Hubble's Law said the velocity of distant galaxies was faster than that of nearer ones. It is only in 1998 that we discovered the universe's expansion is accelerating, i.e. that Hubble's "constant" is shifting.

We found this out by very precisely measuring the brightness of a very specific type of supernova, a Type Ia supernova, which has a very consistent intrinsic brightness (about 5 billion times brighter than our Sun) allowing for distance measurements with an uncertainty of just 5%. This was a novel achievement, enough to merit the 2006 Shaw Prize in Astronomy.