Cone Of Rays Research Articles

Phase Characteristics of Radio Signals received via the Ionosphere

A RADIO wave after reflexion from the ionosphere may be considered to consist of a specular component and a varying diffracted component1, the latter being the result of random scattering from a large number of moving irregularities. If the effect at a point on the ground is considered, the diffracted component may be regarded as a cone of radiation having its apex at the point on the ground and its base spread over a large area of the ionosphere. The specular component appears as a coherent wave the arrival path of which is assumed to be along the axis of the diffraction cone and changes direction slowly compared with the fading rate of the signal2. Information concerning the amplitudes of the specular and diffracted components of a radio wave and of the angular spread of the cone of rays forming the diffracted component is an important factor in the design of some types of receiving aerials. This information may be obtained from the probability distribution of the phase-difference between the two signals which result from the reception of the radio wave at two aerials spaced apart by a known distance.

On the Equivalence of Saddle Point Approximations and Ray Theory in Elastic Wave Problems

Summary It has been known for some time that the Bromwich method of expansion in negative powers of exponentials of the formal solutions of elastic wave problems for stratified media by wave theory methods gives rise to the various reflected and refracted waves predicted by the ray theory of geometrical optics. It is shown here by application to an example how the saddle point evaluation by the steepest descents method of the various terms in such an expansion of the solution leads to exactly the same expressions for the displacements in the reflected and refracted waves as can be obtained by the geometrical theory. The example chosen is that of the elastic waves produced by a harmonic point source of dilatational waves situated in the middle of an internal stratum bounded on both sides by halfspaces of identical elastic properties, all perfectly elastic, homogeneous and isotropic. In the course of the demonstration, we give the reflection and refraction coefficients for the amplitudes of displacements when a plane P or SV wave is incident at an interface between two elastic media. These are in the form in which they occur in the wave solutions of problems involving reflection and refraction at plane interfaces. I. Introduction Bromwich (1916, p. 425-428) studied the problem of a bar with one end fixed and struck at the other by a particle moving in the direction of the length of the bar. He showed that the expansion of the formal operational solution in negative powers of exponentials leads to a solution in terms of pulses. The method has since been applied by Muskat (1938a, b), Pekeris (1948, p. 46 et seq.), Officer (1951), Newlands (1952, p. 222 et seq.), Honda & Nakamura (1953, 1954) and others to the formal solutions of elastic wave problems for stratified media. Whereas Muskat and others studied problems involving plane boundaries, van der Pol & Bremmer (1937) have discussed the propagation of radio waves from a spherical point source situated above a spherical earth. They show (1937, pp. 844-6; see Bremmer, 1949, Ch. V for further detail) that the saddle point approximation for the reflected field gives an expression which may be obtained from the primary field by multiplying it by a reflection coefficient corresponding to the extra divergence acquired by a thin cone of rays on being reflected from a spherical instead of a plane surface. At the same time, the phase factor has to be

On the Determination of Heart Size from the X-Ray Fluoroscopic Image.

1. The author calculated the ratio of enlargement applicable to conversion of the short distance roentgenogram, shch as taken from the fluoroscopic image, into a picture that practically corresponds to an orthodiagram or tele-roentgenogram.If a cone of rays originating from a point source on the z-axis of the three-dimensional rectangular Cartesian coodinate system cast a shadow of a sphere with the center on the z-axis upon the x-y plane, the distance from the z-axis of any point (x, y) on the optical edge on the sphere is expressed by. √x2+y2. Let the “focal” distance onto the fluoroscope be F; the angle between the z-axis and the ray touching the sphere at the point (x, y) be. θ, and the fluoroscopic image corresponding to thelength. √x2+y2 cast on the x-y plane (represented by the fluoroscope) will be F tan. θ. Thus the ratio of magnification, M, isM=F tanθ√x2+y2The author theoretically showed applicability of this formula.2. A model of the heart was cut out from diatomaceous earth (Kieselguhr), and the applicability of the above formula was tested with satisfactory result.The actual site of the optical edge was also determined on a cadaveric normal human heart, and it was confirmed that the calculation with the above formula would not be affected by the displacement of the optical edge due to the change of focal distance.3. Measures representing twelve principal points on the cardiac silhouette and the transverse diameter of the chest, as obtained by the orthoscopic technique in ventro-dorsal and right lateral positions were compared with those calculated from the data on the fluoroscopic image by means of the above formula. The result confirmed the validity of the author's procedure, even in the case of large hearts of athletes.4. The author considered various condition, such as the position of the chest, the phase and depth of respiration, the phase of the cardiac cycle, the half shadoW, and the geometric sharpness of the fluorecent screen. The effect of the displacement of the chest to the right or the left on the breadth of the aorta was very distinct.5. The data obtained by the present method of conversion from the short distance roentgenogram can be compared with those of teleroentgenography with discrepancies not larger than 2%.6. Various convenient procedures on the above principle were also tried and suggested.

High-Intensity Radiation from Beryllium-Window X-Ray Tubes

The low atomic number and low density of beryllium give it the lowest absorption coefficient of any material which might, by virtue of other suitable physical characteristics, be employed for windows in x-ray tubes. The first use of beryllium plates for such a purpose appears to have been in Germany, and shortly thereafter in this country, in the early 1930's, when they were used, not as windows in the external envelope of the tube, but in an internal hood surrounding the target, the purpose of which was to prevent the bombardment of the tube walls by secondary electrons. Beryllium windows permit such hoods to shield completely against electrons while absorbing the x-ray beam to a negligible extent. There is, of course, no requirement that such windows be vacuum-tight, as is the case in the external envelope. The development of malleable beryllium (1) and the production therefrom of thin vacuum-tight sheets led to the first commercially produced tubes with vacuum-tight beryllium windows in the external envelope, as reported by Machlett (2) in 1942. These tubes were designed primarily for x-ray diffraction work, having targets of special materials, such as molybdenum, cobalt, copper, iron, or chromium. The beryllium window was sought for such tubes in order to reduce to a minimum the loss of intensity due to absorption in the window of the characteristic radiation of the target material, which is of relatively long wave length, particularly in the case of the lower atomic number materials like cobalt, iron, and chromium. In these and other tubes (3) designed primarily for diffraction studies, the window may be quite small, since only a narrow pencil of rays is employed. The advantages of this low-absorption window for other applications were soon recognized, and these so-called “diffraction tubes” were used advantageously in such special radiographic procedures as microradiography (4, 5) and the checking of spot-welds of thin aluminum sheets. In some of these applications, a wider beam had to be employed to cover larger areas than was possible with the diffraction tubes, and a larger window was therefore required. As the size is increased, the difficulties involved in the fabrication of vacuum-tight beryllium windows increase many-fold, particularly in the operation of brazing the windows in a permanently vacuum-tight manner to a suitable base for incorporation into the tube envelope. Nevertheless, the necessary technics have been perfected, and tubes with beryllium windows admitting a 40-degree solid angle cone of rays (Fig. 1) have now been available for some time (6). As indicated above, such tubes were first developed to meet the needs of certain special radiographic applications, arising principally in connection with the war effort. It is natural to inquire whether they offer possibilities for advantageous use in the medical field, as well as in other industrial applications.

The Evolution of an Improved Transvaginal Speculum

Anyone who tries to add anything to the solution of the many problems met in the direct application of x-rays to cancer of the uterine cervix (1) must first acknowledge his indebtedness to E. A. Merritt. In 1920 (2) he treated cervical cancer, with rather spectacular results, using unfiltered x-rays through a glass speculum. The technical difficulties were tremendous. Because of the dangers of electrical shock and of accidental overexposure of the vulva, the tedium and discomfort of the treatments, and the impossibility of maintaining the lesion, the speculum, and the tube in fixed relationship, he had to abandon his efforts until high-powered, shock-proof apparatus became available. He then (3) began to apply x-rays to the cervix, and the tissues around it, through a speculum of the Ferguson type made of material transparent to the rays. He introduces the specula with the aid of obturators, and protects the vulva by a ring of opaque metal. The expanding beam of x-rays strikes the inner portion of the vagina and exposes a field surrounding the cervix which is much larger than can possibly be irradiated through opaque cylindrical specula. The dose to the vaginal wall increases as one nears the tube, according to the inverse-square law, but on the other hand, because of back-scatter, the intensity at the edge of a small field is about 30 per cent less than it is at the center. It is obvious, therefore, that the vaginal walls can be exposed for a distance from the cervix equivalent to one-fifth of the total anode-surface distance, without increasing the effective dose to the vaginal wall. My own approach to the problem (4, 5) has been along different lines because of my obsession with the belief that a short (25 to 30 cm.) anode-surface distance should be used. There are three reasons for this belief: 1. As shown in Figure 1, the beam expands much more rapidly. 2. The time of the treatments, which at best are uncomfortable, is considerably shortened. 3. There is less danger of overexposing the rectum. In order to use a short anode-surface distance, it is necessary to find some method of retracting a considerable portion of the vaginal wall. This I tried to do in 1937 with the eight-bladed expanding speculum shown in Figures 2 and 3. The blades of this instrument were 9 cm. long and the diameter of the opening at the introitus was 26 mm. The cone of rays exposed a field 4.5 cm. in diameter. Using 200 kv. and an effective filter of 0.75 mm. copper, and an anode-surface distance of 28 cm., an excellent distribution was obtained. It is shown graphically in Figure 4. It is interesting to compare this with the distribution obtained with the Chaoul technic and with radium. Mayneord (6), discussing rays from the Chaoul tube, says: “We may imitate fairly exactly the radium depth doses.”

On optical pyrometry

The most convenient and accurate instrument for the measurement of high temperatures is undoubtedly the disappearing filament pyrometer. During some work on the vaporisation of palladium and nickel, Mr. C. W. Gibby and one of the present authors had occasion, some years ago, to design a modification of this pyrometer, so as to magnify small filaments of these metals, which were heated to incandescence electrically. Recently, having undertaken investigation of the carbon are at high pressures, the methods of pyrometry then used have been extended, with the object of diminishing some of the difficulties connected with optical phrometry. The first difficulty is that the readings of the oridinary opticl pyrometer are not independent of the distance, when sighted on a small source, such as a filament, for the reason that the cone of rays from the source does not fill the exit aperture completely. It is therefore essential to magnify the source of light. It is unnecessary to describe here the magnifying pyrometer which was constructed, because the design of the optical part of the instrument is similar to that detailed by Fair child and Hoover, and the position of the diaphragms and lenses for good definition agreed with those specified by those authors, although arrived at independently of their recommendations. Provision was made for two different magnifications by removal of the front component of the objective lens, the latter being at a fixed distance (35 cm.) from the lamp. When investigation the temperature distribution over a small source, it is very convenient to be able to suit the magnification to the size of the object or the bounds of the working distance. The working distance for the higher magnification (X 20) was 20 cm., and with the front combination removed about 45 cm. As a precision instrument, the magnifying pyrometer has advantage over an ordinary optical pyrometer, because it can be sighted on a source which, being smaller, is more easily maintained at a uniform and constant temperature.

Consideration of Body Dose in Radiation Therapy

In modem radiation therapy, we usually designate the treatment, by the dose per unit volume of the tissue we wish to radiate (relative to the per cent of erythema skin dose viz e). It is evident that a certain dose of this kind can be given in a number of different ways. The amount of radiation absorbed by the entire body or total body dose is however dependent upon what “fields” we choose for reaching the desired “tumor dose” and the general reaction of the patient. For instance, the change in the blood picture has more to do with the “total body dose” than with the “tumor dose.” We therefore consider it important to keep record of the “total body dose” as well as of the “tumor dose.” The question arises how the unit for the body dose ought to be defined and how the total dose ought to be figured. Wintz has recently published an article1 in which he calls attention to the importance of the body dose. He uses a certain unit “a.” The unit we have been using for some time is approximately 100 times smaller. I have designated it Ax and have defined it in the following way. The X -ray tube is excited by 200 kv. (measured with sphere-gap) alternating 60 cycle current with double way rectification and the rays filtered through 0.5 mm. copper and 5 mm. wood. If an erythema dose is given on the skin of a 10 × 10 cm. field then 100 Ax will be absorbed by the first 5 cm. of tissue presupposing that it is surrounded in all directions by tissue so that a very small part of the scattered radiation is lost laterally. A variation in the distance between the target and the skin does not influence the “body dose” enough to be considered as long as the whole ray cone passes entirely through the tissue. The absorption by different layers of tissue is given in Table 1.

ROENTGEN RAY INTOXICATION

X-rays which injure intestinal epithelium (and presumably other body or tumor cells) travel in straight lines from the target through the living tissues, forming a cone or beam of rays as controlled by impervious screens. It is probable that secondary radiation is formed, especially deep in the body tissues, but such radiation does no injury to intestinal epithelium outside of the cone or path of radiation. Lesions in the stomach and intestine may be confidently predicted from a knowledge of the size and form of the cone or beam of x-rays given over the abdomen. These lesions even more than skin burns do not heal and may in fact go on after many weeks to perforation. Even in the depths of the abdomen the duodenal lesions are as clean-cut as a peptic ulcer, indicating the lack of dispersion or scattering of the primary or secondary rays in passage through the living tissues. Transition from normal to necrotic mucosa rarely occupies more than 2 to 3 mm. and often can be observed in a single low power microscopic field.

Thermal Qpalescence in Crystals and the Colour of Ice in Glaciers

IN a previous communication to NATURE (vol. 109, page 42) it was pointed out that the thermal agitation of the atoms in crystals causes optical heterogeneity which should give rise to a noticeable scattering when a beam of light is sent through the substance, and that this effect may actually be observed with suitable arrangements in clear quartz or rock-salt. I have recently found that the same phenomenon is conspicuously exhibited by ice. If a block of clear ice, free from air-bubbles, striae, or other obvious inclusions, and having flat sides, be held squarely and a narrow pencil of sunlight concentrated by a lens be passed through it, the track of the pencil shows a beautiful blue opalescence. It is advisable not to use a very highly-condensed cone of rays, as this would cause internal melting of the ice with formation of cavities which reflect white light and distract the eye. A dark background should be provided against which the track may be viewed. With small or irregular lumps of ice, the observation may easily be made by immersing the ice in clear distilled water contained in a glass flask which is painted black outside, windows being provided for ingress and egress of light and for observation of the opalescent track. Even with ice which at first looks unpromising owing to internal flaws or inclusions, portions in which the blue opalescence is not overpowered by disturbing effects may be picked out. A suitable orientation of the block with reference to the direction of the incident rays is often useful in avoiding reflections from cavities in the ice.

Are Eyes ever Autophanous?

I VENTURE to suggest the following simple explanation of the phenomenon described by Colonel Herschel in NATURE of January 18. At the distance at which his experiments were made the light from the lantern or other source enters the lens practically as a pencil of parallel rays, which is concentrated as a bright spot on the retina. The divergent light from this bright spot, which passes backwards through the lens, is again made into an almost parallel pencil. If the retina is exactly in the focal plane of the source of light, and the image an absolutely sharp one, the whole of the light is again concentrated on to the bull's-eye of the lantern, and without the use of a transparent, but partially reflecting, surface, it must be impossible to see it. But the least blurring of the image, from whatever cause, leads to a slightly divergent pencil, which, however, is still narrow enough to concentrate the returning light within a degree or so from the direction of the original source. To an observer within this cone of rays the bright spot on the retina will appear to fill a part or the whole of the pupil, just as a black dot may be made to fill the whole aperture of a lens to an observer at a distance by holding the lens at its focal distance from the point in question.

On the α Rays from Radium B

A RECENT number of the Physikalische Zeitschrift (x., 46, 1909) contains an article, by Frederic A. Harvey, in which he states that radium B gives out α particles, the ionisation range of which in air lies between 2.6 mm. and 3.0 mm. In investigating these short-range α particles he used a modification of the method employed by Bragg and Kleeman (Phil. Mag., x., 318, 1905), but on account of the limited range of the radiation he did not use a cone of rays.

On an Optical Proof of the Existence of Suspended Matter in Flames

Dear Professor Tait,-—I write to put on paper an account of the observation I mentioned to you to-night, in case you should think it worth communicating to the Royal Society of Edinburgh.In the course of last summer I was led, in connection with some questions about lighthouses, to pass a beam of sunlight, condensed by a lens, through the flame of a candle. I noticed that where the cone of rays cut the luminous envelope there were two patches of light brighter than the general flame, which were evidently due to sunlight scattered by matter in the envelope which was in a state of suspension.

Our Astronomical Column

MOTION OF STARS IN THE LINE OF SIGHT.—Prof. H. C. Vogel, in Monthly Notices R.A.S. for December 1891, fully describes the method used at Potsdam for determining the velocity of stars in the line of sight, and states the chief results that have been obtained since the work was begun in 1887. In order to insure great stability with the smallest possible weight, the frame of the spectroscope is made of cast steel. The camera is also constructed of steel, and the dark slides are of brass. It may be worth remarking, however, in this connection, that stability would have been secured if aluminium had been used instead of steel and brass, and this with a little more than one-third the weight. A spectroscope similar to Prof. Vogel's, but with an aluminium frame, has been made for the Observatory at Kensington, and gives every satisfaction. The comparison spectrum used at Potsdam has been furnished by a Geissler tube placed directly in the cone of rays of the refractor, at a distance of 40 cm. from the slit, the tube being at right angles to the optical axis of the refractor and the slit. The slit is set parallel to the line of the diurnal motion, and width is given to the spectrum by making the driving-clock move slightly slower or faster than its proper rate. A uniform exposure of one hour has been employed, the proper intensity being obtained by changing the rate of the driving-clock, so that the error increases with increase of brightness. The photographs are measured with the aid of a microscope having a sliding apparatus on its table, movable by a fine micrometer screw. One revolution of the screw corresponds to a difference of wave-length of 0˙324 μμ, which, expressed in miles per second, is 139˙13. After describing the methods of measuring the displacement of lines in stars of different types of spectra, Prof. Vogel brings together the results which have formed the subject of several previous communications. It is said that the probable error in the determination of the radial velocity of a star of Class II. is ± 1˙34 miles per second, and for stars of Class 1., ±2˙31 miles. Measurements have been made independently by Prof. Vogel and Dr. Scheiner, and each star has been observed on the average 3˙3 times, wherefore it is concluded “that the probable error of the definitive values for both spectral classes will amount to less than one mile.” A list of the observed velocities of forty-seven stars will soon be published. The mean motion in the line of sight is 10˙6 English miles per second; six stars have a velocity less than 2 miles per second and five greater than 20 miles, α Tauri heads the list with a velocity of about + 36 miles per second. Fifteen of the stars have a positive, and thirty-two a negative motion.

XXI. Researches in circular solar spectra, applied to test residuary aberration in microscopes and telescopes, and the construction of a compensating eyepiece, being a sequel to the paper on a searcher for aplanatic images

The researches detailed in the present paper were commenced in May 1871. The results arrived at were largely obtained from using the microscope. Similar but less brilliant and more scanty appearances can be obtained with the telescope; but the very high power and ready adaptability of the former confers some advantages not offered by the latter. In both, however, the same principles are illustrated. A cone of rays of small angular aperture having the object-glass for its base in each case engages the eyepiece and emerges parallel, and the eyepieces are similar in each.