>Einstein's Ph.D. dissertation was a principled calculation meant to estimate Avogadro's number. He got it wrong. By a factor of 3.
This is interesting. A quick search can't show me the history of Avogadro's number -- what was it thought to be before? Einstein could have been off by a factor of three, or he could have been off by "only" a factor of three. Context matters.
Note that sub- and super-scripts have not copy-pasted properly.
>Einstein wrote in his 1905 Ph.D. thesis about the size of molecules and the closely related problem of the magnitude of NA. He derived equations for diffusion coefficients and viscosities in which Avogadro's number appears. From experimental values of the diffusion coefficients and viscosities of sugar solutions in water Einstein gave the estimate NA = 2.1×1023. In a later paper derived from his doctorate work he gave a better estimate from improved experimental data: NA = 4.15×1023, close to Maxwell's value of 1873. Later (1911) it was discovered that Einstein made an algebraic error in his thesis and in the paper based on it. When this was corrected the very same experimental data gave NA = 6.6×1023.
Prior to that Perrin's better estimate was 6.2E23