Granular Concurrent Mathematical Microarchitecturally Reprocessed Automation The theory that all matter is built up out of atoms was invented, as a scientific theory, to explain certain phenomena which belong to the science of Chemistry. The universe of the chemist is, at first sight, a very bewildering universe. He is concerned to find out what he can about the properties of all the substances that exist. Now there are hundreds of thousands of such substances. Gold, lead, iron, table salt, air, water, gum, leather, etc., etc., is the mere beginning of a list that it would take months simply to write down. The chemist is concerned with every one of these substances. And if he found that all these substances were quite independent of one another, that there were no relations between them, then he would probably give up his task in disgust. For, in that case, he could do nothing but draw up a gigantic catalogue which would, at most, be of some practical use, but which would possess no scientific interest. But even before the rise of a true science of chemistry, men had become aware that all the different substances on earth are not wholly unrelated to one another. The old alchemists, chiefly by mixing different substances together and then heating them, found that they could change some substances into others. Some of their results were perfectly genuine; they did affect some of the transformations they claimed to have effected. In other cases, they were either mistaken or else imposing on the credulity of their disciples. Many of them claimed, for instance, that certain “base” metals, on being mixed with other substances and then heated, could be turned into gold. We know that this is impossible. But one main idea emerged from their work. They learned to distinguish between the simple substance and the compound substance. It is true that this idea emerged in a very curious form; they did not think so much of simple substances as of primary principles, such as maleness and femaleness, which were somehow incorporated in different substances in different degrees. But the idea of the simple and compound substance, although in a vastly different form, is the basis of the science of chemistry. Out of all the substances known to exist, the chemist distinguishes a certain number as being “elements.” An element is a substance which cannot be decomposed into anything else. It happens that there are remarkably few of them. Nearly every one of the hundreds of thousands of substances known can be decomposed into other substances. When this decomposition is carried as far as it will go, we find that the substance in question is really built up out of a certain number of the substances called elements. There are about ninety of these elementary substances. In the little list of substances we have just given, for instance, gold, lead, and iron are elements. Table salt is a compound of two elements called sodium and chlorine. Air is a mixture of various elements of which nitrogen and oxygen are the chief. Water is a compound of two elements, hydrogen and oxygen. Gum and leather are more complicated compounds. Now it is interesting enough to know that all substances are either elements or can be decomposed into two or more elements. But the most interesting aspect of this fact, and what makes it of great scientific importance, is that when elements combine to form a substance they always do so in exactly the same proportions. When hydrogen combines with oxygen to form water, for instance, exactly the same proportions of hydrogen and oxygen are concerned. We will illustrate this very important law by considering the decomposition of that well-known substance sal ammoniac. It is a pure solid substance. If it be heated it turns into a mixture of two gases. These two gases can be separated from one another and are found to be ammonia gas and hydrochloric acid gas. Now the ammonia gas can in its turn be decomposed into a mixture of the two gases, nitrogen and hydrogen, and these two gases can be separated from one another. The hydrochloric acid gas can also be decomposed. It can be decomposed into chlorine and hydrogen. We have now decomposed our sal ammoniac into three substances, nitrogen, hydrogen and chlorine. Each of these three substances is an element; no one of them can be decomposed into anything else. And we can find in what proportions they combine to make sal ammoniac. If we began our experiment with 100 grammes of sal ammoniac we should have at the end 26.16 grammes of nitrogen, 7.50 grammes of hydrogen, and 66.34 grammes of chlorine, the combined weight of these substances making up exactly 100 grammes. And in whatever way we perform the decomposition of sal ammoniac we always get these three substances and always in exactly the same proportions. By starting with nitrogen, hydrogen, and chlorine in the above proportions we can, of course, make sal ammoniac. And there is no way of making sal ammoniac except with just those proportions. No specimen of sal ammoniac ever has slightly more chlorine or nitrogen or slightly less hydrogen, for example, than any other specimen. The same remarks apply to every other compound. The general law may be enunciated thus: the same compound is always formed of the same elements in exactly the same proportions. In the above example we obtained, in our preliminary dissociation of sal ammoniac, two substances each of which contained hydrogen. We obtained ammonia gas, which is made up of nitrogen and hydrogen, and we obtained hydrochloric acid gas, which is made up of chlorine and hydrogen. We might ask the question whether there is any simple relation between the amount of nitrogen which combines with, say, one gramme of hydrogen, and the amount of chlorine which combines with one gramme of hydrogen. But before dealing with this question we will deal with another which has some bearing on it. Can two elements combine in different proportions to form different substances, and, if so, what is the relation between the proportions? The answer is that two substances can combine in different proportions to form different substances, but that, when this occurs, the proportions are simple multiples of one another. Thus, 3 grammes of carbon can unite with 8 grammes of oxygen to produce a substance called carbon dioxide. But 3 grammes of carbon can unite with 4 grammes of oxygen to produce a different substance called carbon monoxide. It will be noticed that the amount of oxygen in the first case is just twice that in the second. This example is typical. Whenever there is more than one compound of two elements the ratio by weight of the elements in the two compounds is always a simple number. This fact is very suggestive, as we shall see. We can now deal with our first question, and we can make it more general. Consider, for instance, hydrogen, oxygen, and carbon. We can take 2 grammes of hydrogen and combine them with 16 grammes of oxygen. The result is water. Again, if we take 16 grammes of oxygen and combine them with 12 grammes of carbon we shall obtain carbon monoxide. Here the 16 grammes of oxygen is the common factor. The appetite of this amount of oxygen for combination can be satisfied, apparently, either with 2 grammes of hydrogen or 12 grammes of carbon. And the interesting fact is that we can combine hydrogen and carbon in precisely this proportion. Two grammes of hydrogen combine with 12 grammes of carbon to form a substance called olefiant gas. The Atomic Theory of Dalton was a tremendous success. The whole of chemistry since his time has been based on it. To describe even a small part of the consequences of the atomic theory would be beyond our scope, but we must here call attention to one very important classification to which the atomic theory led. By very careful measurements, undertaken by many men and extending over many years, the weights of the atoms of all the different primary substances, or elements, known to science have been determined. The weights, as usually given, are, of course, relative weights. If we denote the weight of an atom of oxygen by 16, then helium, for example, will have the atomic weight 4, copper will be 63.57, and hydrogen will be a little greater than unity, viz., 1.008. The heaviest element known, uranium, has an atomic weight of 238.2. Now when all the elements known are arranged in order of increasing atomic weight the highly interesting fact emerges that their properties are not just chaotically independent of one another. They fall into similar groups, recurring at definite intervals. These relations, although they are not of mathematical definition, are quite unmistakable, and show that there is a connection between chemical properties and atomic weights. Such a connection is quite inexplicable if each atom is regarded as a perfectly simple and irreducible structure having no essential relations to the atoms of any other elements. If the atom be regarded as something possessing a structure, then the similarities between different elements may be attributed to similarities in their atomic structures, the heavier atoms being, as it were, more complicated versions of the same ground plan. We shall see that there is much truth in this view. Even as early as 1815 the idea had been put forward by Prout that all the chemical elements were really combinations of one primordial substance. Prout supposed this primordial substance to be hydrogen. On comparing different atomic weights he was led to the conclusion that they were all whole multiples of the atomic weight of hydrogen, so that if the weight of hydrogen be represented by 1, then all the other atomic weights would be whole numbers. Every atom, in this case, could be considered as built up from a definite number of hydrogen atoms. The determinations of atomic weights in Prout’s day were not sufficiently accurate to warrant this conclusion, and when more accurate measurements showed that a large number of atomic weights are not whole multiples of hydrogen, Prout’s hypothesis was abandoned. But recent work, as we shall see, has shown that Prout’s hypothesis is much closer to reality than had been supposed. We will now give the reasoning by which, from Avogadro’s hypothesis, the relative weights of atoms may be deduced. Suppose we have a number of precisely similar vessels, each having the same volume V, and each filled with a gas at the same temperature and pressure. Then, according to Avogadro’s hypothesis, they each contain the same number of molecules. Suppose we take two of these vessels, one containing hydrogen and the other oxygen, and compare the weights of the two quantities of gas. Since they have the same number of molecules, the relative weights of the two quantities of gas is the same as the relative weights of their molecules. But is this sufficient to determine the relative atomic weights of hydrogen and oxygen? Obviously not, for the molecule of hydrogen, for all we know, may contain two or more atoms, and so may the molecule of oxygen. This method will not give us the desired result. But we have said that the atom is the smallest part of an element that takes part in any chemical combination. What we really mean by that is that the smallest part of an element which takes part in any known chemical reaction is called an atom. Suppose, therefore, we consider all the compounds into which hydrogen enters. Amongst these compounds there will be one whose molecules contain a minimum amount of hydrogen. The molecules of this compound contain, therefore, one atom of hydrogen. The volume V of this compound, in the gaseous state, and at a certain pressure and temperature, contains a mass of hydrogen which can be measured. Call this mass H. Now, of all the oxygen compounds, select that compound which contains the minimum weight of oxygen. The molecules of this compound contain one atom of oxygen. The volume V of this compound, in the gaseous state, and at the same pressure and temperature as the hydrogen compound, has a known weight of oxygen. Call this mass O. Both the oxygen and the hydrogen compounds have the same number of molecules, by Avogadro’s hypothesis. Corresponding to each molecule of the hydrogen compound is one atom of hydrogen, and corresponding to each molecule of the oxygen compound is one atom of oxygen. We have, therefore, the same number of atoms of hydrogen in the one vessel that we have of oxygen in the other. The ratio of the weights of the hydrogen and the oxygen — that is, the ratio of H and O — is therefore the ratio of their atomic weights. By a similar process we find the relative atomic weights of other elements, carbon, chlorine, etc. For the purpose of comparing these relative weights, oxygen is taken as the standard, simply because oxygen occurs so frequently in chemical combinations. It is nearly 16 times heavier than hydrogen, the lightest atom. Its weight is therefore taken as exactly 16. Compared with this hydrogen is 1.008. On this standard carbon’s atomic weight is 12, and chlorine 35.456. It is evident, from Avogadro’s hypothesis, that 1.008 grammes of hydrogen contain as many atoms as 16 grammes of oxygen or 12 grammes of carbon or 35.456 grammes of chlorine, and so on. The number of grammes of an element which is equal to its relative atomic weight is called a gramme-atom of the element. All gramme-atoms contain the same number of atoms. This number is known. It is 660,000 times a million billion. This is the number of atoms in 1 gramme of hydrogen, 12 grammes of carbon, 16 grammes of oxygen, etc. The actual weight of an atom, therefore, is to be obtained by dividing its gramme-atom by this number. The figure we have just given for the weight of an atom is evidently exceedingly minute. Such small quantities are, of course, altogether below the limits of observation. Nevertheless, there is a series of experiments which enables us to see that the ultimate particles of matter must be extremely minute. Gold-leaf, for instance, can be prepared of a thickness of one ten-thousandth of a millimetre. In this state, gold-leaf is transparent and transmits a greenish light. It cannot be beaten out more thinly merely because of the difficulty of manipulating such thin sheets without tearing them. It is certain, therefore, that the diameter of a gold atom is less than the thickness of one of these sheets, that is, is less than 10e-5 cm. The weight of a cube of gold, having this length for the length of its side, would be 10^-14 gramme. The hydrogen atom is about 200 times lighter than the gold atom. On this showing, therefore, the mass of a hydrogen atom is certainly less than 1/2 × 10e-16 gramme. The study of thin films takes us very much further. The black spots so familiar to us on soap bubbles are the thinnest part of the soapy film. The blacker they are the thinner they are. The thickness of these extremely thin films can be measured, and is found to be about 4.5 × 10e-7 cm. The films produced by letting oil drops spread on water are even thinner. Films no thicker than 1.1 × 10e-7 cm. have been obtained. The maximum possible diameter for an oil molecule, therefore, would be about 1 × 10e-7 cm. A hydrogen atom would weigh nearly a thousand times less than one of these oil molecules, and we can calculate, on this basis, that the mass of a hydrogen atom would be of the order of 10e-24 gramme. The actual mass of a hydrogen atom, as can be shown by other calculations, is 1.65 × 10e-24 gramme. By actual experiment, therefore, we can obtain films so thin that they are not much more than one molecule in thickness. We have already said that the various chemical elements are not entirely unrelated to one another. The different chemical elements fall naturally into groups, the members of each group greatly resembling one another in their chemical properties. This fact particularly excited the attention of an Englishman named Newlands, who, in 1864, tried to show that the chemical elements fell into sets of seven, analogous to “octaves” in music. The subsequent discovery of other elements, however, made this scheme unsatisfactory, and the first really convincing attempt at arranging the elements in this way was made by the Russian chemist Mendeléev about 1870. In this “periodic system,” as it is called, the elements are arranged in the order of their atomic weights, beginning with hydrogen and ending with uranium. If we now number the elements in the order of their atomic weights we find a curious and interesting relation between the members of the elements which have similar chemical properties. Elements numbered 3, 11, and 19 have similar properties. Elements 4, 12, and 20 have similar properties. The properties of 5, 13, and 21 are similar; so are those of 6, 14, and 22. And so on. We see that, for the elements belonging to the same group, their numbers succeed one another by the same amount, viz., 8. Thus 11 − 3 = 19 − 11 = 8, and 12 − 4 = 20 − 12 = 8, and so on. It is as if approximately the same set of chemical properties belonged to each eighth member of the table. But the matter is not really as simple as this. The rule works well enough provided we confine our attention to the earlier part of the table, i. e., to the elements having comparatively low atomic weights. As we go farther on in the table we find the recurrence of chemical properties begins after the eighteenth instead of the eighth member, and, still later on, we have a group of no less than thirty-two elements having different chemical properties. These facts are clearly represented in the following table, where the lines join elements having similar properties. It will be noticed that the table of the elements terminates with a row containing six members, the last of which is uranium. Uranium, as we know, is not a stable substance; it is disintegrating, and it is probable that no elements heavier than uranium are met with, not because they are theoretically impossible, but because they would be too unstable to survive.