(a) RASHI explains that when there are two different measurements for the
Techum Shabbos, it must be that one of them was mistaken. However, we do not
assume that one of them made a mistake in the actual measuring. Rather, we
assume that one of them made a mistake in the Halachos of measuring. They
both measured correctly; they are both experts in the science of surveying.
We assume that one of them made a mistake in the Halachah, and that Halachic
mistake caused him to come out with a different measurement. If we can
attribute the difference in their measurements to a Halachic mistake causing
one of the measurements to come out too short, then we may follow the larger
measurement. If there is no way to attribute the difference to a mistake in
Halachah, then we would have to be stringent and follow the smaller
measurement.
Therefore, when the Mishnah says that if one person's measurement was larger
than another's then we follow the larger measurement, we assume that the one
who measured the smaller measure erred in the Halachah and did not stretch
the rope as much as he was required to by Halachah.
Abaye adds that even if there is a larger difference between the two
measurements than that which could come about from not stretching the rope
properly, we still may assume that one of them erred in Halachah, as long as
the difference between the two measurements is not more than the difference
between 2000 Amos and the diagonal of a square whose sides are 2000 Amos
(that is, the difference between 2000 Amos and 2800 Amos -- or 800 Amos). If
the difference is less than 800 Amos, then we assume that the one who
measured the shorter measure did not know that he was supposed to measure
the diagonal of 2000 Amos (2800 Amos) in the diagonal direction from the
corner of the city and he instead measured only 2000 Amos.
(b) TOSFOS has a different approach. We do not attribute the difference in
measurements to *any* mistakes, neither a mistake in measuring nor a mistake
in Halachah. Rather, the case of the Mishnah is when two people measured
from two different points of the city. If one person came out with a larger
measurement and the other came out with a shorter measurement, we assume
that they are both correct and that the person who came out with the shorter
measurement must have had some slopes along the line of his measurement and
had to use different measuring techniques for those slopes which may have
caused his assessment of the Techum to be shorter than the other person's
(as we saw on 58a).
When Abaye says, "... as long as one's measurement is not greater than the
size of the city's diagonal," he is referring to a case where both
measurements were made on the same side of the city. We compare the
difference between the two measurements to the size of the diagonal of the
entire city; that is, from one corner of the city to the far, opposite
corner. If the difference is greater than the diagonal of the entire city,
then we assume that there was a mistake and we must be Machmir and follow
the shorter measurement. If the difference between them is *less* than the
diagonal of the entire city, then we assume that when the first one measured
the Techum, there were only a few houses in the city, located in one corner
of the city. More houses were built and the city grew, and the second person
measured the Techum from the opposite corner of the original dwellings in
the city. The length of the diagonal of the city represents the amount that
the city grew between the two measurements, and that distance was added on
to the city's Techum. We may therefore assume that both measurements are
correct; the first one was made before the city grew, and the second one was
made after the city grew.