In the 1800's fifty to sixty of the elements in the current periodic table were already discovered. This prompted the scientist of the time to try to construct a table with all the elements of the time in it. Most of the scientists were trying to construct the table by order of atomic mass or by small groups of similar elements. In 1817 a German scientist, Johann Wolfgang Dobereiner, found that certain elements formed groups of three with similar characteristics. Dobereiner found fifteen of these groups of elements. These are called the triad series. Then in 1863 in England a scientist named John Newlands set up a table of seven rows by seven columns. He noticed that every eight one had a similar characteristic; this was the law of octaves and worked up to the twentieth element.
Then in 1869 there was a breakthrough in Russia by Dmitri Mendeleev, he arranged elements by order of atomic mass. Mendeleev also allowed rows to vary, left blank spaces, and he reversed order of a few pairs of elements. This was the best periodic table that had been made at that time even though other scientist talked against it. Later in 1869 a German scientist, Lothar Meyer, came up with a similar table. The original table is credited to Mendeleev because he published two months earlier but Meyer's work proved Mendeleev's theory.
In 1913 Idenry Moseley used x-rays to find the number of protons in an atom. He used this to find the atomic number of atoms. When he found the atomic numbers and placed them on the table it was in the order that Mendeleev put the elements in. This further proved his work. Later on, in the 1950's, Glenn Seaborg, from the United States, advanced the periodic table by adding the lanthanoid and actinoid series to it.