wave-lengths. If the coefficient of reflection were as small as Compton's experiments would indicate, the reflected energy would be difficult of detection. The fact that it is very easy to observe indicates at once that the reflection must be very good. Another indication that the radiations are strongly reflected from a crystal is furnished by the experiments of Rutherford on the reflection of the gamma rays from radium. The intensity of the photographic traces leads to the conclusion that the intensity of the reflected beam was of the same order as that of the original.

A careful experimental investigation of the reflectivity of calcite has been in progress for some months at the Phoenix Physical Laboratory of Columbia University. A double X-ray spectrometer is used in these experiments. A nearly monochromatic beam of X-radiation lying in a region A is obtained by reflection of the general radiation from the first crystal. These monochromatic rays fall on a second crystal and are reflected into the ionization chamber. The coefficient of reflection is defined as the ratio of the intensity of this beam after the second reflection to its intensity before such reflection. The reflectivity is very large when the two crystal faces become exactly parallel. When this condition obtains all the radiation from the first crystal meets the second crystal at the proper angle for maximum reflection at the same setting. The following table gives the results for the first order reflection from calcite./

The third column gives the values obtained from Darwin's expression assuming the absorption to vary as 24. This value of the exponent of λ is less than has been found by experiment. The calculated curve rises rapidly at small angles. This rise at small angles becomes very great if μ is taken proportional to X3.

An interesting result was obtained in these experiments with two crystals. When the two crystals are so placed that their reflecting planes are exactly parallel it can be shown that every ray coming

from the first crystal will strike the second crystal at the proper angle for maximum reflection. Nevertheless when the second crystal is turned through a small angle some energy is still reflected. The angle at which there was some reflection was about one minute each side of the maximum. The curves plotted between the reflection and the small deviation of the second crystal have a constant area for the whole range of wave-lengths investigated.

THE DECREASE OF ELECTRON VELOCITIES ON PENETRATING THE

TARGET

A knowledge of the laws of decrease of electron velocities of the cathode electrons penetrating into the target is indispensable to the formulation of any theory of X-ray emission. On account of its importance it is perhaps worth while to review here the small amount of work that has been done on this subject and to call attention to the need of further investigation.

It is evident that the X-rays are not only excited at the surface of the target but throughout that region within which the electrons still retain a considerable velocity. This has been shown experimentally by W. R. Ham24 and L. D. Davey.25 They both measured the mean depth of formation of X-rays within the target. The values obtained ranged from 2 × 10-4 to 6 X 10-5 cm., depending on the target and the voltage applied to the X-ray tube. The limit of penetration must of course have been considerably greater than this mean depth.

The decrease of velocity of swiftly moving electrons in matter has been theoretically treated by Sir J. J. Thomson. 26 It is shown that the law of velocity decrease should be

x

where To is the initial kinetic energy and T, is the kinetic energy at any depth x. This law has been experimentally investigated by Whiddington. 27 The method employed was to measure, by the magnetic deflection, the velocity V of electrons after passing through a thin film with a known initial velocity v.. Experiments were made with aluminum and gold foils. The theory of Sir J. J Thomson was confirmed. Whiddington expresses his results in terms of the velocities:

The constant a was found to have the value of 7.32 X 1042 for aluminum and 25.4 X 1042 for gold. It does not appear to depend

in any simple manner on atomic weight, atomic number density or other property of the metal. Two methods of determining this constant directly by means of experiments with X-rays have been pointed out by Bergen Davis. 28

The latter method is comparatively simple. A thin film of the metal to be investigated is deposited on a backing of some metal such as molybdenum that gives a characteristic radiation convenient to observe. The electrons will only cause the characteristic to appear when they have penetrated the film with sufficient velocity to excite such radiation. This critical velocity is already known for each element. The velocity at which they enter the film can be calculated from the voltage applied to the tube. The velocity is thus determined at each boundary of a film of known thickness.

Bibliography

Total Emission of X-Rays

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Intensity of Characteristic Spectra

18 Hull, A. W., Proc. Am. Phys. Soc., Phys. Rev., March 1916.

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Intensity of Reflection of X-Rays from Crystals

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Decrease of Electron Velocities on Penetrating the Target

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28 Davis, B., Phys. Rev., June 1918.

PROBLEMS OF X-RAY EMISSION

BY DAVID L. Webster

QUANTUM PHENOMENA IN THE GENERAL RADIATION SPECTRUM The quantum theory, as first developed by Planck, was concerned primarily with heat radiation confined to about five octaves of the visible and infra-red spectrum. The phenomena of this region were not such as to suggest quanta of energy at all obviously; so in spite of the success of Planck's theory and the need for a constant of the dimensions of his h, which he pointed out in connection with the Wien displacement law, there were still many who doubted whether quanta had any real significance. Like atoms, to seem real, they needed to be detected individually.

The first opportunity for such detection was in the photo-electric effect, but there the experimental difficulties threw doubt on the results previous to those of Millikan. Even this spectral region, however, was not the most promising. The quantum energy must be proportional to its frequency-exactly so, according to Planck's reasoning and the X-ray region was known to be 8 or 10 octaves higher in frequency than the ordinary ultra-violet. In X-rays, therefore, we might expect quanta to be most in evidence.

As applied to X-ray emission, the quantum theory would indicate that the energy of each cathode ray that can produce X-rays of a certain frequency must be at least as large as a quantum of the frequency produced. To test the law, we have only to measure the cathode ray energy and the X-ray frequency. To measure the cathode ray energy demands a source of uniform cathode rays, with a means of measuring either the potential drop that accelerates them, or their velocity as they strike the target. Since the cathode rays ordinarily used in X-ray work are far from uniform, this demands special apparatus. The ideal source of current for this purpose is a high tension battery. This was first used from 1898 to 1900 by J. Trowbridge,' who built a battery of 20,160 Planté cells for this purpose. But, unfortunately, no means were available during these years for sorting out the X-rays, which are far from homogeneous, even with cathode rays of a uniform speed, and there was no means of measuring their frequencies.

The use of more nearly homogeneous X-rays was first made possible by Barkla's discovery of characteristic rays. Such rays