, he must wait. He may not eat with a cloth. In back he must go only one Mil, for it is an exertion. If it is a Safek whether he will find water within four Mil or one Mil in back, he may eat with a cloth. Shomerim or gardens need not go a full Mil, for they cannot leave what they guard.

Bi'ur Halachah (DH bi'Rchok): When one is traveling on a fast camel, we do not measure based on distance, rather, based on the time to walk four Mil, i.e. 72 minutes. This is only if he is very hungry.

Kaf ha'Chayim (2): If one travels with a caravan and if he seeks water, they will not wait for him, he may eat with a cloth (Kitzur Shulchan Aruch).

Mishnah Berurah (5): Presumably, the Mechaber requires wrapping both hands in a cloth, even though he uses only one hand to eat, lest the other touch the food. According to the Rema, one may be lenient. This requires investigation.

Kaf ha'Chayim (9): Also, a cloth is in place of Netilas Yadayim, which is for both hands.

Kaf ha'Chayim (7): Bigdei Yesha understood that the Mechaber discusses a cloth only for bread. Pesach ha'Dvir disagrees. A food dipped in a liquid is totally like bread.

Rema: Or, he eats using a spoon.

Gra (DH Oh): The Tur (Sa'if 2) forbids this. This requires investigation.

Mishnah Berurah (7): A cloth totally covers his hands. Here, his hands are exposed. Perhaps he will touch the food! If one has a cloth, he should use it, and not a spoon.

Bi'ur Halachah DH (Yadav): The Rema connotes that it suffices to cover one hand in a cloth. It reminds him not to touch with the other hand. However, the Acharonim questioned the Rema's law.

Kaf ha'Chayim (8): The Rema is unlike the Rambam, but the Acharonim agreed to the Rema. It seems that the Rema permits a spoon for bread only if it is already in pieces, or he holds it through a knife and eats using a spoon. If one has a cloth, it is better to eat with a cloth.