A note on diurnal phase changes of very-low-frequency waves for long paths

It is now well known that the phase of a VLF carrier, observed at long distances, exhibits a regular variation throughout the day [Pierce, 1955, 1957; Allan et al., 1956; Crombie et al., 1958]. Although the pattern is changed during solar or magnetic disturbances (A. G. Jean, private communications, and many unpublished VLF phase data), it is of considerable importance to predict the regular diurnal change for a given path. Some important work in this direction has been carried out recenfiy by a group at the Royal Aircraft Establishment in Farnborough [Blackband, 1962].