Before us is Mishnah 7 in the fourth chapter of Maseches Eruvin, which deals with a person who wishes to establish a place of Shabbos residence for himself other than the place where he is standing when Shabbos begins.
The case in the Mishnah:
A person is traveling on the road on Erev Shabbos and the day grows dark upon him, and he is about four thousand amos away from his home, so he cannot reach his house before Shabbos. But he spots a landmark in the distance: a certain tree or a certain fence, and he says: "Shevisasi tachas oso ilan" - my Shabbos residence is beneath that tree (or alongside that fence). That landmark is slightly less than two thousand amos away from him, and from there to his home is another two thousand amos. His intention is that the tree or the fence should be considered the center point of his techum, so that he will be able to reach it on Shabbos and continue from there to his home, since his home will stand at the edge of the two thousand amah boundary.
Why this designation does not help:
The Mishnah rules that this designation is ineffective. The Gemara explains the reason: since he did not single out a specific point at that tree or at that fence, and we are speaking of an area larger than eight amos, we have no way of knowing where exactly his Shabbos residence was established. Perhaps he meant the four amos at this end of the tree, and perhaps the four amos at the other end, while he himself never specified which four amos would be his place of residence.
At the moment of his declaration it was also clear that he did not want his Shabbos residence to be in the place where he was actually standing, but rather somewhere else. The result, therefore, is that he has no Shabbos residence at all:
He does not have two thousand amos from the place where he is standing, since he did not want to establish his residence there.
He does not have two thousand amos from the tree or from the fence, since he did not clearly single out a specific spot there.
All that remains to him are the four amos of the place where he is standing.
When the tree is smaller than eight amos:
If the tree is less than eight amos, even though he did not specify the exact spot and his intention could have been to either end, nevertheless, since the area is smaller than eight amos, there is necessarily a zone of overlap between the two possibilities, even a single amah or less, which is certainly included in his place of residence. In such a case he acquires his Shabbos residence in that place, since it is sufficiently clear that there is at least some area there that is definitely his place of residence.
"Shevisasi be'ikaro" - a precise designation:
A further illustration of this principle is found in the next ruling in the Mishnah: one who says "Shevisasi be'ikaro" - my Shabbos residence is at its base, meaning at the trunk of the tree itself - has been precise in his designation, and we know clearly where it is. This is not a doubt between these four amos and those four amos, but a defined and identifiable place. Since he singled out a specific spot, the Mishnah says: "Mehalech mimkom raglav ve'ad ikaro alpayim amah, ume'ikaro ve'ad beiso alpayim amah, nimtza shemehalech mishetechshach arba'as alafim amah" - he walks from the place of his feet to its base two thousand amos, and from its base to his home two thousand amos, so that he walks four thousand amos once it becomes dark:
From the place where he is standing when Shabbos begins until the trunk of the tree - slightly less than two thousand amos.
From the trunk until his home - another two thousand amos.
It turns out that in this case he can walk four thousand amos once it becomes dark, because we view him as though he is standing at the outer edge of his techum: he walks the two thousand amos to the tree, and from there another two thousand amos to his home.
In summary: designating a Shabbos residence in a distant place is effective only when the place is clearly identified. A landmark wider than eight amos, without singling out a specific point, deprives him of a Shabbos residence anywhere, and he is left with only four amos; a landmark smaller than eight amos leaves a definite zone of overlap, and therefore he acquires his residence there; and one who says "Shevisasi be'ikaro" has singled out a precise spot, and he is able to walk four thousand amos once it becomes dark, all the way to his home.