It has been shown [says Professor Darwin in his Presidential Address at the South African meeting of the British Association (1905)] that the atom, previously supposed to be indivisible, really consists of a large number of component parts. By various lines of experiment it has been proved that the simplest of all atoms, namely that of hydrogen, consists of about 800 separate parts; while the number of parts in the atom of the denser metals must be counted by tens of thousands. These separate parts of the atom have been called corpuscles or electrons, and may be described as particles of negative electricity. . . The mechanism is as yet obscure whereby the mutual repulsion of the negative corpuscles is restrained from breaking up the atom, but a positive electric charge, or something equivalent thereto, must exist in the atom so as to prevent disruption... It is only just a year ago that Thomson suggested, as representing the atom, a mechanical or electrical model the properties of which could be accurately examined by mathematical methods. . . Thomson's atom consists of a globe charged with positive electricity, inside which are some thousand or thousands of corpuscles of negative electricity, revolving in regular orbits with great velocities, comparable to that of light, namely 200,000 miles a second. Since two electrical charges repel one another if they are of the same kind, and attract one another if they are of opposite kinds, the corpuscles mutually repel one another, but all are attracted by the globe containing them. The forces called into play by these electrical interactions are clearly very complicated, and you will not be surprised to learn that Thomson found himself compelled to limit his detailed examination of the model to one containing about seventy corpuscles. It is indeed a triumph of mathematical power to have determined the mechanical conditions of such a miniature planetary system as I have described.
Professor J. J. Thomson's atomic model is thus a simplified ideal construction in which certain electrical conceptions are carried to their ultimate limits. Only thus can the problem of the atom be solved; and the solution representatively fits the case of the more complex atoms of the chemical elements.
Take now the case of the first law of motion. This asserts that if a body be in motion it will continue to move in a straight line and with a uniform velocity unless there are accelerating conditions. But there is no moving particle in this universe that is not in some degree accelerated. We do find, however, that the more we can reduce or eliminate these alien accelerations the nearer do we get to an actual example which shall illustrate the truth of the assertion. But the law itself applies to a state of things under extreme conditions which can be approached but never reached. It is carried to its ultimate limits in a scheme of ideal construction. Next let us take the case of a planet in motion and at the same time affected by the presence of the sun. Its uniform rectilinear motion is converted into an elliptical orbit. It may here be noted that in the calculations of astronomers the case is further simplified by substituting for the actual bodies material particles or mathematical points to each of which is attached a numerical equivalent representing the mass. Now according to Kepler's second law, the radius vector, or straight line joining the mathematical points, always sweeps over equal areas in equal times. That was a grand generalisation, and it is perfectly true of the ideal construction we frame under the supposed conditions. But as a matter of fact in no case is the orbit of any one of the planets in the solar system an ellipse; and in no case does the radius vector actually sweep over equal areas in equal times. The other planets cause perturbations, and to determine the actual motion of any one of them is a problem of great complexity. The astronomer has to extend his ideal construction so as to introduce all the important factors. He has to frame a scheme of a number of material particles at different distances from each other, each with its mass coefficient, and then to calculate the movements of any one under the joint influence of all the rest.
Such a material scheme is what is called a configuration. Given the configuration at any selected moment, the motion of any point therein can be calculated. But in the actual solar system there are a number of points the numerical coefficients of which are so small as to be negligible. So that the ideal construction only approximately represents the actual state of the case.
Nevertheless the physical astronomer believes, and asks us to believe, that if we introduce into his ideal construction all the factors, it will hold good of the actual solar system. He claims that he has proved its accuracy so far as observation goes; he urges that wherever we have been able to apply it to the given facts of experience, it fits them to a nicety. Why not go further and believe where we are unable at present to know? I for one am prepared freely and fully to admit the cogency of his appeal. I am a believer within the courts of the temple of astronomical physics. Most of us I think are. But analogous methods may be applied, with far greater difficulty it is true, in other cases where there are different types of configuration—in physiology for example. The configurations here are indefinitely more complex; the influences of the material particles upon each other are much more subtle; it is far less easy, even if it be possible, to treat the changes within the configuration in terms of mathematical formulae; an ideal construction in terms of mechanism is at best tentative and hypothetical. Many physicists regard a scientific interpretation of physiological processes in terms of physical mechanism as not yet within the range of practical politics. But thorough-going advocates of naturalistic interpretation have a more robust faith. They are ready to accept, in an attitude of belief, a great deal more than they can definitely prove. What shall be our attitude towards them? Well, I should say: Don't let us attempt to disparage the beliefs which may be all they have to aspire to. And don't let us deny what they may some day, though that day seems somewhat distant, be able to establish, I myself confess to a belief that an interpretation of all the material phenomena of the wide universe in terms of a strictly naturalistic configuration is the ideal which every man of science as such should steadily keep in view, and that his living faith in its ultimate attainment should win our admiration.