ACE. The ratio I/I。 (ratio of transmitted to incident radiation in the equation IIe) will be given by * It is obvious that the finite width of the slit has in this case introduced no error in the observed ratio I/Io. If, however, (1) the spectral energy distribution in the incident radiation. is not uniform, and (2) the absorber, because of variation of absorption-coefficient with wave-length, transmits different amounts at each wave-length, the result is somewhat different. To take a concrete case-Certain measurements of absorption-coefficients have been reported in which the slitwidths were such that the angle ajoa, of fig. 5 was about 30 minutes of arc. Let us consider the error introduced in measuring the absorption-coefficient of copper at a wavelength 0-3 Å., when the spectral energy distribution in this region is that corresponding to the continuous spectrum excited by some 50,000 volts. In this case the spectral range A to λ of fig. 5 corresponds to, roughly, 0·06 Å. (calcite crystal). The spectral energy distribution over this range is represented by the line eye of fig. 6, the ordinate at λo being arbitrarily taken as unity. Let the copper absorber be chosen of such thickness that at λ=0·3 Å. it transmits 0.50 of the incident energy. Then, assuming the approximate linear relation between 3 and the mass absorptioncoefficient in this region, the ratio Io/I of the incident to the transmitted radiation at each wave-length λ in the region 0.27 <x<0.33 is given by the line 2 of fig. 6. Multiplying each ordinate of the triangle ACE by the corresponding ordinate of the spectral energy distribution curve of the incident radiation (ee) gives ABCDE, which is the spectral energy distribution of the radiation I, as reflected into the ionization chamber. Dividing the ordinates of this latter curve by the ratio II at each wave-length gives AB'C'D'E, which is the energy distribution in the radiation I (i. e., the radiation entering the ionization chamber after passing through the absorber). The observed ratio I/I, is given by * A linear relation is assumed for the energy distribution between A, and A, for simplicity in computation. The final result is not materially changed by this assumption. This ratio is not quite equal to the ratio OC/OC=0·500, which is the ratio to be expected if an infinitely narrow slit system were used. By measuring the two areas, and observing how much the observed ratio I/I, differs from 0-500, one can obtain the error in the resulting value of the mass absorption-coefficient. As an illustration of order of magnitude, there are given in Table V. the errors, computed as above, for copper of three thicknesses such as to transmit, respectively, 1/10, 1/2, and 4/5 of the incident beam, and for spectral energy distributions corresponding roughly to 50,000 and to 60,000 volts. TABLE V. Errors, in per cent., in measuring mass absorption-coefficients of copper at λ=0·3 A. with a slit system 0·06 Å. wide, at two voltages. A positive error means that the observed value is too large. Of course, the values are only approximate because of the simplifying assumptions which have been made. For elements of higher atomic number than copper the error becomes greater (so long as λ=0·3 is in the K-absorption region). The error becomes greater at shorter wave-lengths and vice versa. The error becomes rapidly smaller the smaller the slit-width (rather, the smaller the ratio ^/^). While these errors are not large, they must be taken into account when attempting to measure absorption-coefficients with a precision of the order of 1/10 per cent. Either a correction for the finite width of the slit must be made, or one must use a slit system sufficiently narrow so that the error is less than the desired precision. This latter is made somewhat difficult by the fact that the energy transmitted by a slit system of the type shown in fig. 5 decreases as the square of the slit-width. Summary. 1. The question has been raised: Are there in X-ray absorption spectra discontinuities corresponding to the so-called "spark" lines analogous to the K, L, K. . . . discontinuities corresponding to the diagram lines? The present evidence seems to indicate that the processes which give rise to the spark lines are secondary processes, and we should not therefore expect to find evidence concerning their origin in absorption spectra. But in any event the spark lines are so weak compared with the diagram lines that existing data on X-ray absorption-coefficients are not sufficiently precise to detect such discontinuities as might occur. 2. It is shown that a straight line (Moseley graph) results when one plots the square root of the difference in frequency between a spark line and its "parent" line as a function of atomic number. This suggests the possibility that spark lines may originate in two-electron transfers. 3. In making precise measurements of X-ray absorptioncoefficients, it is necessary to use slits sufficiently narrow to eliminate the "slit-width" error. The magnitude of this error is computed for one special case, and it is shown that with slit-widths as wide as some which have been used, errors as large as several per cent. may occur in the neighbourhood of 0·3 Å. Göttingen, January 14, 1928. By VI. Polarization of Infra-red Radiation by Calcite. I Introduction. N a recent communication (1) it was shown by examination between wave-lengths 8 and 14μ that interference effects are to be observed in the absorption spectrum of a thin slice of calcite, and it was further suggested that a great many absorption bands which were found by Schaefer, Bormuth, and Matossi (2) in their work on various carbonates, and which they attributed to "combination tones" formed from the several fundamental frequencies of vibration, were spurious and in reality owed their origin to * Communicated by Dr. E. K. Rideal. interference within the crystal film. That these bands are not, however, ail due to such a cause is shown by the fact that, while the wave-lengths of successive maxima or minima when substituted in an interference formula (1/λ-1/M) = 1/2ne, where z is the thickness of the crystal film, give a series of values for n, the refractive index of the material, which indicate the general course of the X, n curve, the experimental points lie very raggedly about the mean, having divergencies considerably greater than would be expected solely from error in observation. This must imply that the bands found are due to the superposition of interference fringes upon a real variation in intensity caused by selective absorption at particular wave-lengths. It may be remarked that the greatest raggedness occurs about A 11.3, where there is known to be an intense absorption band for waves having any component of their electric vector along the axis of the crystal, and it is reasonable to suppose that other gross divergencies from the mean line are similarly due to the presence of real absorption. = Accordingly some method was sought by which the true absorption could be differentiated from interference effects. The immediately obvious one of using thicker slices of the absorbing material, thereby causing the interference bands to become finer and less pronounced and the absorption bands to be intensified, did not appear practicable owing to the fact that general absorption usually masked the whole when thicker slices were employed, the more particularly because in the most debatable region from 8 to 14 μ the spectral energy is very weak. In the following pages is described a method, based on polarization of the infra-red radiation by the absorbing crystal itself, by which the desired analysis has been effected. Method. The three fundamental frequencies of vibration in carbonates, which are active in absorbing radiation (3) (i. e. which involve a periodic variation of the electric moment of the CO, group), lie at wave-lengths of about 7μ, 11μ, and 144), and are polarized with the electric vector of the first and last perpendicular to, that of the other parallel to, the the optic axis. If, therefore, a thin slice of crystal be cut parallel to the optic axis, radiation of wave-length approximating to any of these fundamentals will, on transmission normally to the slice, suffer partial absorption, and the transmitted beam will be more or less polarized with the electric vector at right angles to that of the particular vibration concerned in the absorption. Clearly, if such radiation be now allowed to fall upon a second crystal similarly cut, the final intensity of the transmitted beam. will depend upon the angle at which the optic axis of the second crystal is disposed relatively to that of the first, being a maximum when the axes are parallel and a minimum when they are perpendicular. In short, the two crystals will behave in the infra-red region at the appropriate wave 40 80 120 160 200 240 280 320 360 B= Angular setting of rotating crystal lengths, just as two crystals of tourmaline do in the visible, the first acting as a polarizer, the second as an analyser. To test this the author examined the behaviour of two pieces of calcite 0.1 mm. and 0.05 mm. thick respectively, which were cut parallel to the optic axis. Observed under crossed nicols in sodium light the orientation of the crystals appeared to be perfectly accurate, so far as could be judged by eye from the character of the interference brushes. |