The Phase stable at Higher Temperatures.

According to Petrenko there should be a phase present in the range 15-35 atomic per cent. Al, stable only at higher temperatures. The following observations have confirmed the correctness of this statement.

When specimens of alloys having the said composition were polished and electrolytically etched with nitric acid, a macroscopically visible granular structure was revealed. The size of the grains amounted to several millimetres. X-ray photograms obtained by reflexions against these surfaces showed, however, no single spots, as might have been expected, but continuous lines of a somewhat diffuse appearance, which is a proof that the large grains had been broken up into a very fine structure by some transformation

in the solid state.

There are reasons for believing that the phase stable at higher temperatures has a structure analogous to the B-phase of the Cu-Zu-, Ag-Zn-, Au-Zn-, Cu-Al- and Cu-Snsystems, i. e. a body-centred cubic lattice; but to settle this it must be investigated in a camera designed specially for high temperature work. Attempts to obtain the phase at the ordinary temperature by quenching heated specimens failed.

Summary.

1. An X-ray analysis of the Ag-Al-system has confirmed the statement of Petrenko that it has two intermediate phases at ordinary temperature, both formed through transformation in the solid state.

2. As Petrenko also found, one of them is Ag Al. It is cubic, having an elementary cube with an edge of 6·920 Å., containing 20 atoms. It is isomorphous with B-manganese.

3. The other intermediate phase, which is homogeneous in a range from 27 to 40 atomic per cent. aluminium, is a solid solution of close-packed hexagonal structure. Its lattice dimensions change continuously from a1 = 2.865 A., a3=4·653 Å., and ag/a1=1·625 when saturated with silver to a1=2·879 Å., az=4·573 Å., and az/a1=1·588 when satu

rated with aluminium.

One of the authors is indebted to the Royal Commissioners for the Exhibition of 1851, for a Senior Studentship which enabled him to undertake this investigation, which was carried out at the Metallographic Institute, Stockholm.

Westgren and Phragmén, loc. cit. p. 3.

XXVII. Radio Transmission Formula. By G. W. KENRICK, Sc.D., Moore School of Electrical Engineering, University of Pennsylvania, Pa., U.S.A.*

E

ARLY studies of the problem of the propagation of electric waves over the surface of the earth considered the problem to be that of determining the field at any point on the surface of an isolated conducting sphere due to an oscillating doublet located at a given point P on its surface †. While these investigations were valuable contributions to theoretical optics, they led to a transmission formula giving an attenuation much greater than that experimentally

observed.

The explanation of the departure is, of course, to be found in the important role played by the conductivity of the Kennelly-Heaviside layer.

Much successful work has recently been carried out with a view to explaining the phenomena of short-wave transmission by means of a study of the reflexion and refraction of electric waves by ions and electrons in a magnetic field, but less attention has been given to modifications produced in the classical Hertzian solution for the field at a distant point due to an oscillating doublet when multiple-order reflexions are considered.

G. N. Watson first attacked this problem in 1919 ‡, and obtained a solution for two concentric spherical shells of finite conductivity and sharply-defined boundaries. Dr. Watson's method of attack involved the setting down. of Maxwell's equations and an investigation of their solution in terms of series expansions involving spherical or zonal harmonics.

While admirable from the point of view of the mathematician, the method of Watson was too involved to adapt itself to extension to the consideration of the gradually varying conductivity of the upper atmosphere and other related problems of considerable importance in short-wave transmission. For this reason, perhaps, the work of Watson is not frequently referred to by engineers and physicists

* Communicated by Dr. Balth van der Pol.

H. M. MacDonald, Proc. Roy. Soc. lxxii. pp. 59-68 (1903); xc. pp. 50-61 (1914). G. N. Watson, Proc. Roy. Soc. A, xcv. pp. 83-99 (1918-19). J. W. Nicholson, Phil. Mag. xx. p. 172 (1910). B. van der Pol, Phil. Mag. xxxviii. p. 365 (1919). O. Laporte, Ann. d. Phys. lxx. p. 595 (1923).

IG. N. Watson, Proc. Roy. Soc. xcv. pp. 546-563 (1919). Phil. Mag. S. 7. Vol. 6. No. 35. August 1928.

U

working in this field, who have adopted the optical point of view of directly-transmitted and singly- or multiply-reflected or refracted rays in their further studies of this problem.

A modification in the coefficient of the exponential in Austin's formula, suggested by Watson's analysis, has also apparently escaped attention, due, perhaps, to the fact that it is implicitly contained in Watson's expression for the Hertzian function rather than explicitly set down in an expression for the field.

Watson's formula involved physical hypotheses which while far from accurate in the general case, are nevertheless probably adequate to the treatment of long-wave communication, from which Austin's formula was originally derived. It is of interest to note that the results obtained by Watson may also be obtained with slight approximation by an application of the optical point of view of reflected

rays.

It will be the purpose of this paper to derive such an expression for the field between two concentric conducting spheres by a direct summation of the reflected waves, and to consider the application of the formula thus derived to the problem of long-distance radio communication.

1. Review of Classical Solution for the Oscillating Doublet.

The classical problem of determining the field at a point P due to an electronic charge e vibrating at the origin, with an electric moment A sin wt (see fig. 1), gives for the electric and magnetic field intensities at the point P*

It is not unusual, although not strictly rigorous, to apply

this theory to the case of a radio antenna †. Admitting this

G. W. Pierce, Electric Oscillations and Electric Waves,' p. 432 t seq. (McGraw Hill, 1920).

+ Pierce's computations of radiation resistance for flat-topped loaded antennæ make it possible to correct the results computed on the oscillating doublet theory if such a correction is desired in a particular case. (See text-reference above.)

approximation, we evaluate the constant A in terms of the antenna constants.

Thus we may write, where i is the antenna current in absolute electrostatic units, 2 the length of the doublet, e the electronic charge (2le=A),

If I represents the maximum amplitude of i, we may write 271=Aw, and hence (with appropriate choice of the

axis of t)

By the elementary theory of electrostatic images, the field is unaltered by the introduction of a perfectly conducting

π

plane in the horizontal plane = (see fig. 1). The

2

solution given in equation (6) is therefore the solution for