Define the law of multiple proportions. Explain it with two examples. How does this law point to the existence of atoms?

The 'Law of Multiple Proportions' was proposed by Dalton in $1803$. It states that when two elements combine to form more than one compound,the masses of one element that combine with a fixed mass of the other are in the ratio of small whole numbers.
Example $1$: Hydrogen and oxygen form water $(H_2O)$ and hydrogen peroxide $(H_2O_2)$.
In $H_2O$,$2 \ g$ of hydrogen combines with $16 \ g$ of oxygen.
In $H_2O_2$,$2 \ g$ of hydrogen combines with $32 \ g$ of oxygen.
The ratio of the masses of oxygen $(16:32)$ is $1:2$,which is a simple whole number ratio.
Example $2$: Carbon and oxygen form carbon monoxide $(CO)$ and carbon dioxide $(CO_2)$.
In $CO$,$12 \ g$ of carbon combines with $16 \ g$ of oxygen.
In $CO_2$,$12 \ g$ of carbon combines with $32 \ g$ of oxygen.
The ratio of the masses of oxygen $(16:32)$ is $1:2$.
This law supports the existence of atoms because it implies that elements combine in discrete,fixed units (atoms) rather than in arbitrary amounts,leading to fixed ratios of mass.