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The key of this question is not simply stating the content of his theory, but telling what results or principles he had at that time and how could they lead to the theory. He was as such the first person to measure relative atomic weights.

Specifically what idea of technique was used and how to measure relative atomic weights using macroscopic measurements?

PS: Both wiki states that it was based on the principles of mass conservation and definite proportion. How?

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    $\begingroup$ In Mlodinow's book the Upright Thinkers he deals withDalton as the first to weigh atomic weights. the first atomic physicist. The book is a scientific story of how the ideas developed. Dalton was very methodical, was the first person who determined some atomic weights from macroscopic measurements. Not a trivial thinking feat, when atoms were still uncertain. He weighed pure compounds, eg, two different oxides of copper, one may use 4 gm of copper for each gm of oxygen, the other one 8. He used that to compute relative atomic weights. The first atomic experiment. It's worth a longer answer $\endgroup$ – Bob Bee Aug 23 '16 at 3:42

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