Bava Metzia, Chapter 3, Mishnah 7. The main topic of the Mishnah is depositing foodstuff with a watchman: when the depositor is absent for a prolonged period, some of the food will naturally be lost - mice gnawing at it, wind scattering it, mold, and so on. Therefore, the Mishnah rules that when the watchman returns the deposit, he may deduct the amount that could reasonably be expected to be lost due to ants and mice.
As a preface: a watchman is not supposed to mix his own produce together with the items he is guarding. If a pile of wheat was deposited with him, he must place it in his storehouse in a safe place and by itself. In such a case, when the depositor comes and claims his wheat, the watchman returns whatever is there - whatever was eaten is eaten. The watchman fulfilled his obligation by storing the wheat in his storehouse, and whatever the mice took, they took, and no calculation of any kind is necessary.
Two cases where a calculation is required:
The watchman acted improperly and mixed his wheat with the depositor's wheat, and now everything is mixed up and there is no way to know how much remains of the depositor's original wheat.
The depositor himself permitted it and said: "You do not have space to guard my wheat separate from yours - put it all together with yours, and even use it," meaning from the joint inventory of wheat. Here too, there is no way to know what remains of mine and what is already yours.
In both of these cases - and this is the application of our Mishnah - the calculations presented in the Mishnah are made, in order to clarify how much must be returned and how much may be deducted, based on the assumption that some was lost by mice and the like.
The Mishnah goes into technical details and specifies precise rates of deduction, operating on the assumption that the storage was done in the Land of Israel during the time of the Mishnah. Today, in an era of air conditioning, climate control, and mouse poison, there are no plagues of mice and such things, and therefore these measurements are not practically relevant - but the principle is certainly valid.
The words of the Mishnah: "Hamafkid peiros eitzel chaveiro... harei zeh yotzi lo chesronos" - One who deposits grain with his fellow, and the latter mixed it with his own and used his own grain, until it is impossible to know exactly how much of the original grain is there. At the time when he returns the grain to its owner, he is permitted to deduct the expected and reasonable losses that occurred over time.
Before detailing the measurements, let us clarify the units of volume:
Kav - the standard grain measurement, about two liters.
Seah - six kavin.
Kor - thirty seah, and it is the largest unit of volume.
It turns out that in one kor there are one hundred and eighty kavin (six times thirty). Furthermore, all the rates below are stated on an annual basis: if the wheat was deposited for two years, the watchman will return only ninety-five percent of what was deposited with him.
The rates of loss:
"Lechitin ule'orez - tishah chatza'ei kavin lechor" - four and a half kavin out of one hundred and eighty, meaning two and a half percent (one fortieth) per year. Regarding 'orez', the commentators disagree: according to Rashi the reference is to millet, which is a type of grain, and according to Tosafos the reference is to actual rice, and this is the accepted translation in practical Halachic Hebrew.
"Lise'orin uledochan - tishah kavin lechor" - nine out of one hundred and eighty, meaning five percent.
"Lekusmin ulezera pishtan - shalosh se'in lechor" - three seah out of the thirty in a kor, meaning ten percent.
The Gemara asks about flaxseed: Ten percent a year does not just disappear, so where does it go? It answers that this refers to flaxseed still in its stalks, and the stalks indeed shrink quite a bit.
"Hakol lefi hamiddah, hakol lefi hazman" - The calculation is done relatively, according to the volume and the amount of time. According to the volume: For one kor of barley, nine kavs are deducted, for two kor - eighteen kavs, for three - twenty-seven, and so on. According to the time: For every twelve months, the stated amount is deducted, and for twenty-four months, eighteen kavs are deducted for each kor, and so on.
The opinion of Rabbi Yochanan ben Nuri:
Rabbi Yochanan ben Nuri disagrees: Where does the grain go? Primarily to rodents, and mice only eat a certain amount, so there is no reason to calculate this relatively. In the words of the Mishnah: "Vechi mah ichpat lahen la'achbarim, vahalo ochlos bein merubeh bein muat, ella eino motzi lo chesronos ella lechor echad bilvad" - A deduction is made only from the first kor: For one kor of barley, nine kavs are deducted, and even for two or three kor, nine kavs are deducted per year, since the amount mice eat is limited.
The Gemara rejects this opinion for two reasons:
How do we know that mice are the only destination of the grain? There are cracks, wind that scatters it, and other factors.
When there is abundant food, rats call their friends and hold a massive rodent feast there - the more food there is, the more rodents come.
The halachah follows the Tanna Kamma, insofar as this is relevant.
The opinion of Rabbi Yehudah:
Rabbi Yehudah adds another factor that must be taken into account - the humidity in the air. In the summer, the air in the Land of Israel is dry, and the grain dries out and shrinks. This is also the way it is stored: It is brought into the storehouse at the end of the summer, when it is dry, so that it will not mold, and then it is more or less at its minimal volume. But when it is returned to the depositor about half a year later, during the winter, the grain absorbs the moisture of the air and swells, increasing its volume.
The basis of his words: With ten kor deposited from the beginning of the summer until the middle of the winter, the amount that mice are expected to eat is offset exactly against the amount of swelling due to moisture absorption, and therefore the watchman returns the exact same volume that was deposited with him.
With less than ten kor or more than that, as well as when it does not involve transitioning from the summer to the winter, the calculation changes, and therefore the halachah does not follow Rabbi Yehudah. In the words of the Mishnah: "Rabbi Yehudah omer: Im hayisah middah merubah, eino motzi lo chesronos, mipnei shemosiros" - If there was a large quantity, which the Gemara explains refers to ten kor, which is an enormous amount, no deductions are made at all, "mipnei shemosiros" - because the grain swells due to moisture absorption, and this offsets the depletion.
Halachah: The halachah follows the Tanna Kamma - it is permitted to make a deduction in a case where the watchman mixed the deposit with his own food and ate from it. However, a priori, one should not act this way at all, but should rather store the deposit separately and return it as is, in whatever condition it is found.