Law of multiple proportions

Two elements which form more than one compound between them will have compounds whose mass ratio between the two elements are related to each other as a ratio of small whole numbers.

For example, considering two of the carbon oxides: CO and CO₂.

In the first, the ratio is 1/1 and in the second 1/2. The ratio between these ratios is a ratio between small whole numbers, or

1/1 : 1/2 = 2:1

This law may seem obvious to you. But it is not! The above gives an example of the fact that the law is consistent with the use of chemical formulas. But can chemical formulas be proof of the law? No! Chemical formulas are not laying around in nature. But masses of substances are laying and flying around in nature. We can compare masses of substances that we allow to react with the masses of the products and find that substances combine in particular proportions of mass.

If the mass proportions of the original substances do not equal these definite proportions, there will something of one of the origional substances be left over. Note that this is special, it could as well have turned out to be possible for substances to combine in any proportion. So we find the law of definite proportions. Wauw! Now, continuing are tests, we can find that in cases were more than one definite proportion is possible for two substances, the definite proportions are multiples of each other. Wauw! we found the law of multiple proportions. Now we should be baffled and wonder how on Earth could that be so? And then we could think of substances being made of small particles (atoms) or groups of such particles (molecules) to explain the laws of nature that we found. So the laws of definite proportions and multiple proportions are (partially) proof for the existence of atoms which combine into molecules. The laws are the real thing and atoms and molecules and their chemical formulas are the ideas we make to understand the laws.

Finding the laws is not easy. It took about 10 years. We could for example take some carbon and some oxygen (that's a gas, so it is not particularly easy to `take' it, but it can be done) and allow them to react (in this case, the carbon is combusted) and weight the product or products and what is left of the origional substances. They have to be weighted all separately, so you would have to separate the gases, which is very difficult, or find some way to ensure that only one gas is produced and no oxygen is left over. The gases are not flying around as small chemical formulas, but we will recognize them by their properties. E.g. carbon dioxide will not allow a candle to burn, while oxygen does. Carbon monoxide is poisonous (well, don't identify the gas this way). You would have to check many more properties to identify the substances. Then you can be sure for these substances, but to be sure of a general law, you have to show it to be true for many more combinations of substances...