Part 35

Röntgen’s discovery excited intense interest among laymen as well as in scientific circles. Of the many X-ray photographs taken, those of Wright (=1=, 235, 1896) of Yale were the first to be produced in this country. His experiments were made immediately on receipt of the news of Röntgen’s research, and resulted in the publication of a number of photographs showing the translucency for these rays of paper, wood, and even aluminium.

As X-rays are undeviated by electric or magnetic fields, Schuster, and later Wiechert and Stokes, suggested that they might be electromagnetic waves of the same nature as light, but much shorter and less regular. The great objection to this hypothesis was the failure either to refract or diffract these rays. In fact Bragg contended that they were not etherial disturbances at all, but consisted of neutral particles moving with very high velocities. Finally Laue[164] demonstrated their undulatory nature by showing that diffraction took place under proper conditions. Just as the distance between adjacent lines of a grating must be comparable to the wave length of light for a spectrum to be formed, a periodic structure with a grating space of their very much shorter wave length is necessary to diffract X-rays. Such a structure is altogether too fine to be made by human tools. Nature, however, has already prepared it for man’s use. The distance between the atoms of a crystal is just right to make it an excellent X-ray grating, and Laue had no difficulty in obtaining diffraction patterns when Röntgen rays were passed through a block of zincblende. The distance between adjacent atoms of this cubic crystal can be computed at once from its density and molecular weight, and then the wave length of the radiation calculated from the deviation suffered. In this way X-rays are found to have a length less than one thousandth as great as visible light. Further study of this phenomenon, particularly by the two Braggs, father and son, has revealed many of the structural details of more complicated crystals.

The most significant investigation in the field opened up by Laue’s discovery is that undertaken by Moseley[165] only a couple of years before he lost his life in the trenches at Gallipoli. Using many different metals as anticathodes in a vacuum tube, he measured the frequencies of the characteristic rays emitted. He found that if the elements are arranged in order of increasing atomic weight, the square roots of the characteristic frequencies form an arithmetical progression. If to each element is assigned an integer, beginning with one for hydrogen, two for helium, and so on, the square root of the frequency of the characteristic radiation is found to be proportional to this atomic number. Even though Uhler has shown recently that over wide ranges Moseley’s law does not hold within the limits of experimental error, there is undoubtedly much significance to be attached to this simple relation.

_Radioactivity._—The year following the discovery of X-rays, Becquerel found that a photographic plate is similarly affected by radiations from uranium salts. Two years later the Curies separated from pitchblende the very active elements polonium and radium. Passage of the rays from these substances through electric and magnetic fields revealed the existence of three types. The alpha rays have been shown by Rutherford and his co-workers to be positively charged helium atoms; the beta rays are very rapidly moving electrons; and the gamma rays are electromagnetic pulses of the same nature as X-rays but somewhat shorter. In 1902 Rutherford and Soddy advanced the theory of atomic disintegration, according to which the emission of a ray is an indication of the breaking down of the atom to a simpler form. Thus in the radioactive substances there is going on before our eyes a continual transformation of one element into another, a change, by the way, which appears to be in no slightest degree either hastened or delayed by changes in temperature (H. L. Bronson, =20=, 60, 1905) or external electrical condition of the radioactive element. Uranium is the progenitor of a long line of descendants, of which radium was supposed for some time to be the first member. Boltwood (=25=, 365, 1908) of Yale, however, showed that the slow growth of radium in uranium solutions is incompatible with this assumption, and soon isolated an intermediate product which he named ionium. Radium itself disintegrates into a gas known as radium emanation, which in turn gives rise to a succession of other products. Analyses by Boltwood (=23=, 77, 1907) of radioactive minerals from the same locality show such a constant ratio between the amounts of uranium and lead present that it is natural to conclude that lead is the end product of the series. This hypothesis is confirmed by the fact that the oldest rocks show relatively the greatest amounts of this element.

In addition to the Ionium-Radium series two others have been discovered. Of these Boltwood’s (=25=, 269, 1908) investigations seem to indicate that the one which starts with actinium is a collateral branch of the radium series and comes from the same parent uranium. The other begins with thorium and comprises ten members. As yet the end products of the actinium and thorium series have not been identified, although there is some reason for believing that an isotope of lead may be the final member of the latter.

As the amount of a radioactive element which disintegrates in a given time is proportional to the total mass present, an infinite time would be required for the substance to be completely transformed. Hence the life of such an element is measured by the half value period, or time taken for half the initial mass to disintegrate. This time varies widely for different radioactive substances, ranging from a small fraction of a second for actinium A to five billion years for uranium. Boltwood’s (=25=, 493, 1908) original determination of the life of radium from the rate of its growth in a solution containing ionium gave 2000 years as its result, although recent measurements by Miss Gleditsch (=41=, 112, 1916) agree more closely with the value 1760 years obtained by Rutherford and Geiger from the number of alpha particles emitted.

Under the action of X-rays or the radiations from radioactive substances, gases acquire a conductivity which has been attributed by Thomson and Rutherford to the formation of ions. Zeleny has found that ions of opposite sign have somewhat different mobilities in an electric field, and experiments of Wellisch (=39=, 583, 1915) show that at low pressures some of the negative ions are electrons. T. S. Taylor (=26=, 169, 1908 _et seq._) and Duane (=26=, 464, 1908) have investigated the ionization produced by alpha particles, and Bumstead (=32=, 403, 1911 _et seq._) has studied the emission of electrons from metals which are bombarded by these rays. The investigations of Franck and Hertz, and McLennan and Henderson, show a significant relation between the ionizing potential (energy which must be possessed by an electron in order to produce an ion on colliding with an atom) and a quantity, to be considered later in more detail, which has been introduced by Planck into the theory of radiation.

_Methods of Science._—Scientific progress seems to follow a more or less clearly defined path. Experimentation brings to light the hidden processes of nature, and hypotheses are advanced to correlate the facts discovered. As more and more phenomena are found to fit into the same scheme, the hypotheses at first proposed tentatively, although often only after extensive alterations, become firmly established as theories. Finally there may appear a fundamental clash between two theories, each of which in its respective domain seems to represent the only possible manner in which a large group of phenomena can be correlated. The maze becomes more perplexing at every step. At last a genius appears on the scene, approaches the problem from a new and unsuspected point of view, and the paradox vanishes. Such changes in point of view are the milestones which mark the progress of science. That science is stagnant whose only function is to collect, classify and correlate vast stores of experimental data. The sign of vitality is the existence of clearly defined and fundamental problems any possible solution of which seems irreconcilable with the most basic truths of the science in question. The greater the paradox grows, the more certain the advent of a new point of view which will bring one step nearer the comprehensive picture of nature which is the goal of natural philosophy.

_The Ether._—From the earliest times philosophers have been attracted by the possibility of explaining physical phenomena in terms of an all-pervading medium. So strong had this tendency become by the middle of the nineteenth century that the English school of physicists were attributing rigidity, density and nearly all the properties of material media to the ether. In fact most physicists seemed to have forgotten that no experiment had ever given _direct_ evidence of the existence of such a medium. Not until the first decade of the twentieth century was it realized that the experimental evidence actually pointed in quite the opposite direction, and that a new point of view was needed in dealing with those phenomena of light and electromagnetism which had been previously described in terms of a universal medium. Some account of the development of the ether theory and of the origin and growth of the point of view which has its principal exemplification in the principle of relativity is essential for an understanding of present tendencies in formulating a philosophic basis for scientific thought.

In the time of Newton and for a century after there was much controversy between the adherents of two irreconcilable theories of light. Hooke had suggested that light is a wave motion traveling through a homogeneous medium which fills all space, and Huygens had shown that the law of refraction can be deduced at once from this hypothesis if it is assumed that the velocity of light in a transparent body is less than that in free ether. However, Newton, impressed by the fact that a ray obtained by double refraction in Iceland spar differs from a ray of ordinary light just as a rod of rectangular cross section differs from one of circular cross section, and seeing no way of explaining this dissymmetry in terms of a wave motion analogous to longitudinal sound waves, adhered to the view that light consists of infinitesimal particles shot out from the luminous body with enormous velocities. So great was his reputation on account of his discoveries in other fields that this theory of light held sway among his contemporaries and successors until the labors of Young and Fresnel at the beginning of the nineteenth century definitely established the undulatory theory. However, in spite of the fact that a corpuscular theory of light made the assumption of an ether unnecessary in so far as the simpler of the observed phenomena are concerned, even Newton postulated the existence of such a medium, partly in order to explain the more complicated results of experiments in light, and partly in order to provide a vehicle for the propagation of gravitational forces.

Now an ether, if it is to explain anything at all, must have at least some of the simpler properties of material media. The most fundamental of these, perhaps, is position in space. As a first approximation in explaining optical phenomena on the earth’s surface, the earth might be supposed to be at rest relative to the ether. But the establishment of the Copernican system made the sun the center of the solar system and gave the earth an orbital speed of eighteen miles a second. It may be remarked parenthetically that the speed of a point on the equator due to the earth’s diurnal rotation is quite insignificant compared to its orbital velocity. Hence as a second approximation the sun might be considered at rest relative to the ether and the earth as moving through this unresisting medium.

The first indication of this motion lay in the discovery of aberration by the British astronomer Bradley in 1728. Bradley noticed that stars near the pole of the ecliptic describe small circles during the course of a year, while those in the plane of the ecliptic vibrate back and forth in straight lines, stars in intermediate positions describing ellipses. The surprising thing, however, was that the time taken to complete one of these small orbits is in all cases exactly a year. Bradley concluded that the phenomenon is in some way dependent on the earth’s motion around the sun, and he was not long in reaching the correct explanation. For suppose the earth to be at rest. Then in observing a star at the pole of the ecliptic it would be necessary to keep the axis of the telescope exactly at right angles to the plane of the earth’s orbit. However, as the earth is in motion, the telescope must be pointed a little forward, just as in walking rapidly through the rain an umbrella must be inclined forward so as to intercept the raindrops which would otherwise fall on the spot to be occupied at the end of the next step. The angle through which the telescope has to be tilted is known as the angle of aberration, and the tangent of this angle may easily be shown to be equal to the ratio of the velocity of the earth to the velocity of light. Knowing the velocity of the earth, the velocity of light can then be calculated. This method was one of the first of obtaining the value of this important quantity.

More recently, terrestrial methods of great precision have been devised for measuring the velocity of light. The most accurate of these is that employed by the French physicist Foucault in 1862. A ray of light is reflected by a rotating mirror to a fixed mirror placed at some distance, which in turn reflects the ray back to the moving mirror. The latter, however, has turned through a small angle during the time elapsed since the first reflection, and consequently the direction of the ray on returning to the source is not quite opposite to that in which it had started out. This deviation in direction is determined from the displacement of the image formed by the returning light, and from it the velocity of light is calculated. In order to make the deflection appreciable the distance between the two mirrors should be very great. As originally arranged by Foucault, it was found impractical to make this distance greater than twenty meters, and consequently the displacement of the image was less than a millimeter. Such a small deflection limited the accuracy of the experiment to one percent. In 1879, however, Michelson (=18=, 390, 1879), then a master in the United States Navy, improved Foucault’s optical arrangements to such an extent that he was able to use a distance of nearly seven hundred meters between the two mirrors. With a rate of two hundred and fifty-seven revolutions a second for the rotating mirror, the displacement obtained was over thirteen centimeters. This experiment gave 299,910 kilometers a second for the velocity of light, with a probable error of one part in ten thousand. Later investigations by Newcomb and Michelson (=31=, 62, 1886) gave substantially the same result. So great has been the accuracy of these terrestrial determinations that recent practice has been to calculate from them and the angle of aberration the earth’s orbital velocity, and hence the distance of the earth from the sun. This indirect method of measuring the astronomical unit has a probable error no greater than the best parallax methods of the astronomer. (J. Lovering, =36=, 161, 1863.)

Aberration is a first order effect, i. e., it depends upon the first power of the ratio of the velocity of the earth to the velocity of light, and at first sight it seemed to prove conclusively that the earth must be in motion relative to the luminiferous medium. Other questions had to be settled, however, and one of these was whether or not light coming from a star would be refracted differently when passing through optical instruments from light which had a terrestial origin. Arago subjected the matter to experiment, and concluded that in every respect the light from a star behaved as if the earth were at rest and the star actually occupied the position which it appears to occupy on account of aberration. Finally optical experiments with terrestrial sources seemed to be in no way affected by the motion of the earth through the ether.

In order to account for these facts Fresnel advanced the following theory. To explain the refraction that takes place when light enters a transparent body, it is necessary to assume that light waves travel more slowly through matter than in free ether. Now the velocity of sound is known to vary inversely with the square root of the density of the material medium through which it passes. Hence it is natural to assume that ether is condensed inside material objects to such an extent that this same relation connects its density with the velocity of light traveling through it. But when a lens or prism is set in motion, Fresnel supposed it to carry along only the _excess_ ether which it contains, ether of the normal density remaining behind. This assumption suffices to explain Arago’s results, and yet fits in with the phenomenon of aberration. It gives for light traveling in the direction of motion through a moving material medium of index of refraction _n_ an absolute velocity greater than that when the medium is at rest by an amount

(1 − (1/_n^2_))_v_,

which is only a fraction of the velocity _v_ which would have to be added if convected matter carried along all the ether which resides within it. This expression was tested directly, first by Fizeau in 1851, and later by Michelson and Morley (=31=, 377, 1886) in this country. The experiment consists in bifurcating a beam of light, passing one-half in one direction and the other in the opposite direction through a stream of running water. On reuniting the two rays the usual interference fringes are produced. Reversing the direction of motion of the water causes the fringes to shift, and from the amount of this shift the velocity imparted to the light by the motion of the stream is computed. The divergence between the experimental value of this quantity and that calculated from Fresnel’s coefficient of entrainment was found by Michelson and Morley to be less than one percent, which was about their experimental error. Thus Fresnel’s expression for the velocity of light in a moving medium is entirely confirmed by experiment. The derivation of it accepted to-day, however, is very different from his original deduction.

It has been noted that the phenomena of polarization led Newton to reject the wave theory of light. The only type of wave known to him was the longitudinal wave, in which the vibrations of the particles of the medium are in the same direction as that of propagation of the wave, and it was impossible to suppose that such a wave could have different properties in different directions at right angles to the line in which it is advancing. But in 1817 Young suggested that this inconsistency between the wave theory and the facts of polarization could be removed by supposing the vibrations constituting light to be executed at right angles to the direction of propagation. Thus in ordinary light the vibrations are to be conceived as taking place haphazard in all directions in the plane perpendicular to the ray, while in plane polarized light these vibrations are confined to a single direction. This supposition explained so many of the puzzling results of experiment, that it was accepted at once and led to the complete vindication of the undulatory theory.

_Elastic Solid Theory._—Shortly afterwards Poisson succeeded in solving the differential equation which determines the motion of a wave through an elastic medium. His solution shows that such a medium is capable of transmitting two types of wave—one longitudinal, the other transverse. If κ denotes the volume elasticity, η the rigidity and ρ the density of the medium, the velocities of the two waves are respectively

√((κ + (⁴⁄₃)η)/ρ) and √(η/ρ)

Now a solid has both compressibility and rigidity, and transmits in general both types of wave. A fluid, on the other hand, on account of its lack of rigidity, cannot support a transverse vibration. Hence it was natural that Green, in searching for a dynamical explanation of the ether, should have proposed in a paper read before the Cambridge Philosophical Society in 1837 that the ether has the elastic properties of a solid. One great difficulty presented itself; disturbances inside an elastic solid must give rise to compressional as well as to transverse waves. But no such thing as a compressional wave had been found in the experimental study of light. Green attempted to overcome this difficulty by attributing an infinite volume elasticity to the ether. The expression above shows that longitudinal waves originating in such an incompressible medium would be carried away with an infinite velocity, and it may be shown that the energy associated with them would be infinitesimal in amount. The next step was to calculate the coefficients of transmission and reflection for light passing from one material medium to another. Here the elastic solid theory is not altogether successful. If the ether is supposed to have different densities in the two media, as in Fresnel’s theory, but the same rigidity, certain of these coefficients fail to give the values demanded by experiment, while if the densities are assumed the same but the rigidities different, other of the coefficients have discordant values. In connection with the phenomena of double refraction even more serious difficulties are encountered.

_Electromagnetic Theory._—It was beginning to be felt that an ether must explain more than the phenomena of light, for Faraday’s conception of electromagnetic action as carried on through the agency of a medium had added greatly to its functions. Finally Maxwell’s demonstration that electromagnetic waves are propagated with the velocity of light made the theory of light into a subdivision of electrodynamics. Maxwell himself did not apply electromagnetic theory to the explanation of reflection and refraction. This deficiency, however, was remedied by Lorentz in 1875. The results obtained, as well as those for double refraction (J. W. Gibbs, =23=, 262, 1882 _et seq._), and metallic reflection (L. P. Wheeler, =32=, 85, 1911), provided a complete vindication of the electromagnetic theory of light. This is all the more significant when the extreme precision obtainable in optical experiments is taken into account. For instance, Hastings (=35=, 60, 1888) has tested Huygens’ construction for double refraction in Iceland spar and found that “the difference between a measured index of refraction ... at an angle of 30° with the crystalline axis, and the index calculated from Huygens’ law and the measured principal indices of refraction” is a matter of only 4–5 units in the sixth decimal place. Since Maxwell’s time the gamut of electromagnetic waves has been steadily extended. The shortest Hertzian waves merge almost imperceptibly into the longest heat waves of the infra-red, and from there the known spectrum runs continuously through the visible region to the short waves of the extreme ultra-violet recently disclosed by Lyman. Here there is a short gap until soft X-rays are reached, and finally the domain of radiation comes to an end with gamma rays a billionth of a centimeter in length.