This paper gives dispersion curves derived from the Appleton-Hartree formula in the case of zero absorption. The value of the magnetic field is taken as that of the earth's field at Slough. The curves are drawn to show the value of the squares of the indices of refraction and attenuation as functions of the electron density for a series of twelve frequencies, which are chosen to illustrate the various classes of curve and the boundary curves separating the classes and, in the case of frequencies above 1.321 megacycles per second, the various regions of short and ultra-short waves. The derivation and general properties of the Appleton-Hartree formula and the various possible modes of propagation are also discussed. The dispersion curves are classified according to the infinities they contain and a diagram is given to show how the classes of curve holding for any angle of inclination of the direction of propagation to the magnetic field H depend on the ratio of the longitudinal component of H to H itself. The use of the zeros and infinities of the dispersion curves in the interpretation of propagation phenomena is described and a summarising diagram is given, showing how the possible propagation of zero, one or two basic modes for any frequency depends on the electron density. The polarisation corresponding to each dispersion curve is shown graphically and the general properties of the polarisations of the basic propagation modes are discussed.

The author's interim report of progress in her heroic investigation of the theory of propagation of electromagnetic waves in an ionised medium under an external magnetic field is timely and valuable. I was, some years ago, so strongly impressed by the need for such a general investigation and by the formidable difficulties of bringing together adequate mathematical and physical skill and adequate computing facilities for bringing the problem to numerical solution that I suggested to the Radio Research Board that the work should be taken up at Slough, where close contact with experimental work would be a valuable guide to the mathematical investigator.

The results now presented ... are of a kind required by all investigators concerned with the mechanism of return of wireless waves from the ionosphere, and this paper will stand as a source from which initial data for new investigations can be obtained without duplication of effort.

All experimental workers in the field of ionospheric investigations will welcome Dr Taylor's exhaustive representation of illustrative magneto-ionic dispersion curves. It is only by having the theory so fully worked out for us at the first stage that we are able to make the next step and consider the effects of collisional friction in differentiating between the attenuation experiences of the ordinary and extraordinary rays in their ionospheric journeys.

This work was carried out at the Radio Research Station, Slough, as part of the programme of the Radio Research Board of the Department of Scientific and Industrial Research, and is published by permission of the Board. Thanks are due to Mr R A Watson Watt, Superintendent of the Station, for his interest in the work and for the provision of facilities for conducting it; to Prof E V Appleton and Prof D R Hartree for valuable discussion, and suggestions as to the presentation of the paper; to Dr L J Comrie, for advice on the arrangement of the calculations; to Miss A C Stickland for assistance in the calculations and to Mr E C Slow for help in drawing the curves.

I do not think it is possible to over-estimate the usefulness of the author's elucidation of the magneto-ionic formula to experimental workers in this field. The wave-lengths chosen for the graphical illustration are most suitable and illustrate the variety of phenomena we are to expect.

Ernest Clive Slow: Clive started his working life in the shadow of the Portsmouth Dockyard, following his father as an apprentice engineer there. He set about educating himself and was rewarded with a London B.Sc. (external) and then found his first job at the Slough Radio Research Station, where his work with Watson-Watt and Wilkins drew him into the radar story, and provided him with a wife, Dr Mary Taylor, a brilliant mathematician. She it was who had done most of the calculations for Watson-Watt and Wilkins when he was presenting his evidence about 'Death Rays' and the possibility of aircraft detection to the Tizard Committee. When they married, under Civil Service Rules, she had to resign her post, losing for the Scientific Civil Service one of its most outstanding mathematicians. Clive was seconded to Bawdsey Research Station, and from thence he went to ADEE at Christchurch at the outbreak of war. He remained with the Establishment on its subsequent move to Malvern. During his time at Christchurch, he did most of the design work, including the aerial system for the Army GL2 equipment and saw it into production at EMI (aerials and display system) and Metro Vickers (Transmitter). At Malvern, he oversaw the development of a 25cm radar for close control of the Bofors gun.

Dr Mary Taylor, a brilliant mathematician. She it was who had done most of the calculations for Watson Watt and Wilkins when he was presenting his evidence about 'Death Rays' and the possibility of aircraft detection. When she married Slow, under Civil Service Rules, she had to resign her post, losing the Scientific Civil Service one of its most outstanding mathematicians.