In 1817, Dobereiner arranged elements into groups of threes, known as Dobereiner's triads.
According to Dobereiner, the atomic weight of the middle element is nearly the same as average of the atomic weights of other two elements.

In 1864, Newlands organised elements into groups of eight, known as Newlands' Octaves, in order of increasing atomic weight.
This arrangement of elements showed a regular repeating pattern.
A number of elements had to be placed into incorrect groups and the trend quickly broke down.

In 1869, Dmitri Mendeleev organised the elements in a periodic table in order of their atomic weights.
He found that when ordered this way, the properties of the elements repeated themselves periodically.
He left gaps and reversed the positions of some elements so that the chemical properties of the elements would match the group they were in.
For example, he switched the positions of Tellerium and Iodine.
Mendeleev was able to use his table to make predictions about elements that had not yet been discovered.
The table did not contain the halogens.

Moseley discovered that if sorted in order of atomic number, none of the orders need be reversed.
Moseley's periodic table is the basis of the modern periodic table. (shown below)

Modern Atomic Model