Mishnah 5 in the ninth chapter of Menachos deals with the measures used in the Beis HaMikdash: "Kol ha-midos she-hayu ba-Mikdash hayu nigdashos, chutz mi-shel Kohen Gadol, she-hayah godshah le-sochah" - all the measures in the Beis HaMikdash were heaped, except for that of the Kohen Gadol, whose heap was contained within it.
Every vessel used for measuring in the Beis HaMikdash was used with a heaped quantity: the vessel itself - for example, the issaron vessel - held less than an issaron, and a heap of fine flour above its rim was needed to make up the full measure. The exception is the vessel used for preparing the chavitin of the Kohen Gadol, in which the quantity was measured level: it is filled to the rim only and no more. The reason is the need for precision, since this minchah was divided into two halves, and one must make sure that the two halves are equal and that nothing falls to the floor.
The connection to Mishnah 1 of the chapter:
In the first mishnah of the chapter, the Tanna Kamma and Rabbi Meir disagreed as to whether the measures in the Beis HaMikdash were heaped or level: according to the first opinion one uses a level measure and not a heaped one, whereas according to Rabbi Meir the measures were heaped, except for the chavitin vessel of the Kohen Gadol.
Now here is something interesting: our mishnah is taught as a stam mishnah following the view of Rabbi Meir, and nevertheless the halachah is not decided in accordance with it. On the face of it this is a departure from the usual rule - when one mishnah teaches a dispute, and another mishnah in the same tractate teaches the law anonymously, without the other side of the dispute, the halachah follows the anonymous teaching. Yet here the halachah was decided like the Tanna Kamma of the earlier mishnah, that the measuring vessels were larger and are not to be heaped.
Why, then, do we depart from the rule?
A look at the continuation of the mishnah reveals that the dispute is taught again on this very subject, and if so we do not have a complete anonymous teaching before us.
Another fascinating possibility: we have a rule that "a stam mishnah is Rabbi Meir," and since Rabbi Meir is one of the opinions in the dispute here, it is as though the matter was not taught anonymously at all, but rather as Rabbi Meir teaching his own view as an individual.
"Biruzeihen" - what is the overflow?
Whether the measure is heaped or filled level, as the halachah was decided, the question arises as to the status of the overflow. The mishnah uses the word "biruzeihen," an uncommon word. The Bartenura explains - and his explanation is somewhat difficult - that it refers to the heaped quantity above the rim of the vessel, which is not actually contained within the vessel. But most of the Rishonim explain that it refers to what spills over the vessel and runs down its sides to the floor, and the word derives from the root "peretz" (the letters beis and pei interchange), in the sense of breaching a fence - that which goes beyond the boundaries of the vessel.
And these are the words of the mishnah: "Midos ha-lach biruzeihen kodesh, u-midos ha-yavesh biruzeihen chol" - as for the measures for liquids, their overflow is consecrated, and as for the measures for dry goods, their overflow is unconsecrated. When measuring liquids, even what spills down the sides of the vessel to the floor is consecrated, because it becomes consecrated by means of the vessel itself; but when measuring dry substances, such as flour, what spills over the edges is not consecrated at all.
Three approaches to the reason for the law:
Three views are stated in the mishnah, and they all agree with the final ruling - that the overflow of the liquid measures is consecrated and the overflow of the dry measures is not - and they differ only as to the reason for it.
Tanna Kamma: When Moshe Rabbeinu consecrated the original measuring vessels, he anointed the liquid measures both inside and out, and therefore even what spills over onto the sides is consecrated, since everything - including the outside - was made holy. The dry measures, however, were anointed with the anointing oil on the inside only: what is inside the vessel is consecrated, while what rises above its rim never enters the vessel at all and is not consecrated.
Rabbi Akiva: "Midos halach kodesh, lefichach beirutzeihen kodesh; midos hayaveish chol, lefichach beirutzeihen chol" - the liquid measures were consecrated inside and out, and therefore anything that enters them or comes out of them is consecrated by virtue of its contact with a service vessel that was invested with the power to consecrate. The dry measures, the isaron measure, were never consecrated in the first place; what enters them is not holy, and all the more so what never entered at all but spilled over the rim.
It emerges that according to Rabbi Akiva the measuring vessels for the fine flour do not consecrate at all. The fine flour becomes consecrated through a verbal declaration, when a person announces: "This is my isaron of fine flour with which to bring my minchah," and that is monetary sanctity; sanctity of the body comes at the next stage of the service - in the mixing with oil, which applies to most menachos, and in a minchah that has no mixing - in the kemitzah.
Rabbi Yosei: "Lo mishum zeh, ela shehalach ne'echar vehayaveish eino ne'echar" - in his view the vessels, both those for liquids and those for dry goods, were consecrated on the inside only, with no relevance to the outside, and whatever enters a service vessel becomes consecrated. The difference lies in the actual physical reality of liquids as opposed to solids.
The illustration is this: a vessel filled to the brim with a red liquid, and when clear water is added to it, the liquid that overflows onto the sides will be red. Whatever enters immediately mixes with what is already in the vessel, and there is nothing that can sit on top without blending into what is beneath it, and the same is true of wine and oil. With a solid, however, this is not the case: a vessel filled with flour dyed red, and more flour is added to it so that it heaps above the rim or spills over the sides - the flour that falls past the edges will remain white and will not mix in.
The word "ne'echar" is a borrowed expression: like clear water in which a person kicks up the dirt at the bottom and renders it murky. So too the liquid that rises above the rim becomes "murky" by mixing with what is beneath it, whereas the solid does not become murky - and this is the logic behind Rabbi Yosei's approach.
The halachah:
The Rambam rules that the outside of the dry measure, the isaron measure, is not consecrated, while the outside of the liquid measure is consecrated - and the inside of both vessels is consecrated. It emerges that he ruled like the Tanna Kamma of our mishnah.