The Law of Multiple Proportions is the third postulate of Dalton's atomic theory. It states that the masses of one element which combine with a fixed mass of the second element are in a ratio of whole numbers.
Therefore, the masses of oxygen in the two compounds that combine with a fixed mass of carbon should be in a whole-number ratio. In 100 g of the first compound (100 is chosen to make calculations easier) there are
57.1 g O and 42.9 g C.
The mass of O per gram C is: 57.1 g O / 42.9 g C = 1.33 g O per g CIn
the 100 g of the second compound, there are 72.7 g O and 27.3 g C. The mass of oxygen per gram of carbon is:72.7 g O / 27.3 g C = 2.66 g O per g C
Dividing the mass O per g C of the second (larger value) compound:
2.66 / 1.33 = 2
Which mean that the masses of oxygen that combine with carbon are in a 2:1 ratio.
The whole-number ratio is consistent with the Law of Multiple