Measurement units can, possibly, describe some agency that already has other units including SI units, but be an island unto themselves regarding relative accuracy better than the accuracy with which their conversion factors to the other units are known.
For example, early in the history of the angstrom length unit, its value was more precisely known than the length of the metal bar that defined the meter at the time. I think this was because it entered into angle determinations in X-ray crystallography.
For another example, the astronomical unit was originally more precisely defined within its own usage and its usage in defining the parsec, relative to how precisely the length of an astronomical unit was known in any other distance units.
I think the electron volt may have ben like this too. It was a unit of energy, but to convert it to other units of energy you have to know the electron’s charge in coulombs, and I’m not sure that was so accurately known. I could be wrong on that one, but you get the idea. And it might be argued that it isn’t a unit of energy, but, rather, an experimental result, just as one might argue an inch of water column isn’t a pressure unit but rather a description of an experimental outcome. Messy, maybe.
So, you can convert feet and inches and meters and miles with perfect accuracy and trivial effort, but there are these other units out there that are more strongly linked together within their own usage than they are to the main units used elsewhere.
One current example of this is that the product G*m[sub]sun[/sub] is more precisely known than either of those factors separately. Or, in fact, G times the mass of nearly any celestial body.
Another example is that it was possible to determine molar masses before Avogadro’s number was actually found. So you might know that a given sample contained 1.2 moles of something, without having any good idea of how many molecules it contained.
Joey P, a derived unit is something like a newton, which is just another name for a kgms^-2.
Many such units may fall under this category. For example many argue that Cavendish did not really measure G but rather some form it considering earths density etc. Maybe Chronos can elucidate.
The Volt or voltage itself initially was defined differently and so was the ampere. Same goes for pH
And the really really really messy units of radiation come to mind too.
No, I don’t mean units that are derived from other units, nor units whose definitions change, not units that are actually typically measured by some proxy (even mass is like this, as it is most often measured indirectly through weight, and it’s the scale’s job to account for the fact that the local strength of gravity is significantly different than it would be in other locations).
I mean units for an ordinary measurement, such as length, that are used in closed systems of measurement with great precision even though the definition of the unit in the overall system of measures is much less certain.
Chronos got it. The Avogadro’s number example is perfect. To take that example further, perhaps it was possible before Avogadro’s number was found to state that Sample A has 22.5 moles of something whereas Sample B has 23.1 moles of that same thing, while the magnitude of the mole unit itself might have been unknown within a factor of 2 or 10 or 100 (or whatever it was).
Not exactly what you are looking for, but it may help your search to use the term natural units, which are based on fundamental or physical constants rather than the old system of prototype measurements.
At the time of Cavendish’s experiment, the radius of the Earth and little-g (the surface acceleration) were both well-known, but the mass of the Earth, its density, and big-G (the constant in Newton’s law of gravity) were only poorly known. What Cavendish measured directly was big-G, but that, combined with the other knowns, enabled easy determination of the other unknowns, so it’s also fair to describe him as “weighing the Earth”, or whatever.
Before him, the first knowledge of the value of G came from Newton himself. He estimated the overall density of the Earth based on the density of materials near the surface, and the observation that the average density increases as you go deeper. He then used that estimated density, together with the known g and radius, to produce an estimate of M[sub]earth[/sub] and G. In retrospect, the number he actually got was pretty good, better than one would expect from such a crude method, but one would still expect the method to better than an order of magnitude or so.