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Thought for the Day: עירובי תחומין -- Which Side Is the Leniency?

I know what you are thinking... good grief, more philosophy?  Enough already; let's zip over to the laws of עירובי תחומין.  In broad strokes, a person's תחום is 2,000 cubits in each direction from wherever he makes his residence on Shabbos.  Pretty much your residence is where you live.  However, suppose you want to spend most of Shabbos at home, but you want to go to hear a particular rav speak on Shabbos afternoon, and he will be speaking 4,000 cubits due west of your house.  That's where עירוב תחומין comes in.  [NB: עירובי תחומין are only allowed for either a mitzvah or other pressing need.]  Basically, again in broad strokes, Chazal allowed you to establish an effective residence and then use that location as the center of your תחום.  Thus, if you establish your residence 2,000 cubits due west of your house, then you can eat and sleep at your house before walking 4,000 cubits (2,000 to your effective residence plus 2,000 more to its west) due west to hear the rav.

Now let's flesh out some details.  Your effective residence can be established in one of two ways.  First, you can actually go there and sit till after dark.  When you do it that way, you are "walking (find... sitting) the talk" and having intention to establish your effective residence there is enough.  The second way is to put (or have an agent place -- more on that later) food for two meals at the place where you want to establish your effective residence.  In that case, since you are sitting at home, you need to actually speak out that you are establishing your effective residence there.

Note, if you will, that an עירוב תחומין does not extend your תחום, it merely shifts your תחום.  In other words, whatever you gain on one side, you lose from the other.  As an extreme example, suppose you have a suit owned jointly by two brothers who live 4,000 cubits apart; one 2,000 cubits to the east of their parents' house (where they stow the suit) and one 2,000 cubits to the west.  A suit (or any other vessel/article of clothing) takes on the תחום of its owner.  In this case, then the suit cannot be moved on Shabbos -- it is already at the western edge of the eastern brother's תחום and the eastern edge of western brother's תחום.  I hope it's not such a fancy suit, as they are only going to be able to wear it during the week or when eating Shabbos or Yom Tov meals at their parents home.  (Ah... cagey parents who want to see their kids more often; but only one at a time.)

Here's a really cool problem:  Suppose someone mistakenly thought he could establish one תחום for Friday night and another for Shabbos day (he wants to hear two different shiurim on different sides of his תחום).  This is a mistake, so (at least) one of the עירובים is not effective; but which one?  We cannot apply "in case of doubt about a rabbinic obligation, go for the leniency" because there is no clear leniency here; each comes with a stringency.  Moreover, since he definitely had intention to not establish his residence at home, he has lost that also.  He is stuck wherever he started his Shabbos till after havdala.  Cases of two day Yom Tov or Yom Tov followed/preceded by Shabbos is tricky.

I have never personally set up עירובי תחומין; in fact, I don't know anyone who has.  Yet, the Mishna Brura (technically, Biur Halacha) says in a few places that lots of people make big mistakes for this or that reason.  Apparently עירובי תחומין used to be much more common.  It is a sad commentary on our time and/or here in America that you can have a suburb with thousands of Jews and yet no minyan; whereas in Europe you have tiny communities with a few families who regularly made עירובי תחומין so they could daven together in a minyan.
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