It became evident early in the science of chemistry that certain elements could be grouped together by the similarities of their physical properties. For example, lithium, sodium and potassium have similar properties as do fluorine, chlorine, bromine and iodine.

In 1829, the German chemist Döbereiner, became the first to propose a relationship between atomic weights and the properties of elements. He was able to show that strontium has properties about midway between calcium and barium.

The English chemist Newlands, in 1865, saw a correlation between the atomic weights and the properties of the elements. Mendeleev in Russia and Lothar Meyer in Germany, in 1870, working independently and unaware of Newlands, outlined this relationship in detail.

This led to a statement that the properties of the elements are periodic functions of their atomic weights. The below series illustrates the point:

In each row elements differ quite a bit in properties. There is, however, an interesting graduation of properties as atomic weight increases. Note that elements in a vertical column have similar properties. For example, lithium is similar to sodium.

Moseley showed that atomic number rather than atomic weights are the determining factor of chemical properties. If you check the Periodic Table you can see that argon (At. Wt. 39.948) precedes potassium (At. Wt. 39.098). There are other reversals in the table as well. This is due to the abundance of heavier isotopes of some elements. This affects the atomic weight which is an average.

The formal statement of the Periodic Law is:

Properties of elements are periodic functions of their atomic numbers.