Radio waves in the ionosphere was first published in 1961. Since then there have been many major advances that affect the study of radio propagation, and three in particular. The first is the use of space vehicles and rockets, which have enabled the top side of the ionosphere to be studied and have revealed the earth's magnetosphere and magnetotail. The second is the advance of the subject ‘plasma physics’ which has transformed our knowledge of the physical processes in ion plasmas. The third is the use of computers, large and small, which, by removing the need for laborious calculations, have changed our attitude to theoretical results, even though they are sometimes wrongly used as a substitute for clear physical thinking. Moreover some important textbooks have appeared in the intervening 20 years. They are too numerous all to be mentioned, but four have a special bearing on the subjects of this book. These are: T.H. Stix (1962), Theory of plasma waves; K. Rawer and K. Suchy (1967), Radio observations of the ionosphere; K. Davies (1969), Ionospheric radio waves; and V.L. Ginzburg (1970), Propagation of electromagnetic waves in plasma.

Some of the topics mentioned in Radio waves in the ionosphere, here abbreviated to RWI, are of importance in other branches of physics. Two in particular have formed the subject of numerous mathematical papers. These are (a) ‘W.K.B. solutions’, and (b) the study of ordinary linear homogeneous differential equations of the second order.