I really cannot see why the Brownian motion is linked with the being of atoms. Cannot it be explained without atoms? You just need some fluctuations.

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    $\begingroup$ Perrin wrote a very famous semi-popular book on his work, and an English translation appeared in 1916 that is freely available on the internet. I'd be very surprised if your concerns are not very adequately addressed in his book, so I recommend looking there. $\endgroup$ – Dave L Renfro May 11 '17 at 14:59
  • $\begingroup$ Perrin performed his experiments in 1908 after Einstein and Smoluchowski came up with a detailed quantitative theory of Brownian motion based on the atomic theory and Boltzmann's statistical mechanics. "Some fluctuations" could not make predictions which Perrin confirmed, so his results were seen as confirmation of both atomism and statistical mechanics (which Boltzmann unfortunately did not live to see). $\endgroup$ – Conifold May 12 '17 at 21:56

More precisely it has to do with existence of molecules. The demonstration was obtained after Einstein and Smoluchowski developed a QUANTITATIVE theory (based on the molecular theory) whose predictions could be measured. Measuring parameters of Brownian motion (by Perrin) confirmed the theory. There was no better (or competing) explanation of these measured parameters.

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