The relative reviis

The following is an analysis of a seeming inconsistency in the Torah's prescribed volume of oil for the various types of korban animals, offering two opposing views in its reconciliation

 The Torah (Bamidbar 15) assigns specific amounts of oil for the menachos that accompany korbanos, and an equal and corresponding volume of wine for the accompanying nesachim.

For a כבש it is 1/4 of a hin, for an איל a third and for a בן-בקר one half. Now, the amount of flour in their menachos are 1,2 and 3 tenths of an ephah (in that order) respectively.

Ostensibly these are the amounts of oil required to do a proper belilah with the given number of esronos (with the wine mimicking).

The problem is that the ratio of oil to flour does not seem to be consistent. If each isaron of flour requires 1/4 of a hin of oil to be well mixed (as is laid down for the כבש) then 2 esronos should need 1/2 a hin and 3 esronos 3/4s (not the 1/3 & 1/2 which are stated), and conversely, if each isaron only needs 1/6 of a hin (1/6 hin*2 esronos=1/3 which is what is mandated for the איל, and 1/6*3=1/2 which is what is required for the בן-בקר) then the one isaron of the כבש should only require 1/6 of a hin (not the mandated 1/4).

Tur, in his long peirush in the above cited chapter, verse 4, picks up on this: סולת עשרון בלול ברביעית ההין – תימא למה אין הפסוק משוה כאן לשיעור השמן שלפי מה שצריך לעשרון סולת רביעי׳ ההין שמן הטעם עשרון סולת צריך רביעית ההין להבלל בו א״כ לפי זה צריך לנסכי איל שהם שני עשרוני׳ חצי ההין שמן ולנסכי פר שהן ג׳ עשרונים הין פחות רביע ולא הי׳ כן אלא לאיל שלישית ההין ולפר חצי ההין ואפשר שאע״פ שעשרון צריך רביעית אין צריך בהרבה הקמח לעולה (אלא?) שמן לפי החשבון, offering a solution that takes the reviis as the baseline amount.

As the progression of the fractions still seem difficult to square and as 2/3 of the animal types tell a story of 1/6th of a hin of oil per isaron of flour sufficing, I'd like to offer an approach that reflects that, with the כבש being the odd one out. 

To wit, that technically 1/6th of a hin of oil is sufficient for 1 isaron of flour as far as belilah is concerned. The reason why it is brought up to 1/4 is because less than a reviis isn't considered a substantial amount (שיעור חשוב). As the larger two animals already surpass that crucial threshold they revert back to the standard of 1/6th hin oil per isaron flour, clocking in at 1/3rd and a 1/2 respectively.

Theres a comment by Netziv to the above pasuk that points out another anomaly in how the כבש is treated compared with the other two categories: בלול ברביעית ההין שמן – דייק הכתוב להקדים ״רביעית״ ל״שמן״, ולא כמו אינך דכתיב ״שמן״ קודם למדה (למשל שְׁנֵ֣י עֶשְׂרֹנִ֑ים בְּלוּלָ֥ה בַשֶּׁ֖מֶן שְׁלִשִׁ֥ית הַהִֽין) , see there his explanation.

I think it supports the above well, as when it comes to the latter two menachos the Torah is saying that you've gotta stir in a sufficient amount of oil to be able to mix the (2 or 3 esronos of) flour well, placing שמן first, which then come out to amounts x and y; whereas when it comes to the single isaron of the כבש there the Torah is saying that you've gotta make sure to stir in a שיעור חשוב of oil, which amounts to a reviis of שמן, even though it exceeds the amount of oil an isaron of flour technically requires to be well mixed.

Now, although the shiur reviis as it relates to chashivus typically refers to 1/4 of a log and here the Torah is discussing the significantly larger amount of a hin (1 hin = 12 log), I believe—given the above data—that it is not unreasonable to speculate that the shiur reviis is not statically fixed to signify the volume of a quarter log but rather is a constant that is relative to the relevant volume under discussion. In other words, when a measurement is expressed as a fraction of something larger then it ceases to be substantial once it dips under a quarter of the measure under discussion. When it comes to drinking, with the log being the measure of choice, then a reviis mandates x amount of volume to qualify as significant, whereas when it comes to menachos with the larger hin the useful measure, then the reviis—as an objective measure of importance—subjectively fixes a 1/4 of a hin as the minimum amount of oil for menachos purposes, as less than that lacks significance in this specific context.

Theres a mishnah is menachos (9:2, tb 87b) that goes as follows: שֶׁבַע מִדּוֹת שֶׁל לַח הָיוּ בַמִּקְדָּשׁ. הִין, וַחֲצִי הַהִין, וּשְׁלִישִׁית הַהִין, וּרְבִיעִית הַהִין, לֹג, וַחֲצִי לֹג, וּרְבִיעִית לֹג. רַבִּי אֱלִיעֶזֶר בַּר צָדוֹק אוֹמֵר, שְׁנָתוֹת הָיוּ בַהִין, עַד כָּאן לְפַר, עַד כָּאן לְאַיִל, עַד כָּאן לְכֶבֶשׂ.

Now certainly according to the latter tanna it works out nicely as they are all in the same hin measuring cup, with markings to demarcate the differing amounts, however even according to the tanna kamma that there were separate vessels, still and all they were expressed as fractions of the hin. 

Theres a mishnah in eiduyos (1:3) that records a disagreement about how much mayim sheuvim invalidates a mikvah. Three opinions are given: 1) a hin, 2) 9 kav and 3) 3 log. Raavad ad loc explains that a hin is the largest liquid measure mentioned in the Torah and a quarter of it is apparently significant as seen from what accompanies the כבש. 

Now that works well according to what was proposed as the shiur reviis isn't utilitarian but rather bespeaks significance in it's own right, however according to the Tur that a reviis is simply necessary to mix an isaron with, where does one see importance?

The Rosh (pesakim bk 7:3) actually provides a different source for the significance of 3 log regarding mayim sheuvim, quoting a gemara in bshab 14a that pegs that quantity of water as sufficient to rinse ones body. 

The Tur can very well subscribe to his father's peshat, which anyway has the advantage of being related to submersing ones body in water and with the mishnah articulating the critical volume as 3 log and not expressing it as a reviis hahin.

(אחרי כמה זמן מצאתי את שאהבה נפשי בתורה תמימה לבמדבר ו:ג: ולכן נראה כמש״כ התוס׳ בעירובין ד׳ ב׳ דמכוין לשכר דנסכים בפ׳ פינחס, וערך הדמיון הוא משום דפחות מרביעית אין חשיבות בכלל, וכמו כזית באכילה, ורק בניסוך מודדין ברביעית ההין, ובשתיה – ברביעית הכוס.)