OPINIONS: The Mishnah (58b) states that if two people measured the same Techum but their measurements resulted in different distances, we follow the longer measurement. Abaye says that we follow the longer measurement only when the difference between the longer and the shorter measurements is not more than "the measure of the diagonal of the city." What exactly does this mean?

(a) RASHI writes that when two people take different measurements for the same Techum Shabbos, it must be that at least one of them is mistaken. However, we do not assume that they 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 it is possible to attribute the difference in their measurements to a Halachic mistake that one of them made, then we may follow the larger measurement. If there is no way to attribute the difference to a mistake in Halachah, then we must be stringent and follow the smaller measurement.

Therefore, when the Mishnah says that if one person's measurement was larger than the other'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 would result from not stretching the rope properly, we still may assume that one of them erred in the 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 measurement 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 where two people measured from two different points of the city. If one person's measurement was larger than the other's, we assume that they are both correct and that the person 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. Those different measuring techniques may have caused his measurement of the Techum to be shorter than the other person's (as the Gemara on 58a demonstrates).

When Abaye says, "... as long as one's measurement is not greater than the size of the city's diagonal," he refers 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 stringent 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 person measured the Techum, there were only a few houses in the city, and those houses were located in one corner of the city. Later, 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 to the city's Techum. We 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.