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Volume 18, Issue 7, 01 July 1947
18(1947); http://dx.doi.org/10.1063/1.1697813View Description Hide Description
Silver iodide particles have been found to serve as nuclei for the formation of ice crystals in super‐cooled water and in water vapor super‐saturated with respect to ice. It is believed that silver iodide serves as a very effective nucleus because it very closely resembles ice in crystal structure. Both dimensions of the unit cell of ice and silver iodide are the same to within approximately one percent. The maximum temperature at which the silver iodide particles serve as nuclei is approximately −4°C for particles one micron in diameter, and −8°C for particles 100 Angstrom units in diameter. A silver iodide smoke generator has been constructed which consumes 1 mg of silver iodide per second and produces 1013 effective nuclei per second.
18(1947); http://dx.doi.org/10.1063/1.1697814View Description Hide Description
An equation for waves in elastic tubes is developed and applied to cylindrical tubes with Hookian and with elastomeric walls. The former application yields the Moens‐Korteweg formula, which has been found inadequate. The latter application leads to a rather complicated equation for the pulse‐wave velocity.
Values of pulse‐wave velocities are computed for the thoracic aorta by means of the foregoing equation, and the results are compared with measured mean velocities for the entire aorta. Graphs and tables are given, so that a graphical analysis of this velocityequation can be applied to any large artery; and the method is illustrated by computing the pulse‐wave velocity in the left common carotid. The relation , for the mean velocity over a tube of length l, is shown to be valid for the aorta and large arteries.
18(1947); http://dx.doi.org/10.1063/1.1697815View Description Hide Description
An electronic synthesizer is described for determination of atomic positions in crystals. The synthesizer sums the two‐dimensional Fourier series representing planar, centro‐symmetric projections of electron densities in a crystal unit cell; and the projection is presented by a television scan on the screen of a cathode ray oscilloscope. The specific advantage of the device is the immediate observability of effects on the projection of alterations in signs of one or any number of Fourier coefficients.
18(1947); http://dx.doi.org/10.1063/1.1697816View Description Hide Description
Fixed and variable length re‐entrant resonant cavities designed for the measurement of dielectric constant and dissipation factor are described. These cavities operate in the frequency decade of 108 to 109 cycles per second, a region avoided by many experimenters because the frequency is too high for the application of circuit techniques and not high enough for the convenient use of coaxial lines or wave guides. The theoretical considerations in the design of these cavities are presented. The well‐known susceptance variation method, widely used in the frequency range of 104 to 108 cycles per second, was extended to apply to these cavities; it yields a rapid measuring technique and very simple expressions for calculating the values of the dielectric properties. The performance of this apparatus is discussed and the results of the measurements of a few typical dielectrics are given.
A Variable Capacitor for Measurements of Pressure and Mechanical Displacements; A Theoretical Analysis and Its Experimental Evaluation18(1947); http://dx.doi.org/10.1063/1.1697817View Description Hide Description
A variable capacitor is described for measuring (1) small displacements, (2) small volume changes, and (3) pressure differences. The capacitor consists of a deflectable diaphragm and a fixed electrode. The diaphragm is metallic, plane‐parallel, clamped at the edges, and at ground potential; the electrode, at an a.c. potential, has a plane surface parallel to the undeflected plate across an air gap. For use in displacement measurements, the diaphragm's center is deflected by a point contact from a mechanical link to the observed system, or by a uniform pressure load from a fluid link to the system. The fluid link is used also when measuring volume changes and pressure differences. The plate deflection results in a change in the air gap, and thus generates a capacitance signal. This signal is measured by electrical methods.
A theoretical analysis of this variable capacitor is presented; sensitivity and alinearity factors for the three uses of the device are derived. The experimental performance shows reasonably satisfactory agreement with the derived theory. The displacement of the plate's center was measured with an interferometric method, using a yellow He line as a standard of reference; the applied pressure, with a liquid manometer; and the capacitance signal, with a standard capacitor substitution procedure. The gauge can be used so as to give quantitative electrical indications of displacement, volume change, or pressure difference; or can be used as a null indicator device in which an unknown pressure is balanced against a known one on opposite sides of the diaphragm. In order to achieve large volume an displacement sensitivities, small air gaps (5.10–4 cm) are employed. Details of a construction method to assure small values are presented.
18(1947); http://dx.doi.org/10.1063/1.1697818View Description Hide Description
Methods of measuring effective conductivities at microwave frequencies are described. These consist of either measuring the transmission loss in a long waveguide, or in measuring the Q's of resonant cavities. Both methods have been applied to measurements at 1.25 cm. Results for a number of metals are presented. Deviations from d.c. conductivity are thought to be due to surface roughness.
18(1947); http://dx.doi.org/10.1063/1.1697819View Description Hide Description
In this paper are presented the approximate formulas for the components of radiation vectors of a short‐circuited circular loop with non‐uniform current distribution. The formulas are valid for the ratio of loop perimeter to wavelength of the order of 0.5 or less, and assume the current distribution of the hyperbolic cosine form. These formulas lead to the radiation intensity formula from which the expressions for the horizontal and vertical field patterns are derived. The latter formulas are further simplified assuming that the attenuation constant is much smaller than the phase constant. From the expression for horizontal field pattern, it follows that the pattern is symmetrical about the loop axis of symmetry. Moreover, this horizontal pattern exhibits a directional effect with maximum field in the direction of the feeder end of the loop. This directional effect is a function of loop dimensions. The theoretical horizontal pattern agrees very closely with the experimental one. From the expression for vertical field pattern, it follows that the non‐uniform current distribution produces a pattern intermediate between that for horizontal dipole and horizontal small loop with uniform current distribution. The field intensity in the zenithal direction is again a function of loop dimensions. Using the expression for radiation intensity, formulas for a radius of equivalent circular horizontal field pattern, power gain, average power gain, and radiation resistance are derived. It is shown that the average power gain is essentially a function of loop radius and decreases with the increase of the latter. Finally, the approximate expression for the attenuation constant of the transmission line equivalent to the loop is derived.
18(1947); http://dx.doi.org/10.1063/1.1697820View Description Hide Description
Dynamic shortening of one‐half inch long copper cylinders is achieved by striking them with a hardened steel projectile at high velocities. The average strain rate was about 1200 per second. Energy per unit volume absorbed by the copper is plotted against strain. A true stress‐logarithmic strain curve is computed. This curve is compared with a similar curve derived from high speed tests on copper in tension.
18(1947); http://dx.doi.org/10.1063/1.1697821View Description Hide Description
18(1947); http://dx.doi.org/10.1063/1.1697822View Description Hide Description
The Fourier transform method of determining the response of a linear system to an arbitrary input signal often has its practical usefulness impaired because of difficulties in evaluating the necessary integrals. One possibility of overcoming these difficulties lies in the application of graphical methods to the transformations. Three such graphical procedures are described, all based upon fundamental properties of the transforms. Each method involves an analysis of the curves of the function to be transformed as a sum of curves of simpler functions whose transforms are known. The methods are useful in cases where the problem is too complicated for a simple analytic solution, or where part of the necessary data is available only in the form of a curve obtained, say, from experimental measurements of transmission characteristics or wave shapes. The accuracy of the methods is restricted only by that of the graphical plotting and curve fitting. If only approximate results are required, they may be obtained relatively quickly by these methods.
18(1947); http://dx.doi.org/10.1063/1.1697823View Description Hide Description
The calculation of structure factors in x‐ray structure analysis is one of the most laborious operations. Two mechanisms are described which have proved of great service in several analyses. The simpler of the devices is of general application and can be constructed with comparatively limited workshop facilities.
18(1947); http://dx.doi.org/10.1063/1.1697824View Description Hide Description
In this paper a method is developed for determining the electromagnetic field produced by a microwaveantenna at points on the horizon, and on either side of it, where neither the ray theory nor the normal mode theory can be used conveniently. The theory is developed for a condition of standard atmospheric refraction, by use of a space in which the earth is flattened and the rays are curved. This allows us to make a simple derivation of the ray theory, valid in the optical region, and of the normal mode theory, suited for the shadow zone. For the intermediate region centered around the horizon we use the original integral for the potential to obtain expressions for the field under the restriction of maximum absorption, which for typical ground conditions applies to wave‐lengths less than about a meter. Three cases are treated in which the transmitter, or receiver, are either situated on the ground or are elevated several natural units of height. For an elevated transmitter and receiver the Hertzian potential ψ due to a point source at the origin is in the vicinity of the horizon given by,with,where x denotes the horizontal distance r expressed in natural units, z 1 and z 2 the heights of transmitter and receiver in natural units, r̄ the distance of receiver from transmitter when the former is on the horizon. F(p) (see Eq. (68) below) has been evaluated, and is given in Table IV, while the integral in (A) can be expressed in terms of the tabulated Fresnel integrals. In the limit of very short wave‐lengths the field on the horizon approaches the value 1/(2r̄) which would result from the diffraction of the direct ray only by a straight edge placed at the point of tangency of the horizon with the earth. A comparison of the field obtained from (A) with exact values computed by van d. Pol and Bremmer, using the ray theory and the normal mode theory, is shown in Figs. 6 and 7.
When the transmitter is at zero elevation and the receiver is elevated several units of height, the potential in the vicinity of the horizon is given by,for vertical polarization and horizontal polarization, respectively. Here ε1 denotes the complex dielectric constant,ac the effective radius of the earth, and λ the wave‐length. G(p) is given in Eq. (78) and is shown in Fig. 4. A comparison of (B) with exact values obtained by van d. Pol and Bremmer is shown in Fig. 8.
When both the transmitter and receiver are at zero elevation, it is found that the potential can be expressed as the sum of the surface wave appropriate for a flat ground and an integral depending on the radius of the earth. At great distances, the two terms tend to cancel out. Under conditions of maximum absorption this leads to,.H(p′) is given in (84) and g(p′) is shown in Fig. 5, where it is compared with results obtained previously by van d. Pol and Bremmer using the normal mode theory.
For points on the horizon Eq. (A) reduces to,while in (B) and (C) we put |G(0)| = 2.13.
- LETTERS TO THE EDITOR
18(1947); http://dx.doi.org/10.1063/1.1697826View Description Hide Description