“Gentlemen, let us consider a piece of cheese. With a knife we can cut it in two, thus obtaining smaller pieces. We can then cut one of these smaller pieces in two, obtaining still smaller pieces. We can think about repeating this process over and over to get smaller and smaller pieces of cheese. Now can this process be continued without limit, or will a time come when we arrive at the smallest possible piece of cheese? In other words, is there a piece so small that we must have at least that much or none, with no choice in between?”
It is probable that most people who thought about this question at all during the next two thousand years answered the last question in the negative. The prevailing notion was that matter was continuous, with no theoretical limit as to how small a piece of cheese, or anything else, might be.
This concept was humorously expressed by the British mathematician Augustus De Morgan (1806-1871) in these lines:
Great fleas have little fleas upon their backs to bite ’em,
And little fleas have lesser fleas, and so, ad infinitum.
The Atomic Theory Is Confirmed
De Morgan evidently did not keep up with the latest developments in science, however, because two years before his birth, John Dalton, an English schoolteacher, had changed the atomic theory of matter from a philosophical speculation into a firmly established principle. The evidence that convinced Dalton and many other contemporary scientists of the reality of atoms came from quantitative chemical analysis.
Dalton knew that many chemical substances could be separated into two or more simpler substances. Chemicals that could be separated further were called compounds; those that could not were called elements. Careful experiments by Dalton and others showed that whenever two or more elements combined chemically to make a compound the relative amounts of the elements had to be carefully adjusted to fit a definite proportion in order to have no elements left over after the reaction was finished. For example, if hydrogen and oxygen were combined to form water, the weight of oxygen had to be eight times the weight of hydrogen; otherwise, either some hydrogen or some oxygen would be left over.
This fundamental truth is now called the Law of Definite Proportions. Another important principle, called the Law of Multiple Proportions, is illustrated by hydrogen peroxide, which is made up of the same two elements that are found in water. The weight of oxygen in hydrogen peroxide, however, is 16 times the weight of hydrogen or exactly twice the relative weight found in water.
These principles of chemical combination convinced Dalton that each chemical element consists of small, indivisible units, all just alike, called atoms, and that each chemical compound also has basic units, called molecules, which cannot be divided without reducing the compound into its elements—that is, destroying it as a compound. He visualized a molecule of a compound as formed by the uniting of individual atoms of two or more elements. It was obvious to him that in any molecule of a compound, the weight of each atom of a component element bore a proportionate relationship to the weight of the entire molecule which was equal to the proportion, by weight, of all that element in the compound. And although Dalton had no idea how heavy any individual atom really was, he could tell how many times heavier or lighter it was than an atom of another element.