1) ONE LETTER IN THE MORNING, ONE IN THE EVENING
OPINIONS: The Mishnah at the end of the Perek cites an argument between Raban Gamliel and the Chachamim with regard to one who writes "two letters in two lapses of awareness, one letter in the morning and one letter in the evening." What exactly is the case of one who writes one letter in the morning and one in the evening?
(a) RASHI explains that the Mishnah refers to two different cases. The first case is where one writes two letters in two lapses of awareness. The second case is where one writes one letter in the morning and one in the evening. Since he had so much time in between the two letters to find out that it was Shabbos (or to find out that writing on Shabbos is forbidden), he is considered as though he wrote the two letters in two separate lapses of awareness.
(b) TOSFOS disagrees. We never find that an extended period between two forbidden acts done unknowingly at two different times in the day is considered like two lapses of awareness. Rather, Tosfos explains that the Mishnah refers to a case in which the person indeed remembered that it was Shabbos between writing the two letters, and thus he had two lapses of awareness. The reason why the Mishnah mentions that there was such a long period of time between the writing of the two letters is to teach that even in such a case, Raban Gamliel argues with the Chachamim and says that the person is Chayav to bring a Korban for writing two letters on Shabbos.
2) ONE WHO SETS UP TWO "BATEI NIRIN" ON SHABBOS
OPINIONS: The Mishnah says that one who sets up two Batei Nirin is Chayav, whether in "Nirin" or in "Kirus." (See D.A.F.'s photograph of a homemade loom in Graphics section, Photo #1.) Abaye explains that this means "two in the Batei Nira and one in the Nira." To what do these parts of the loom refer?
A few words of introduction are necessary. The general function behind the loom's operation is to raise one row of warp threads (Shesi) and to lower the other so that one may pass the woof thread (Erev, which is wound in the Buchiyar, or shuttle) between them, and then to reverse the action and raise the row that was lowered and lower the row that was raised so that one may again pass the woof thread between them and thereby form a weave. The "heddles" are the parts of the loom which lift and lower the rows of warp threads. The heddle is a frame that contains rings through which the warp threads are threaded. When one heddle is lifted, all of the warp threads that pass through its rings are also lifted, so that one may then pass the shuttle (that contains the woof thread) between the two rows of warp threads. Each ring in the heddle is held in place by a taut string that is attached to the top of the frame of the heddle and by a taut string that is attached to the bottom of the frame of the heddle.
(a) The TOSFOS YOM TOV explains that "two in the Batei Nira and one in the Nira" means that one warp thread is passed through one hole in the first heddle (so that the thread is lifted when the first heddle is raised) and then that thread is passed between the rings in the second heddle (so that the thread is not lifted when the second heddle is raised), and then the thread is passed through the comb which is held at the end of the warp threads right before they are woven. This comb is used to press each woof thread against the previous one after it is woven. Even though this comb is called the "Nira" here, it is normally called the "Kirus."
(b) The TIFERES YISRAEL (in Kalkeles ha'Shabbos) says that it means that two strings are passed through one ring of one heddle and one other string is passed through one ring of the other heddle.
(c) RASHI may understand that "two in the Batei Nira and one in the Nira" refers to two threads that are passed through two adjacent rings, and one string is passed in the open space between the two rings. "Batei Nira" refers to the rings, and "Nira" refers to anywhere within the heddle frame, but not in the rings. (M. KORNFELD)
(d) The TOSFOS RID in the seventh Perek (73a) writes that "making two Batei Nirin" does not mean passing threads through the rings in the heddle. Rather, it refers to actually making the rings themselves. Accordingly, the Gemara may mean as follows. Each ring has two strings tied to it that hold it in place ("two in the Batei Nirin"), and the other ends of the strings are each attached, respectively, to the top and bottom of the heddle ("and one in the Nira" -- since only one string is attached to each side of the heddle's frame).

105b----------------------------------------105b

3) ONE WHO TEARS HIS CLOTHING IN MOURNING ON SHABBOS
QUESTION: The Mishnah states that one who tears his clothing on Shabbos out of anger or in mourning over the death of a relative is exempt, because his act is not a constructive one but a destructive one. The Gemara points out that there is a contradiction between the Mishnah and a Beraisa that states that one who tears his clothing for the death of a relative is Chayav, since he accomplishes something positive -- he fulfills the Mitzvah of tearing Keri'ah. The Gemara concludes that the Mishnah refers to the death of a distant relative for whom one is not Chayav to tear Keri'ah, while the Beraisa refers to the death of a close relative for whom one is Chayav to tear Keri'ah.
Why does one fulfill the Mitzvah of Keri'ah on Shabbos? The act of Keri'ah should constitute a "Mitzvah ha'Ba'ah b'Aveirah," a Mitzvah that was done through a transgression!
ANSWER: The RITVA quotes the Yerushalmi that asks this question. The Yerushalmi asks what the difference is between one who tears Keri'ah on Shabbos and one who eats stolen Matzah on Pesach (in which case one does not fulfill the obligation to eat Matzah, because it is a "Mitzvah ha'Ba'ah b'Aveirah"). The Yerushalmi answers that in the case of Matzah, "the act of eating is an Aveirah," but here, "the person himself transgresses the Aveirah." The case here is no different from a case in which one eats Matzah that was carried from Reshus ha'Yachid to Reshus ha'Rabim; he nevertheless fulfills his obligation. What exactly does the Yerushalmi mean?
(a) Some Rishonim explain that when one steals Matzah to eat on Pesach, the transgression has an effect on the object (the Matzah), and that effect remains on the Matzah until the moment he eats it. A stolen piece of Matzah is subject to an obligation to return the stolen object to its rightful owner, and therefore the object itself is an "object of Aveirah." In contrast, when a person tears his clothing upon hearing of the death of a relative on Shabbos, the transgression has no effect on the object, and thus one fulfills his obligation. The concept of "Mitzvah ha'Ba'ah b'Aveirah" applies only when the object is affected by the transgression and is an object whose very nature contains an element of transgression. (RITVA to Sukah 30a)
(b) Other Rishonim explain that "Mitzvah ha'Ba'ah b'Aveirah" applies only when the Aveirah itself is the cause of the fulfillment of the Mitzvah. That is, without the Aveirah, the Mitzvah would not be done (see TOSFOS to Sukah 30a). A person must own the Matzah he eats in order to fulfill the obligation to eat Matzah on Pesach night. When a person steals Matzah, he acquires it when the owner gives up hope of ever retrieving (Yi'ush). Thus, it is the Aveirah (the act of stealing) that causes the Matzah to become his and enables him to fulfill the Mitzvah. In contrast, in the case of one who tears his clothing on Shabbos in mourning, the transgression of tearing on Shabbos is not what enables him to fulfill the Mitzvah. Since the person could fulfill his obligation to tear this garment without transgressing Shabbos (such as by tearing it on Sunday), his act on Shabbos is not considered a "Mitzvah ha'Ba'ah b'Aveirah."