In 1863, a 44 year old French geologist, A. E. Béguyer de Chancourtois created a list of the elements arranged in order of increasing atomic weight. The list was wrapped around a cylinder so that several sets of similar elements lined up, creating the first geometric representation of the periodic law. He called his arrangement the "Telluric screw".
John Newlands (1838-1898) tried to find some mathematical relation between the atomic weights (or 'equivalents') of elements which were chemically similar. He extended the work of Dobereiner and Dumas. Several of his communications were published in Chemical News in 1863-1864.
He arranged the elements in order of their atomic weights, placing them in rows of seven, indicating that the eighth element had properties similar to the first, and the ninth was similar to the second, and so on. Perhaps it was the use of the word 'triad' applied to Dobereiner's groups of three elements having chemical similiarities which led Newlands to apply the word 'octaves' to his grouping of the elements. As he said, "the eighth element starting from a given one is a kind of repetition of the first, like the eighth note of an octave in music".
Read this brief outline showing how the idea of Chemical Periodicity developed from Dobereiner, through Newlands, Mendeleev and Moseley.