First reference to this expression can be found in Exodus 30:13:
13 This they shall give, every one that passeth among them that are numbered, half a shekel after the shekel of the sanctuary: (a shekel is twenty gerahs:) an half shekel shall be the offering of the LORD.
13 זֶ֣ה׀ יִתְּנ֗וּ כָּל־הָעֹבֵר֙ עַל־הַפְּקֻדִ֔ים מַחֲצִ֥ית הַשֶּׁ֖קֶל בְּשֶׁ֣קֶל הַקֹּ֑דֶשׁ עֶשְׂרִ֤ים גֵּרָה֙ הַשֶּׁ֔קֶל מַחֲצִ֣ית הַשֶּׁ֔קֶל תְּרוּמָ֖ה לַֽיהוָֽה׃
Seems that one(1) Silver Shekel (primary unit of measure) was equal to twenty(20) of these "gerahs". If one could figure out what this expression means, that would solve most of the problems associated with the units of measure for the Mishkan. Very critical and very important thing to do, but unfortunately it is not as easy as one would hope it would be.
But let's continue looking and see what else we can learn about this elusive "gerah" from Leviticus 11:3:
3 Whatsoever parteth the hoof, and is clovenfooted, and cheweth the cud, among the beasts, that shall ye eat.Ok, so now we actually know that the expression "gerah" has primary meaning of "cud"(particle(s)/ball). In animal science, "cud" is basically a ball (bolus) of regurgitated food that plays an important role in digestive cycle of the ruminants (cows, sheep, deer e.t.c). Yet again, it seems that the original text does not make too much emphasis on the "cud" itself but rather upon the process of "cud chewing" and/or "regurgitation".
3 כֹּ֣ל׀ מַפְרֶ֣סֶת פַּרְסָ֗ה וְשֹׁסַ֤עַת שֶׁ֙סַע֙ פְּרָסֹ֔ת מַעֲלַ֥ת גֵּרָ֖ה בַּבְּהֵמָ֑ה אֹתָ֖הּ תֹּאכֵֽלוּ׃
Here are some videos that explain and show the process of rumination...
This first video shows the entire "bringing-up of the cud":
And this video provides basic explanation of the digestive process of ruminants using Cow as an example...
And this video illustrates the process itself, but unfortunately it is in German...
Either way, it is still very unclear to me what exactly the expression "gerah" means. Yes, it can be referring to a "kernel"(or "pellet"/ "grain") of cereal grass. Yet on the other hand, it might just as well refer to a small bolus of regurgitated food that say Cows chew upon.
I just don't know at this time how to approach this problem and this is very disappointing.