MONOLAYERS AND AVOGADRO
Along the way to ever better determinations of NA, monomolecular layers of oil played a major role, so lets look at monolayers history.
In 1773 Benjamin Franklin was the first to report the phenomenon of oil's power to still troubled waters and to speculate on why it happened.
"After this I contrived to take with me, whenever I went into the country, a little oil in the upper hollow joint of my bamboo cane with which I might repeat the experiment as opportunity should offer, and I found it constantly to succeed." 
In 1891 Lord Rayleigh reported on the experiments of Agnes Pockels,
"a German lady, who with very homely appliances has arrived at valuable results respecting the behaviour of contaminated water surfaces," and proceeded to refine the experiments himself.
Starting in 1917 Irving Langmuir began turning these experiments into a science, and later won a Nobel Prize for it (1932).
"Langmuir was fascinated with surface chemistry and it was for his efforts in this area that he became the first non-academic chemist to receive the Nobel Prize. Along with Dr. Katherine B. Blodgett, he studied thin films and how substances are adsorbed on surfaces. Through their efforts, surface chemistry became a full-fledged scientific discipline" 
Back to our subject of atomic sizes and Avogadro's Number. The best estimates contributed by the study of monomolecular layers seems to have come in the 1920's [4, 5].
"Thin films of sodium oleate assumed to be monolayers on the surface of water led Lecomte de Nouy to estimate the size of a molecule, and from that the number of molecules in a mole as 6.004 x 1023 in 1924." 
 Oil on the Waters, A Letter from Benjamin Franklin to William Brownrigg, 1773 (Cached).