1800s, 30 elements were known. People noticed some like sodium, potassium and lithium shared certain proprties.
In 1864, over 50 elements were known, John Newland arranged them in order and noticed that every eighth element shared certain properties which he called the law of octaves.
Unfortunately, after calcium, his law broke down as he did not know about transition metals.
Mendeleev then arranged a table and left gaps for elements that he said they did not know. He then predicted the elements that he said were not yet discovered and his predictions were correct for the next three elements.
Mendeleev did not keep to the order of atomic mass but just used it as a starting point and then rearranged some elements, like swapping iodine with tellurium as iodine matched the properties of flourine, bromine and chlorine than tellurium did.
When protons were found in the 20th century, it was clear elements should be arranged by atomic number, not mass and Mendeleev's switching did exactly this. Mendeleev's table was accepted because he made accurate predictions about undiscovered elements.
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