Table of contents

The purpose of the enquiry, of which this paper forms the first part, is to show to what extent the working principles of electromagnetism can be soundly based on real experimental facts - that is to say, on experiments that have actually been performed, as distinct from the imaginary experiments, which are common to most expositions of the subject, but which are either quite impracticable or incapable of being performed with an accuracy that would be regarded as significant to-day. By maintaining this sharp distinction between fact and theory we aim at removing from the subject much of the confusion which, as the literature shows, is a continual source of trouble.

This section begins with an outline of the general principles of measurement. Current, resistance, conductance and voltage are then established independently of a knowledge of any other magnitudes. Ohm's Law and the conception of e.m.f. follow. An examination of the relations between these magnitudes and the geometrical and mechanical magnitudes then leads to theoretical conceptions like potential, and to a consideration of the status of Ampère's two laws. That for the force between two circuits is well established and defines the unit of current. That for the torque on a compass needle near a circuit is less well established; but it leads to the recognition of H in a non-magnetic medium as a defined magnitude, whose significance is found to be independent of the existence of magnets.

A discussion is given of the various factors affecting the intensity and sharpness of the multiple-beam Fizeau fringes and fringes of equal chromatic order used for the study of surface topography The effects of absorption in the silver film, phase condition, linear displacement of the beams, finite size of source, departure from parallelism and source line width are considered. It is shown that Fabry-Perot fringes, multiple-beam Fizeau fringes and fringes of equal chromatic order have all the same fringe shape if certain conditions are fulfilled.

The use of effective "centres" and "radii" of curvature permits the well-known formulae relating the tangential and sagittal centres of curvature of a wavefront element before and after refraction to be put into a form which yields formulae and computing schemes identical with those customarily used for computing the paraxial focus, magnification, and equivalent focal length. Simple expressions follow for the T- and S-magnifications and oblique equivalent focal lengths.

After being in use for a few months, the computing schemes have now been adopted as standard calculations.

The theoretical relation between the lattice strains produced by precipitation in a metal and the corresponding increase in hardness is extended to the case of lattice strains in metallic solid solutions. The elastic limit of a single crystal of a solid solution is calculated on the assumption that the crystal will slip when the applied external stress is equal to the mean value of the internal stress. This mean is taken over the length of a dislocation, assumed to be 1000 atoms. The estimate agrees in order of magnitude with the experimental observations. Similar considerations are applied to the hardness. of polycrystalline solid solutions. The theory is extended to cases in which the increase of hardness produced by alloying is not large in comparison with the hardness of the pure solvent.

Two networks are said to be dual to each other if the following correspondence exists between them: -

1. Each element of one network has a counterpart in the other one.

2. The currents through the elements in one network and the voltages across their counterparts in the other network are proportional to each other.

A network dual to a given one is usually constructed by connecting elements of the appropriate kind in a circuit the diagram of which forms the topological counterpart to the diagram of the original circuit. If this original circuit is a "non-planar" one (i.e. if it cannot be drawn without crossings between some of its branches), then there exists no topological dual, and for this reason it has been said that there exists no dual to a non-planar electrical network. However, if we are interested in an electrical network not because its circuit diagram has certain geometrical properties, but because it constitutes an assembly of a number of passive and active elements which perform in a certain manner (on account of their impedance properties and of certain relations of mutual constraint imposed by Kirchhoff's mesh and junction relations), then there is really no restriction of this kind.

We need only convert the original network into another with the same elements and the same performance, but with a planar circuit diagram and with additional constraints implemented by ideal transformers. This equivalent network can be then converted into its dual counterpart, which is another planar network subject to the dual counterparts of the transformer constraints of the first case. In this way we arrive at an assembly which performs in the required dual manner.

Introducing thus the concept of physical duality as opposed to geometrical duality, the paper explains in an elementary manner a number of ways in which this conversion into equivalent planar networks can be achieved. These methods are: -

1. A method originally published by Julia.

2. The dual counterpart of this method.

3. The method of fictitious junction points (an electrical analogue to F. Schur's method of fictitious junction points in pin-jointed frameworks).

4. The method of the transferred terminal.

5. The general method of separation.

Some of these methods require a smaller number of ideal transformers than Julia's original method.

The paper ends with a short discussion of the errors introduced when the dual network is set up on a network analyser and when the ideal transformers have to be replaced by real ones; the numerous methods available for the realization of an equivalent network enable a choice to be made so as to minimize these errors, or possibly eliminate them altogether.

The existence of a dual to a non-planar network is of some interest in connection with electro-mechanical analogies as it removes a restriction to which the "direct" analogy would otherwise be subjected.

A coordination rule of discrete molecular energy terms cannot be deduced from the non-crossing of the energy eigenvalue curves of the two-centre model. Clear distinction is to be made between the potential curves of unperturbed electronic states and the energy eigenvalue curves of the two-centre problem, the approximate existence of potential curves being the consequence of the averageability of the interactions with respect to the electronic motions which can also be influenced by the motion of the nuclei.

The study of the absorption spectra of SnSe and of SnTe (Walker, Straley and Smith, Phys. Rev.53, 140 (1938); Barrow and Vago, Proc. Phys. Soc.56, 78 (1944)) has been extended to cover the ultra-violet region down to 2100 A. New systems of both molecules have been analysed vibrationally. The results, including those derived from the d-x systems already known, are summarized in the following table:

Molecule	State	νe	ωe	xeωe	yeωe	D (eV.)
SnSe	F	(47850)	(290)	-	-	-
	E	30738.9	196.6	-0.77	-0.0016	0.7
	D	27549.6	225.1	-0.69	-	1.1
	X	0	331.2	-0.736	-	4.5
SnTe	G	(47260)	(230)	-	-	-
	F	44033.5	229.7	-1.25	-0.003	-
	E	(28000)	(150)	-	-	0.6
	D	25444.3	179.1	-0.40	-	0.9
	X	0	259.5	-0.50	-	4.1

An account is given of quantitative measurements of the echo obtained from the sea surface with radars operating at wave-lengths of 1.25, 3 and 10 cm under various weather conditions from calm to very rough. The necessary theoretical treatment is given, and a function f(θ), called the scattering coefficient of the surface, is defined.

Griffith's theory of rupture of brittle materials is extended to materials containing circular cracks. It is found that (a) the tensile strength of brittle material in one direction is not affected by stresses at right angles to it, (b) the result differs from Griffith's by a factor depending on Poisson's ratio of the material and lying between 1.57 and 1 81.

The internal energy, heat content, specific heats and equilibrium constants of the normal products of combustion are expanded as power series in the density. At pressures up to 40 tons/sq. in., corresponding to densities of about 0.35 gm./c.c., only the first three terms need be kept. Thus the pressure-dependence of the thermodynamic properties can be evaluated from a knowledge of the second and third virial coefficients of the various product gases. Tables are presented based on the most recent intermolecular forces, and covering the range from 1600° K. to 4000° K. These tables have found considerable application to internal ballistics, and give "covolumes" of propellants with a systematic error of less than 5%.

A diffraction theory of the Zernike test is developed for the case where the dimensions of the light source are negligibly small, and applied to estimate the sensitiveness of the test for detecting local zones in an otherwise true mirror. The effects of varying the size of the phase-retarding disc on the appearance under test of a true mirror are considered, and the conclusion is drawn that it is these effects, rather than considerations of sensitivity, which mainly determine the upper limit to the useful size of the disc.

It has been supposed that the angle of incidence of the exposing light would influence the apparent resolving power of a photographic material. Experiments have been carried out with a resolving power test object in contact with the photographic material, using illumination at different angles of incidence. The effect is almost indiscernible until angles of 40° are reached, at which it is of the order of 5 to 10% reduction in resolving power with a medium-speed film. With fast film for aerial photography, the effect is barely observable. It is concluded that the drop in resolving power, observed in air camera negatives at points off axis, is not to any appreciable extent due to the above effect.

Corrections to 1945 Proc. Phys. Soc.57 577.

Corrections to 1946 Proc. Phys. Soc.58 481.