[DonaldFisk]

It was inevitable that it was measured to be constant. You need to build a measuring apparatus out of physical matter and use its physical properties to measure things. Use of any reasonable measuring apparatus will have the built-in assumption that c and h are constant, and either particle masses or G is constant, allowing you to measure combinations of lengths, times, and masses.

[euyyn]

> Use of any reasonable measuring apparatus will have the built-in assumption that c and h are constant

The speed of light was measured constant by the famous Michelson-Morley experiment, whose apparatus didn't have any built-in assumption about c (nor had anything to do with h).

[DonaldFisk]

The Michelson-Morley Experiment showed that light velocity had the same magnitude in different directions.

One metre is defined to be the length of the path travelled by light in a vacuum in 1/299 792 458 seconds. Therefore, c = 299 792 458 metres per second. The second is defined in terms of the frequency of electromagnetic radiation emitted during a transition between two specific states in a caesium atom. In other words, it's a unit of time as measured on a kind of atomic clock, which by convention is constant.

It's an open question whether a second on a pendulum clock is the same as one measured on an atomic clock for all time, as that depends on G.