A BRIEF HISTORY OF ATOMS
Democritus (460-340 BC)
Democritus' ideas gave rise to the Epicurean view of the world (Epicurus, 341-270 BC), a philosophy rigorous enough to count such influential Romans as the orator Cicero and the poet Horace among its disciples. The epicurean insistence on material causes for all aspects of our world eventually ran into conflict with the growing influence of Christianity. By the fifth century AD Epicureanism survived only as a marginal philosophy.
 Democritus, University of St Andrews, Scotland.
 Leucippus, University of St Andrews, Scotland.
Lucretius (99-55 BC)
It is hard to mention Epicureanism without mentionning Lucretius, a Roman poet and the author of the philosophical epic De Rerum Natura (On the Nature of Things), a comprehensive exposition of the Epicurean world-view. Rediscovered in the 17th century, the De Rerum has been part of the intellectual background of virtually every evolutionary theorist in Europe from Lamarck to Herbert Spencer -- including Darwin himself .
 Lucretius, The Internet Encyclopedia of Philosophy.
John Dalton (1766-1844)
Dalton did not prove that atoms existed, he postulated that they did. And the postulate proved fruitful as both an explanatory and predictive tool. Dalton understood well the diversity of atoms and their relative masses, but he could not estimate their sizes and he had couldn't count how many existed in a given mass of an element.
 Dalton, Salt Lake Community College.
Loschmidt and the Size of Atoms, 1865
The atomic theory was refined by numerous chemists and physicists. Hardly any scientist of that era did not dabble in atoms and contributions flowed from many quarters. Johann Loschmidt, in 1865, was the first to give a well reasoned and accurate estimate of the size of a molecule of air  and thereby of all small molecules and atoms: one millionth of a millimeter.
 Loschmidt-1865, On the Size of the Air Molecules, John Park's ChemTeam: Classic Papers from the History of Chemistry, (Cached).
Maxwell and the Number of Atoms, 1873
Knowing the size of a small molecule doesn't immediately tell you how many molecules or atoms exist in a given volume of a the corresponding substance. One needs a way to account for the space between the atoms or molecules. In 1873, James Clerk Maxwell gave a first estimate of Loschmidt's Number , the number of molecules in 1 cm3 of air. His experiments used some of Loschmidt's results. He estimated 1.9 x 1019 (nineteen million million million) molecules. Today one prefers Avogadro's Number, NA, the number of molecules in 22.4 liters of a gas, and Maxwell's estimate corresponds to an NA value of 4.25 x 1023. NA is now known to great accuracy and is approximatively 6.02 x 1023.