1) A LULAV-HOLDER
QUESTION: The Gemara discusses whether one must hold the Lulav in his bare hand, or whether he may use a Lulav-holder with which to grasp the Lulav. Rabah maintains that one may not use a Lulav-holder, because it is considered a Chatzitzah (intervention) between his hand and the Lulav. The Torah requires that one grasp the Lulav with a "Lekichah Tamah" (a "complete grasp"), and thus one cannot fulfill the Mitzvah when there is a Chatzitzah. Rava argues and says that a Lulav-holder is not a Chatzitzah, because it is used for the purpose of beautifying the Mitzvah.
The Gemara continues and discusses whether one may hold a Lulav with a handkerchief. RASHI explains that the question is whether one is permitted to wrap the handkerchief around one's hand and hold the Lulav with it. Rabah says that one may not hold the Lulav in such a way, because it is not a "Lekichah Tamah." Rava argues and says that one may hold the Lulav with a handkerchief, because "Lekichah Al Yedei Davar Acher Shemah Lekichah" -- when one holds an object by the way of something else, he is considered as though he is holding the object itself.
In the Gemara's first discussion (about a Lulav-holder), it is clear that even Rava would agree that an intervening item that does not serve to beautify the Mitzvah is considered a Chatzitzah. Why, then, does he not consider a handkerchief a Chatzitzah (but only a "Lekichah Al Yedei Davar Acher")? Since it does not serve to beautify the Mitzvah, Rava should agree that it is considered a Chatzitzah.
Moreover, the Gemara in Pesachim (57a) relates that a sinful Kohen by the name of Yissachar Ish Kefar Barka'i was punished because he performed the Avodah in the Beis ha'Mikdash while he wore gloves. Rashi there explains that the gloves were a Chatzitzah and thus disqualified the Avodah. What is the difference between one who holds the Lulav while he wears a handkerchief around his hand (which is not considered a Chatzitzah according to Rava) and one who performs the Avodah while he wears a glove? (TOSFOS DH d'Ba'ina)
ANSWERS:
(a) In his first answer, TOSFOS (DH d'Ba'ina) suggests that a handkerchief differs from a Lulav-holder in the following way. Since the handkerchief is wrapped around one's hand (and not around the Lulav), it serves the hand and not the Lulav. It is considered subordinate to (and part of) the hand and thus it is not a Chatzitzah.
Why, then, was Yissachar Ish Kefar Barka'i punished because he wore a glove during the Avodah? His glove served his hand and should not have been considered a Chatzitzah. Tosfos answers that he was not punished for performing the Avodah with a Chatzitzah, but rather for disgracing the Avodah by showing that he did not want to touch it directly with his hands.
The RITVA quotes the RAMBAN who answers the question from the case of Yissachar Ish Kefar Barka'i differently. He asserts that the Gemara here is not discussing the question of Chatzitzah at all. There is no concern for a Chatzitzah when one holds a Lulav. Even Rabah, who does not permit one to hold a Lulav with a handkerchief, does not call it a Chatzitzah; he says only that it is not a "Lekichah Tamah."
(In the previous case, although Rabah says that a Lulav-holder is a Chatzitzah, he means that it is not a proper Lekichah, as Rashi there explains. He does not mean that a Chatzitzah itself invalidates one's fulfillment of the Mitzvah of Lulav. However, when the Gemara later (37b) mentions Chatzitzah, it certainly refers to the normal problem of Chatzitzah, because the rules of "Min b'Mino Eino Chotzetz" would not be appropriate to the discussion there if the problem with a Chatzitzah was only that it is not a "Lekichah Tamah." The difference between the Gemara here and the Gemara later is that the Gemara here refers to an intervening object between one's hand and the Lulav. The Gemara there refers to an intervening object between one's hand and the other Minim.)
When one holds the Lulav, a Chatzitzah itself is not a Pesul. Rather, the Torah requires a "Lekichah Tamah." The Gemara here inquires whether something that is wrapped around one's hand when he holds the Lulav is considered a proper Lekichah. In the case in Pesachim, the sinful Kohen was punished because the Avodah may not be done with a Chatzitzah. Even though his glove was serving his hand, it was a Chatzitzah between his hand and the Avodah. In contrast, when one holds a Lulav, there is no requirement that there be no Chatzitzah, but that there be a "Lekichah Tamah." The only case of a Lekichah that is not "Tamah" is where there is an object between one's hand and the Lulav that neither serves the hand (and thus is not Batel to it) nor beautifies the Lulav.
(b) Tosfos (ibid.) eventually rejects this explanation. He answers instead that an object is considered a Chatzitzah between one's hand and the Lulav only when the object is necessary. A Lulav-holder is necessary because it holds the Lulav together with the other Minim, and without it the Arba'as ha'Minim would not be bound together. In contrast, an object which is extraneous, such as a glove, is not considered a Chatzitzah. (Perhaps the logic behind this answer is the principle, "Kol ha'Ra'uy l'Bilah, Ein Bilah Me'akeves Bo"; since the Lulav does not need that object (it is possible to remove it and still fulfill the Mitzvah properly), it is not considered a Chatzitzah.)
Tosfos also rejects this explanation on logical grounds. Tosfos argues (and proves from Yoma 58a) that if the object is not necessary for the Lulav, then, on the contrary, it certainly should be considered a Chatzitzah.
(c) Tosfos concludes that in the case of one who holds a Lulav with a handkerchief, the handkerchief is not wrapped around his hand or around the Lulav. Rather, the handkerchief is arranged in such a way that it serves as a holder for the Lulav: the handkerchief holds the Lulav, while the person's hand holds the handkerchief. (For example, he loops the handkerchief around the Lulav and gathers the two sides of the handkerchief and twists them together. He thereby forms a handle which he holds in his hand.) In this case, the handkerchief actually assists the hand to hold the Lulav, and it does not merely protect the hand. Consequently, with regard to the act of Lekichah (holding the Lulav), the handkerchief is considered an extension of the hand and is not a Chatzitzah.

37b----------------------------------------37b

2) HALACHAH: HOW TO WAVE THE LULAV
OPINIONS: The Mishnah discusses the parts of Hallel at which one should wave the Lulav ("Na'anu'im"). The Gemara describes how these Na'anu'im are performed. According to Rava, the Lulav is waved in the same way as the loaves of the Shtei ha'Lechem are waved on Shavuos in the Beis ha'Mikdash: forward and back (Molich u'Mevi), and then up and down (Ma'aleh u'Morid).
The Yerushalmi (3:10) quotes a Beraisa that states, cryptically, that one must wave the Lulav "three times for each thing." Rebbi Zeira in the Yerushalmi questions whether the movement forward is considered one waving and the movement back is considered a second waving, or whether the full forward-back movement is considered one waving.
What does the Beraisa mean when it says that one must wave the Lulav "three times for each thing"? In addition, how does the Yerushalmi's description of the three Na'anu'im match the description of the Na'anu'im given by the Gemara here (Molich u'Mevi, Ma'aleh u'Morid)?
(a) TOSFOS (DH Kedei), the ROSH (3:26), and the TUR (OC 651) explain that according to the Gemara here, one must point the Lulav towards six directions -- to the four directions (east, south, north, west), and up and down. The Yerushalmi adds that when one stretches his arms to each direction, he also must move his hands back and forth three times (making a smaller to-and-from movement). Rebbi Zeira's question in the Yerushalmi is whether one needs to move his hands back and forth only three times (back, forth, back), or six times (back-forth, back-forth, back-forth).
Tosfos, the Rosh, and the Tur rule that one should be stringent and perform six short wavings since there is no excessive effort involved. Accordingly, one waves the Arba'as ha'Minim a total of 36 wavings (six times in each of the six directions).
(b) The BA'AL HA'ITUR (cited by the Rosh) and the RITVA (in the name of "Yesh Mefarshim") explain that the Bavli and Yerushalmi describe the same wavings but in different words. The Gemara here says that one should wave the Lulav "Molich u'Mevi, Ma'aleh u'Morid," and the Yerushalmi says that those constitute three movements -- "Molich u'Mevi" are two movements, and "Ma'aleh u'Morid" is one movement.
Rebbi Zeira questions whether the single series of "forward and back" (Molich u'Mevi) is considered two movements and thus it suffices to move the Lulav forward and back a single time, or whether the "forward and back" movement is considered only one movement and thus one must do two actions of "forward and back" (forward-back, forward back; or, alternatively, forward-back, side-to-side) in order to achieve two movements. The "up and down" movement is counted as only one movement because "down" is not counted as a separate movement (since it is not possible to go up without coming down).
(c) The RAMBAM (Hilchos Lulav 7:10) rules that the Bavli and the Yerushalmi complement each other and note two different types of movements of the Lulav. The Bavli says that one should extend the Lulav to each direction (as well as up and down). The Yerushalmi adds that when one stretches out his arms, he must also make the top of the Lulav jiggle while his arms are outstretched. This is the Na'anu'a mentioned in the Mishnah earlier (29b). The question of Rebbi Zeira is whether one must also perform these short quivers of the Lulav when one brings his hands back to his body. Accordingly, the Yerushalmi describes an entirely different aspect of waving the Lulav than the Bavli. The Bavli describes moving the Lulav back and forth, and the Yerushalmi describes jiggling the Lulav.
(d) The RIF, RAMBAN, RITVA, and RAN explain, like the Rambam, that the Bavli and Yerushalmi discuss two types of waving. However, according to these Rishonim, the two types of waving are done at two different times. After one performs the Bavli's set of forward and back, up and down, movements, one must jiggle the Lulav three times. This quivering, although much smaller than the forward and back movements, also involves a small forward and back motion. Rebbi Zeira's question is whether this forward and back quivering motion is considered two movements (forward and back), so that it suffices to perform three such movements (forward, back, forward), or whether it is considered one movement (forward-back), so that one must do six movements (forward-back, forward-back, forward-back).
(The last two opinions do not mention that the Lulav must be stretched out to all four directions in addition to up and down. Perhaps they maintain that it suffices to move the Lulav just forward and back (i.e. in two directions), besides up and down. The Ba'al ha'Itur (in (b) above), who maintains that this is the doubt of Rav Zeira in the Yerushalmi, also concludes that, l'Halachah, it suffices to wave the Lulav merely forward and back.)
The RAMBAN and RITVA prove that the Bavli also requires that the Lulav be quivered, even though the Bavli does not explicitly say so. The Mishnah (29b, as explained by the Gemara on 32b) says that the Lulav must extend at least one Tefach beyond the height of the Hadasim and Aravos "in order to shake it." If there is no need to jiggle the Lulav, but only to move it back and forth, why is an extra Tefach on top necessary? It must be that the Bavli also understands that when the Mishnah says "Na'anu'a," it refers to jiggling the Lulav.
This proof can be refuted by the Rambam's explanation there (in Perush ha'Mishnayos). The Rambam explains that the Mishnah does not mean that there must be an extra Tefach on top of the Lulav, but rather that there must be an extra Tefach that extends below the Hadasim and Aravos, at the bottom of the Lulav. The purpose of this extra Tefach is to enable one to grasp the Lulav with his hands in order to move the entire bundle back and forth. "In order to shake the Lulav" means that the Tefach is needed so that one can hold the Lulav in order to move it back and forth. According to this explanation, there is no proof that the Bavli requires jiggling the Lulav (because the top of the Lulav does not extend beyond the Hadasim and Aravos).
(The RAMBAM in Hilchos Lulav, however, does mention the requirement to jiggle the top of the Lulav, as mentioned in (c) above. Perhaps the Rambam retracted the opinion he expressed in Perush ha'Mishnayos. Alternatively, perhaps the Rambam argues with the Ramban and Ritva and maintains that the top of the Lulav does not need to extend a Tefach in order for one to jiggle it; even if the top of the Lulav is level with the top of the Hadasim and Aravos, one still can jiggle it.)
HALACHAH: The SHULCHAN ARUCH (OC 651:9) seems to rule in accordance with the opinion quoted by the TUR in the name of his father, the ROSH (as explained by the Beis Yosef), who mentions major and minor back-and-forth movements to each of six directions. He does not mention jiggling. The REMA adds that one must also jiggle the leaves of the Lulav while he moves it back and forth. In addition, although the Rema agrees with the Shulchan Aruch that one must move the Lulav forward and back three times (for a total of six movements), he argues that those movements are done by stretching out one's arms completely and then bringing the arms back to one's body; the movements are not short, forward and back movements that are done once the arms are outstretched, as the Shulchan Aruch rules (that is, according to the Rema, there are two sets of major movements and no minor movements).

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