But Democritus went farther. Democritus appears to have been a man of exceptional scientific ability (as science went in those days); the geometrical solution of the volume of the pyramid and cone are attributed to him, and Pliny mentions that he spent his life among experiments. At any rate, he appears to have been the first thinker of antiquity (indeed, one of the very few) to display the scientific spirit, that of seeking unity in the various manifestations of nature by reducing quality to quantity. In this respect he initiated what was to become the necessary method of scientific investigation. Accordingly he suggested that all the elementary particles of matter were of the same substance. The qualitative differences which bodies reveal would then be due to differences in the shapes and sizes of their constituent elements or atoms. In this way unity was conceivable; but for this unity to endure, it was imperative that these elementary atoms should themselves constitute imperishable units. They could not be microcosms whose internal parts might suffer changes of position; hence they would have to be indivisible plena. As for cohesion, it was attributed to the atoms hooking on to one another.
As a scientific aspiration, Democritus’ scheme was perfect, but the trouble was that the facts known to him were too few in number. And so his theory was a crude guess at best; and it was only natural that a wider survey of facts should render it untenable. The co-ordination of facts known to modern science has proved, indeed, that atomism, as understood by Democritus, was untenable; for whereas beyond the atom of the Greeks there was no mystery, nothing further to look for, the atoms of matter are now known to be divisible. They differ qualitatively from each other, contain heterogeneities, are subject to change and decay. In other words, the atoms of modern science are new microcosms of baffling complexity, so that the appellation “atom” (meaning indivisible in Greek), retained by custom, is no longer appropriate. When we get beyond the atoms to the electrons and protons, we are in no position to assert that these constitute imperishable units. Further subdivision may be possible, and the existence of sub-electrons has been suggested. We do not know what would happen were it possible to cause a proton and an electron to coalesce—whether or not the result would be a complete annihilation of electricity and matter. Even if we adhere to the view that with these electrons and protons the ultimate atoms have been reached at last, we know so little about them that we cannot even be certain that they possess a definite size or shape. They may extend to infinity, they may reduce to mathematical points or singularities in the electromagnetic field; and this field itself is in no sense a substance. And so we see that atomism, as upheld by Democritus, is far from having been established by modern science. In the present state of our knowledge all we could do would be to guess, just as Democritus did in his day; but in view of the paucity of facts there are to guide us, no interest could be attached to our guesses.
Nevertheless, if by atomism we mean merely the tendency of matter and electricity to congregate into entities of great stability, we are on safe ground and we may consider the doctrine proved. When understood in this more restricted sense, a wide variety of phenomena drive us to the atomic theory. In addition to the mixing of liquids, mentioned by the Greeks, we have to consider the diffusion of gases and of solutions, the compressibility of gases and the phenomenon of osmosis. All these phenomena appear to demand the existence of molecules or atoms. As an illustration let us consider the phenomenon of the compressibility of gases, studied by Boyle in the seventeenth century. We know that when a gas is compressed its volume is decreased. Yet its mass or weight remains unchanged. We cannot assume, therefore, that matter has vanished through compression; hence the simplest alternative is to suppose that the gas is made up of atoms floating or moving in the void. Compression will then result in crowding these atoms into smaller spaces while leaving their total number unchanged. Similar arguments may be advanced in the case of liquids. Thus, when we mix one pint of alcohol and one pint of water, we do not obtain two pints of the mixture, but appreciably less. The simplest way to account for this partial disappearance of volume is once again to assume that our liquids possess a grainy constitution and that vacant spaces exist between the grains or molecules. We may then assume that when water and alcohol are mixed, some of the molecules of water squeeze into the vacant spaces between the molecules of alcohol, or vice versa. Again, we find atomism cropping up in chemistry when Dalton sought to account for the empirical law of constant proportions. Nevertheless, although the corpuscular nature of matter seemed to impose itself if we wished to co-ordinate a large number of phenomena, something more was needed for this hypothesis to be accepted without reserve.
The major reason for the present-day belief in atomicity arises from the following considerations: A celebrated hypothesis due to Avogadro, the legitimacy of which we need not discuss here, suggested that if molecules existed, equal volumes of all gases maintained under the same conditions of pressure and temperature should always contain the same number. This number, called Avogadro’s number
, was taken for the case where the volume selected was one cubic centimetre, the temperature zero centigrade, and the pressure that corresponding to 760 millimetres of mercury. Then it was shown as the result of highly complicated mathematical syntheses that, if molecules existed, a wide variety of phenomena should be influenced by the precise value of Avogadro’s number. The phenomena referred to deal with Brownian movements in fluids (Einstein), the viscosity of gases (Maxwell, Boltzmann, Einstein), the blue colour of the sky (Rayleigh, Keesom), equilibrium radiation (Planck), the specific heat of solids (Einstein), the phenomenon of critical opalescence (Smoluchowski), and many other phenomena which it is not necessary to mention. Accurate observations and experiments conducted on these phenomena should therefore permit us to deduce the value of Avogadro’s number. The results of all these experiments were in striking agreement, always yielding the same value. As this number runs up into quintillions (
), it was scarcely feasible to attribute the marvellous agreement to mere chance; hence we were forced to conclude that our suppositions were correct and that the existence of molecules had been established. It was then an easy matter to determine their masses and to obtain information as to their sizes and other characteristics.
Although we may be repeating ourselves unnecessarily, we must again draw attention to the fact that this knowledge of molecules, which is obtained through a co-ordination of experimental results, is in all respects (other than in degree of certainty) of the same type as our knowledge of the spherical shape of the sun or of our knowledge of space and of the table. On the other hand, it is essentially different from our awareness of feeling hot or tired.
Finally, let us consider a last example, namely, our belief that light is atomic. In this case our knowledge is still more uncertain. The justification for a belief in quanta was arrived at by Planck (as we have explained elsewhere), and arose from the peculiar phenomenon of black-body radiation. The mathematical treatment of problems of this sort is based on the calculus of probabilities. When calculations were conducted on the assumption of the continuous emission of light, we obtained Rayleigh’s law of radiation, which was refuted by facts. Planck noticed that by substituting discontinuous probabilities for continuous ones, the results of observation would be anticipated with great precision. When, a few years later, Nernst and then Einstein showed that the extension of these same discontinuities to the energy of molecular motions would account for the curious anomalies and variations of the specific heats of gases and solids, and when in addition Einstein succeeded in accounting with high precision for the photo-electric effect, Planck’s ideas appeared to gain in probability. The belief was enhanced still further when Bohr presented science with his model of the quantum-emitting atom.