Dimitri Mendeleev, a Russian Chemist arranged the elements in the order of their increasing Atomic Weights as Atomic Number was not found at that time. So he stated his law as "The physical and chemical properties of the elements are a periodic function of their Atomic Weights".
Later when Atomic Number was discovered it was found that the elements were arranged in a correct order whose atomic numbers were their serial numbers. So his law was changed as the above given one. He was successful in grouping all the elements unlike his predecessors who failed at it. To know about them click on below link.
Predecessor's works
To view the model of an atom click below link.
Atom Model