in our interpretation of intensities, in our energy measurements, we base ourselves on comparisons in which the eye is the ultimate judge. It would be easy to conceive an analysis based on a definition of mass derived, say, from the sense of touch; this would not affect the principles I wish to educe or the main features of my argument. In these refined observations, where we are reaching the limits of perception, we find that it is no longer possible to maintain the differentiation between the three aspects of our trinity. There is interaction between the observed phenomenon and the observing mechanism; the perception is further conditioned by the limitations which restrict the response of mind and consciousness. Some partial discrimination between subjective and objective may still bepossible; complete separation of the three components of the trinity will probably remain for ever beyond human capacity, though we are continually extending our means of observation, and there is no need to be dogmatic. We have enlarged the world of our perceptions, but they still set the boundaries to knowledge. 66 eye. Let us examine now a simple case of observation to which the foregoing ideas are applicable. I will take the example, of much interest of late years in relation to the quantum theory, of the hydrogen spectrum. We will suppose the radiation from glowing hydrogen gas to be refracted by a prism, the resulting spectrum being observed by the Using the ideas of modern wave mechanics, the energy from the glowing hydrogen, after passing through a narrow slit, is conveyed in wave-groups to the prism; it does not " pass through" the prism, but is dispersed by it, and after both surface and internal losses, due to the prism, travels on in a number of divergent wave-groups to the eye. Let us suppose the eye to be receiving from one selected direction a single sequence of these wave-groups. The energy transferred to the retina-no doubt by resonance, since the lossof energy is small-is seen as a spectrum "line," so called, actually a spectrum band of small width and of a definite brightness. I have, of course, not followed the whole course of events in detail: I have selected the changes on which I wish for the moment to concentrate attention. The theories of Planck and Bohr tell us that these changes are not continuous in character: they take place by discrete amounts, quanta; they are finite changes, brought about by resonance, from one stationary state to another. The transfer of the energy to the retina is one of these changes and : of the same nature as the rest it takes place by quanta. But let us examine the phenomenon from the receiving end; consider its aspect from the point of view of the eye and the conscious mind behind it. It would be in accord with our general experience to suppose that there is a minimum sensibile, a minimum disturbance below which no effect is produced on the consciousness; a minimum change, also, which is perceptible, which may (or may not) be of identical amount. The eye receives a succession of wave-groups associated with a certain frequency, the group or beat frequency it responds by resonance, after a very brief interval the natural measure of the response is therefore of dimensions energy x time, i. e. of action. Let us suppose that there is a certain minimum of response, the quantum of action, which is perceptible by the eye and the mind behind it. We can now trace back our phenomenon to its objective end, but we must retain our quantum of action as an indivisible unit. We realize at once the reason for the appearance of the quantum in ali visual phenomena; it is inherent in ourselves. Planck's constant h, Bohr's quantum of action, cannot but be identical with it, since any transfer of energy to the eye as a receiving mechanism will be governed by the usual quantum laws. Indeed, it is difficult to suppose that there could be two independent quanta involved in phenomena. Let us continue our analysis. Reception by the eye of the light from the single hydrogen "line" is associated with a definite frequency, the group or beat frequency. The eye is comparable with a heterodyne receiver, capable of responding over a certain range of frequencies; the range is no doubt different for different eyes, as the range of audibility is different for different ears. The group frequency is related to the wave frequency by the Rayleigh formula. If we denote the energy received in the usual manner by Idλ, we realize that the wave-length is a conception, an abstraction, merely; it is one of the boundaries of an integral field. But it is clear that we can think in terms of the ordinary wave theory; and the conclusions reached with the aid of that theory hold good. We note, in passing, that the wave-group has no definite boundaries: it dies away rapidly from a maximum, but may be supposed to extend to infinity in either direction: a succession of *We can conceive that the minimum sensibile may be a submultiple of h, but there would appear to be no means of perceiving such a distinction. wave-groups is a succession of maxima, of singularities, in a wave-field. In considering next the dispersion of the hydrogen light by the prism, we can adopt the usual wave theory; but we must bear in mind in our analysis that we are dealing with indivisible quanta of action, and frame our conceptions accordingly. The transfers of energy which take place again occur by resonance. Tracing our phenomenon further back to the radiating atom, we have the option of treating it by the methods of particle mechanics, or by the new methods of wave mechanics. We must, however, recognize that our particle is comparable with the wave-group, the singularity in a wave-field, and has no definite boundaries. Newton's corpuscular theory of light and the wave theory combine to form a more comprehensive whole. Let us return to the ideas with which we started. To describe our perception of an event, we make use of three conceptions-length, time, and mass; or we may say length, time, and action. There is a natural, indivisible, unit of action, the quantum. Expressed in terms of mass, the dimensions of this quantum are MVT or MVL, where V is velocity, of dimensions L/T. If, now, we choose arbitrary units of mass and length, say the mass of the electron and the wave-length of the red cadmium line, there is a corresponding definite value of V which is not infinite; we must not suppose V to become infinite without at the same time supposing M or L to become infinitely small. We are, in fact, dealing with a "complementarity," to use Bohr's term with a somewhat different significance, a trinity in unity, and we must adjust our conceptions accordingly. We thus reach what we may call an extended theory of relativity, which includes quantum theory, in which length, time, and mass are inter-related and the quantum of action is an invariant. Let us now suppose that in the observation of any phenomenon we wish to follow the changes of some quantity . Our quantum, wave-group, electron or proton is capable of motion in three directions and of rotation about three axes in space. Let its position or configuration at any instant be determined by the variables x, y, z, 0, 4, 4. Other variables involved are t and nh, where n, however, must be an integer, h being Planck's constant, the quantum of action. Our quantity is a function of these variables: (x, y, z, 0, 4, 4, t, nh). Experience indicates that, as a first approximation in considering the changes of p, we can neglect differential coefficients of higher order than the second. The changes will thus be given by a differential equation of the form where denotes any one of the variables and the f's are functions of any or all of the variables *. Our procedure is to try to fit solutions of this equation to the phenomena, remembering that n can only change by integral steps. Various methods of obtaining solutions of this equation in particular cases have been devised by Bohr, Heisenberg, Schrödinger, de Broglie, Dirac, and others, and remain applicable without modification with the conceptions introduced above. It is very instructive to realize how the experimenter, by inductive reasoning, has been led to introduce into his conceptions, in order to explain observed phenomena, the "subjective" unit, the quantum, which was unavoidably involved in the limitations of his powers of perception. I do not propose to follow my subject further in the present note. Much no doubt remains to be done in the devising of rapid methods of calculation applicable in the analysis of observations of the kind to which attention has been devoted, but already good progress has been made. It is hoped that the foregoing may assist the physicist who has not acquired the mathematical technique to grasp at least the rationale of the procedure which is being followed. He will find much further information in Bohr's article published in Nature' on April 14th, to which this note may be regarded as a corollary. I have been concerned with microscopic or, I might say, sub-microscopic phenomena. In dealing with macroscopic or statistical phenomena we can employ the usual procedure; it is only at the surfaces of bodies, or at the boundaries of our field, that we may need to resort to the more complicated technique of the new methods. * Repetition of suffixes implies summation, as in relativity notation. May 28th, 1928. LXXVIII. The Continuous Spectrum of Hydrogen. By F. H. NEWMAN, D.Sc., F.Inst.P., Professor of Physics, University College of the South-West of England, Exeter *. THE [Plate XIII.] 1. Introduction. HE origin and exact character of the continuous spectrum of hydrogen, which has been investigated by many observers, still remains uncertain. In some cases this type of spectrum possesses the peculiar characteristic of occurring without the presence of either atomic or molecular lines, and an explanation of this fact has been advanced by Kaplan †, who suggests that when the hydrogen molecule in the first electronic state possesses more than 0.50 volt vibrational energy, it may split into two atoms with emission of energy as radiation, the value 0.50 volt being derived from the observed short wave-length limit of this continuous spectrum. The absence of observed lines is due to the fact that transitions from the initial excited state of the molecule to lower ones give rise to lines lying far down in the ultra-violet region. This spectrum, which is quite distinct from that one which begins at the limit of the Balmer series and continues towards the shorter wave-lengths, appears in celestial spectra in the absence of the Balmer lines and the secondary spectrum, and its limit on the red side is always at wavelengths greater than λ 3646; for example, as an absorption spectrum it begins in a Cygni at λ 3710, having a maximum intensity at a 3660, approximately, and in Vega it commences at λ 3800, its maximum being at about λ 3710. Crew and Hulburt ‡ found this type of spectrum to be of similar character, although of differing intensity, in a number of sources, including a long hydrogen tube constructed after the manner of Wood with the light coming end-on through a quartz window from the central portion only, an ordinary discharge-tube, the separate striations of the positive column, the condensed spark in hydrogen at pressures above atmospheric, and in the water spark. In all cases it was of appreciable intensity near Ha, rising slowly to a maximum in the rear ultra-violet, and descending slowly in intensity from X 3000 to λ 2200. * Communicated by the Author. + Nat. Acad. Sci. Proc. xiii. p. 760 (1927). |