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(By the way, I find the term "per [unit] volume" rather meaningless,
but that is another story.)
This is an interesting comment that I would be glad to see
developed. The concept of unit volume in itself is not difficult -
at least for liquids under gravity: one picks a bottle without leaks
as a container, and acknowledges that temperature and pressure, maybe
atmospheric humidity are confounding variables.
One thinks of a pyknometer and how this relies on mass measurement:
perhaps that's the cause of Brian's difficulty?
(a certain circularity...)