Text #1: This is the text of the Rashbam.

Refutation #1: This is not correct however, since why can the children not go to sleep without their fathers?

Refutation #2: And the second reason that he gives - 'In case they delay until long after nightfall' (is difficult too) ...

Refutation #2 (cont.): Since then they would not have needed to get up during the day, only at nighttime?

Text #2: The correct text is therefore 'Leilei Pesachim' (on the night of Pesach), since it was customary to learn in the Beis-ha'Medrash on Yom-Tov night ...

Proof: As the Gemara says in Beitzah (Daf 21.) 'It happened one Yom-Tov night that Shimon ha'Timni did not come to the Beis-ha'Medrash; on the next day Rebbi Yehudah ben Bava met him ... '.

Question: This Pasuk is written in connection with Ma'aser Sheini in Parshas Re'ei. Why does the Tana not quote the Pasuk in the same Parshah but in connection with Yom-Tov "Vesamachta (be'Chagecha) Atah u'Vincha u'Vitecha"?

Answer: It prefers to learn from Ma'aser, where it specifically mentions 'Beiso' (i.e. one's wife).

Clarification: But in Bavel. They were expert in ironing (pressing), as the Gemara says in Ta'anis (29:) 'Our ironing is like their washing' (See Rashi there).

Clarification: This applies specifically to nowadays ...

Conclusion: but in the time of the Beis-ha'Mikdash, one can only fulfil the Mitzvah of Simchah with meat.

Question: This Pasuk is written in connection with Har Eival. Why does the Tana not rather quote the Pasuk "Vesamachta be'Chagecha" ...

Question (cont.): From which the Gemara in Chagigah (Daf 8.) learns 'To include all kinds of S'machos in the Mitzvah of Simchah. From here the Chachamim learn that a Yisrael can fulfil his obligation with Nedarim and Nedavos'?

Answer: Because it is here that the Torah specifically writes "And you shall Shecht Shelamim and rejoice".

Clarification: The Rashbam equates this with Tomen ve'Uchla.

Refutation: This is not correct however, seeing as, in 'ha'Mocher es ha"Sefinah' (Bava Basra, Daf 90.) the Gemara lists 'Log, Revi'is ha'Log, Tomen and Uchla', each measure progressively less ...

Conclusion: Whereas the Gemara here implies that 'Tamnisa' is more than a Revi'is.

Question: Our Gemara is difficult for Rashi's Rebbeyim, who explained that "Revi'is" always refers to a quarter of a Kav. According to the calculation here, it is a quarter of a Log. (A Log is a quarter of a Kav. We know that a Mikveh is 1 by 1 by 3 Amos, which is 40 Sa'im, or 240 Kavim. R. Tam will show that the box [of thumbs], which is a Revi'is, is 1 part in 3840 of a Mikveh. Since 3840=16(240), this proves that a Revi'is is 1/16 of a Kav, i.e. a quarter Log. To understand the coming calculation, observe that 3840= 4/3(2880), and 2880=(20)(12)(12). R. Tam shows that the height of the box is (3/4)(1/20) of the height of a Mikveh, and its length and width are each 1/12 of the length and width of a Mikveh.

Explanation: R. Tam explains as follows. The height of a Mikveh is 72 fingers (thumbs. This is 3 Amos, for an Amah is 6 Tefachim, and a Tefach is 4 thumbs.) If we remove a quarter [of the height of the Mikveh, i.e. keep 3/4], 54 fingers remain. One 20th of this is (2.7, which is) 2 + 1/2 + 1/5.

Calculation #1 of the box: Similarly, take 1/12 of the length and width of the Mikveh (1 Amah = 24 fingers, so 1/12 is 2 fingers. This shows that the box,) i.e. 2 fingers by 2 fingers by 2 + 1/2 + 1/5 fingers [is (3/4)(1/20)(1/12)(1/12)=1/3840 of a Mikveh.]

Calculation #1 of the water: Take the same fraction of water in a Mikveh, and you will see that it is a Revi'is [according to Tosfos' definition of a Revi'is, unlike Rashi's Rebbeyim]. Remove 1/4 (of 40 Sai''m of a Mikveh, leaving 30), take 1/20 of the remainder (i.e. divide by 20, leaving 1.5 Sa'im, which is 9 Kavim, which is 144 Revi'yos), and take 1/12 of this twice (divide by 12 twice, leaving 1 Revi'is. Tosfos showed that the box' height is (3/4)(1/20) of the height of the Mikveh. Tosfos now shows another way to express this fraction, which is 3/80. Note that 3/80=(1/24)(9/10).)

Calculation #2 of the box: Alternatively, take 1/24 [of the height of a Mikveh (72 fingers), i.e. 3 fingers], and remove 1/10 [leaving 2.7 = 2 + 1/2 + 1/5. Tosfos will now offer a third way to express the box' height as a fraction of the height of the Mikveh. Note that 3/80=(1/4)(3/4)(1/5).]

Calculation #3 of the box: Alternatively, take 1/4 [of the 72 fingers,] i.e. 18, and remove 1/4, leaving 13.5, and take 1/5 of them. (A fifth of 13.5 is 2.7, i.e. 2 + 1/2 + 1/5]. This is from the Ri. (Tosfos will now show that this fraction, i.e. (1/4)(3/4)(1/5), of the water in the Mikveh, is a Revi'is,

Calculation of the water based on Calculation #3: Take a quarter [of the 40 Sa'im of a Mikveh, i.e. 10] and similarly remove [a quarter of the 10, leaving 7.5] and take 1/5 of them (this leaves 1.5 Sa'im = 144 Reviyos, like above (d)). If we twice divide by 12, the length and width of the box will be 2 fingers, and it holds 1 Revi'is, like above (d). Tosfos now justifies the fraction based on Calculation #2, i.e. (1/24)(9/10).)

Calculation of the water based on Calculation #3: Alternatively, remove 1/10 (of the 40 Sa'im of a Mikveh), leaving 36. Since the Mikveh's height is 3 Amos=18 Tefachim, this is 2 Sa'im per Tefach, which is 1.5 Sa'im for a height of 3 fingers (3/4 Tefach. Since (1/24)=(1/18)(3/4), this is 1/24 the Mikveh's height.)Since we removed 1/10 of the water, we must likewise remove 1/10 of the height of the box, so 2.7 remains. The 1.5 Sa'im [per 3 fingers of height] are for the length and width of the Mikveh. We divide twice by 12, to make the length and width of the box 2 fingers, like above.) According to the Bavli, the calculation works exactly.

Question: However, the Yerushalmi says that the box is 2 fingers by 2 fingers by 1 + 1/2 + 1/3 fingers. A Piyut (Az Ra'isi, for Parshas Shekalim. Ra'avan says that ha'Kaliri (probably R. Elazar b'Rebbi Shimon) wrote it) calls the height 2 less a 1/6, which is the same as the Yerushalmi. This is difficult, for the calculation of the Mikveh is not exact!

Answer #1: The Yerushalmi discusses fingers [based on the measures] of Tzipori. Here we discuss fingers of the Midbar. 2 + 1/2 + 1/5 = 16/6 and another 1/5 of 1/6. When they came to Yerushalayim (1 Midbar finger = 5/6 Yerushalmi fingers, so) this amount fit into (13.5)/6 fingers. (13.5=(5/6)16.2.) When they came to Tzipori (1 Yerushalmi finger = 5/6 Tzipori fingers, so) this amount fit into 11/6 and 1/4 of 1/6. (One Midbar finger = 25/36 Tzipori fingers, so 27/10 Midbar fingers = (27/10)(25/36) = 625/360=15/8 Tzipori fingers. This exceeds the Yerushalmi's height (11/6) by 1/4 of 1/6 (=1/24. Below we compensate for this.)

Adjustment of the width: Similarly, we must deduct from the width, for the Bavli discusses a square box, and the Yerushalmi discusses a round (cylindrical) box. The Piyut alludes to this. It says "the cup is 2 by 2 fingers around". The area of a circle of diameter 2 equals that of a rectangular box 2 fingers by [1 and] a half fingers, since a square is 1/4 [of its own area] greater than a circle [inside it. I.e. a circle 2 by 2 has area 3. This is an approximation used throughout the Gemara, for it is tedious to be precise; perhaps there is a tradition from Sinai to rely on it (Sha'ar ha'Tziyun 372:18).]

The area of the circle: [The area of] a square 2 by 2 Midbar fingers fits into a circle 2 by 2 Tzipori fingers. The circle has an extra 4/6 of a 1/6, which is 1/9 [of a square finger].

Note: Teshuvas Chasam Sofer (OC 153) notes that the calculation based on our text is very errant. A Tzipori finger is 36/25 Midbari fingers. A circle of diameter 2 Tzipori fingers has area 3(36/25)(36/25), which is more than 6 [square] Midbari fingers. A square of 2 Midbari fingers has area 4. How can Tosfos says that it is only 1/9 more?! The Chasam Sofer changed the text to say that Tosfos compares a square 2 by 2 Midbari fingers and a circle 1.5 by 1.5 Tziporiyos fingers. Indeed, this calculation works better, but why would Tosfos discuss this? He sought to resolve the calculation based on the Yerushalmi! I suggest that even though throughout Tosfos, Etzba refers to thumbs, regarding the diameter of the cup, which the Paytan calls "2 by 2 fingers around", we discuss two actual adjacent fingers on the hand. Stam Etzba usually refers to the index finger, which is 1/5 of a Tefach, or 4/5 of a thumb (Menachos 41b). If one must hold it adjacent to another finger and rotate them, this is easiest with the middle finger, which is about the same width. If both are 4/5 of a thumb, the area of a square 2 by 2 Tzipori index fingers is ((36/25))(4/5)) squared, i.e. 20756/15625 square Midbari thumbs. The area of the circle is 3/4 this, i.e. 15552/15625, i.e. .994 of the area of the square. (Pesach Feldman)

Note: Tosfos says that the area is 1/9 more. This is not because the exact area of a circle is Pi/4 = (3.141...)/4 times the area of the square, for the exact area is about 1/7 more than the approximation. Also, Tosfos relies on the approximation! Perhaps it is more because the middle finger is slightly wider than the index finger. (Pesach Feldman)

Resolution #1 of the Bavli and Yerushalmi: Deduct from this (additional 1/9) the excess 1/24 (of the height of the Bavli's box), and a small amount remains. The Yerushalmi was slightly stringent, on the side of stringency (it gave a bigger Shi'ur. The extra 1/9 [square] finger is about 1/27 of the area. The extra 1/24 of the height of the Bavli's box is 1/44 of its total height. Overall, the Yerushalmi's volume is (28/27)(44/45)=1232/1215 times the Bavli's, about 1.4% extra.

Note: Sometimes a bigger Shi'ur for a Revi'is is a leniency, e.g. to exempt from a Berachah Acharonah, to permit Birkas Kohanim or Halachah rulings after drinking wine, to be Metaher blood from Tum'as Ohel... If not for Tosfos, one could say that the calculation is precise, e.g. if we assume that the middle finger is 1/44 wider than the index finger. This would increase the cup's area by 1/44, and exactly offset the extra height of the Bavli's box over the cup. Or, if both fingers are the same, but the Yerushalmi allows a space 1/44 of a finger between them. Eruvin 4a discusses a smiling Tefach, in which there are small spaces between the fingers. It did not say how big the spaces are. The Rashba (cited in Beis Yosef YD 201) says that a smiling Tefach exceeds a sad Tefach (without spaces) by 1/48. Alternatively, the Yerushalmi holds [unlike the Bavli] that the index finger is about 1/88 more than 4/5 of a thumb. (Pesach Feldman)

Resolution #2 of the Bavli and Yerushalmi: He (the Ri) alternatively explains that the Yerushalmi [discusses the same fingers as the Bavli. It] refers to a circle in which one can fit a square 2 by 2 fingers. It (the circle) is a third bigger, like we say (Sukah 8b) "the square in the circle, half." I.e. [the area of the circle exceeds that of the square by] half the [area of the] square. (If the cup has the same volume as the box, its height should be a third less.) If you remove a third of the height [of the box], which is [2.7=] 13.5 fifths, 9/5 remains, which is two less 1/5. The Yerushalmi calls this 2 less 1/6. It was imprecise (about 1.7%) to be stringent [to require a bigger Shi'ur]. The Piyut says "l'Rivu'a for the cup of salvation." It does not mean that it is Ribu'a (square), rather, that the Revi'is prepared for the four cups of Pesach were enacted corresponding to redemption and salvation.

Clarification: A person takes up one square Amah together with his clothes, as the Gemara says in Eruvin (Daf 48.) 'A man takes up one Amah by one Amah'.

Question: In the Sugya of 'Kuchin' in Bava Basra (Daf 101.) however, it is implied that the Kuch (a sepulchral chamber) measures one Amah including the wall of the coffin, in which case a person takes up less than an Amah.

Answer: And the reason that a Mikvah needs to be an Amah is to allow the person to enter into it with his arms not hugging his body.

Implied Question: Even though the height of a person is three Amos minus the head - that is why the Gemara in Bava Basra requires Kuchin to measure four Amos, to allow for the head and the thickness of the boards?

Answer: a Mikvah of three Amos will suffice, because when one Tovels the level of the water rises.

Conclusion: And it must speak where the 'vessel' in which one is Toveling is taller than three Amos. Otherwise, when one enters the water, some of the water will spill over the side, and the Shi'ur will be lacking.

Implied Question: And if, in Targum (Sheini, chapter 9) in the Megilah, it reckons three Amos for each one (of the sons of Haman?

Answer: That is because their heads were cut off.

Question: Even assuming that one Amah could fit into one Amah, how could one Tovel the Shulchan, which measured one Amah in length, but was one and a half Amos tall, in a Mikvah measuring an Amah by an Amah?

Answer: The Shulchan measured one and a half Amos included its legs, which were not attached to it.

Support: And this is also how Rashi explains in Parshas Terumah.

Question: The Yerushalmi asks why it was not Matim She'uvin?

Refuted Answer: Because even though a vessel that holds forty Sa'ah of liquid which is equivalent to two Kur of solids is not subject to Tum'ah, since it cannot be be moved full as well as empty ...

Refutation #1: As far as She'ivah is concerned it is considered a K'li, as we learned regarding the eighteen things (in Shabbos, Daf 16:), in connection with 'Someone who leaves Keilim underneath a pipe'.

Refutation #2: Moreover, the Yam shel Sh'lomoh was made of copper, and is therefore subject to Tum'ah even though it cannot be carried full as well as empty.

Refutation #2 (concl.): Since it is only wooden Keilim that are compared to a sack (in this regard).

Answer: To answer the question, the Yerushalmi establishes it that the feet of the oxen, which had holes large enough to let a pomegranate through were attached to the spring beneath them.

Implied Question: And the reason that it mentions 'Motzi Rimon, is in order to negate the oxen's status of a K'li, so that they not be subject to Tum'ah ...

Answer #1: But to validate the water in the Yam, a hole the size of the opening of a jar would have sufficed.

Source: As we learned in the Mishnah in Mikva'os (6:5) 'One may Tovel in a sedan, a box or a cupboard that have a hole the size of the tube-shaped opening of a flask'.

Answer #2: My Rebbe R. Yechiel however, explained that a Motzi Rimon is required here - because the oxen divide between the actual Yam and the spring, so that it like pouring from one K'li to another, since they were distant from one another ...

Answer #2 (cont.): And the water needs to arrive there (in the Yam) in a gush.

Support: And he brought a proof for this from a Tosefta.

Yerushalmi: We learned there in the Mishnah that 'One may not cook wine of Terumah because boiling reduces it. Rebbi Yehudah permits it, because it improves it'.

Yerushalmi (cont.): Rebbi Yochanan switches the opinion of Rebbi Yehudah' - because the Mishnah says that one is permitted to take Terumah from wine that is not boiled to cover wine that is, but not vice-versa'.

Yerushalmi (cont.): Therefore, he switches the opinions and learns that 'One may not cook wine of Terumah because boiling reduces it; whereas the Chachamim permit it since it improves it.

Yerushalmi (cont.): And Rebbi Elazar argues with Rebbi Yochanan there and does not switch the opinions.

Conclusion: And since the Halachah is like Rebbi Yochanan according to the Rabbanan, one can be Yotzei the Mitzvah of the four cups with boiled wine, and recite Kidush and 'Borei P'ri ha'Gafen' over it.

Implied Question: Even though Rava himself says later that "Veyishm'recha" does not combine for the bad?

Answer: That is only as regards Mazikin, but regarding witchcraft, one would still need to worry about it.