Mishnah 5 in chapter 5 also deals with a mixture of chullin and Terumah. The case before us: one se'ah of Terumah that fell into a hundred se'ah of chullin - a classic case of nullification, and seemingly all is well, since the entire mixture is permitted even to a non-kohen.
The Mishnah's starting point:
One se'ah must be removed from the mixture and given to a kohen. The kohen treats it as Terumah - eating it in a state of purity and according to the laws of Terumah - even though in truth it originates in a mixture that has already been nullified and has the status of chullin, since from that very vessel of a hundred and one se'ah a non-kohen may also eat. Even so, it is clear to us that within the se'ah given to the kohen there is hidden a minute portion of actual Terumah.
Hence the question: what is the law if that se'ah, which for lack of a more precise term we will call 'Terumah of rabbinic status', falls into another vessel of chullin? Does it too create a medumah mixture, even though its origin is chullin and it contains only one part in a hundred and one of Terumah?
The view of Rabbi Eliezer:
Rabbi Eliezer says that it does, and he is consistent with his own approach: we assume that the unit removed from the mixture is the very unit that fell into it - and this is a stringency. Accordingly, when one takes a single se'ah and returns it to the kohen, we assume the most stringent possibility: the entire unit returned to the kohen is full-fledged Terumah. Therefore, if it falls again into a second mixture of chullin, it creates a new medumah mixture, as though pure, undiluted Terumah had fallen into it.
In practice: if the se'ah given to the kohen falls into a second batch of chullin, a hundred units of chullin are needed in the second batch in order to permit the entire mixture to a non-kohen, and once again one unit is removed from it and given to a kohen. But if the second batch does not contain a hundred units, the entire mixture is forbidden to a non-kohen, and all hundred and one units must be given to a kohen alone.
The view of the Sages:
The Sages disagree and do not accept Rabbi Eliezer's stringency. In their view, what is returned to the kohen contains only a minute portion of Terumah, and it does not have the power to render a mixture medumah as full Terumah would. This is what they meant by: "ein hameduma ela lefi cheshbon" - it renders a mixture medumah only according to the amount of Terumah actually contained in it.
The Rishonim understood their words in two different ways.
The view of the Rambam - the calculation in practice:
According to the Rambam, one must make a calculation: how much genuine Terumah is present in that unit returned to the kohen. For the sake of simplicity we will use different numbers, and a liquid, wine:
Nine hundred ninety-nine liters of ordinary wine, into which one liter of Terumah wine fell. That makes one thousand liters in all, a ratio of nine hundred ninety-nine to one - far more than one hundred to one, and therefore the entire mixture is permitted to a non-kohen.
Even so, one liter must be removed and given to the kohen, since his monetary right is to one liter of Terumah. That liter is taken from the mixture that is permitted to a non-kohen, but once it is given to the kohen he treats it as Terumah.
Since the ratio is one in a thousand, it turns out that the liter returned to the kohen contains only one milliliter of actual Terumah, while the other nine hundred ninety-nine milliliters are ordinary wine.
It follows that if that wine falls into a second batch of ordinary produce, only one milliliter of Terumah has actually fallen in. The Rambam therefore understands that it is enough to have one hundred times the Terumah component alone - that is, one hundred milliliters of ordinary wine in the second batch - and the Terumah that fell in is automatically nullified.
According to these figures: if the second vessel held one hundred milliliters of ordinary wine, and the liter given to the kohen fell into it, there would be one thousand one hundred milliliters in all; but in fact there is only one milliliter of Terumah against one hundred units of the new ordinary wine, and that is enough to permit the entire mixture to a non-kohen. One liter must still be drawn off and given to the kohen for monetary reasons, since this is the property of the tribe of kohanim, but the mixture and whatever remains in it are permitted to a non-kohen, for what fell in was once again in a ratio of one hundred to one and was nullified.
The View of the Other Rishonim:
The Rambam stands alone in his opinion. Most of the Rishonim understand that what is in the second vessel makes no difference at all: since what came out of the first vessel was already nullified in a ratio of one hundred to one, there is no concept of creating a mixture of Terumah a second time, for it came from the very same vessel that a non-kohen may eat from, and it is therefore permitted. This is the view of the Rosh and the other Rishonim: it does not render a mixture forbidden a second time.
In summary: Rabbi Eliezer and the Sages disagree about the se'ah given to the kohen out of a mixture that has been nullified: according to Rabbi Eliezer it renders a mixture forbidden like certain Terumah, and according to the Sages "ein hameduma ela lefi cheshbon" - a mixture is reckoned only according to the proportion. The halachah follows the Sages, and certainly not Rabbi Eliezer, meaning that we go according to the proportion. As to what that proportion is, the Rishonim disagree: according to the Rambam one needs one hundred times the Terumah component alone - we do not take into account the ordinary component of what falls in, but rather set the ordinary component of what it fell into against the Terumah component of what fell in; while according to the other Rishonim there is no mixture of Terumah here at all. Whether the halachah follows the Rambam in this remains an open question.