Haselgrove developed her equations at Cambridge University in the 1950s, as a student under Kenneth Budden, by re-applying the earlier work of William Rowan Hamilton and Hamilton's principle in geometrical opticsA. W. Conway and J. L. Synge, The Mathematical Papers of Sir William Rowan Hamilton Vol 1. Gemoetrical Optics, London, Cambridge University Press, 1931. to radio propagation in a plasma.Haselgrove, J.: 1955, Ray Theory and a New Method for Ray Tracing, London Physical Society Report of Conference on the Physics of the Ionosphere. pp. 355–364. Indeed, the application of Haselgrove's equations is often termed Hamiltonian ray tracing. Ray tracing is intrinsically an approximation that is often called geometric. It formulates as the Eikonal equation and is only applicable under certain conditions including that the plasma is slowly varying; nevertheless it has enormous practical use in radio science. Other radio propagation scientists have developed various techniques to explore radio propagation in such media, but Haselgrove's formulation has seen the most widespread application, most likely because the resulting set of differential equations readily lend themselves to numerical solution on a computer. Haselgrove herself used the Cambridge computer, EDSAC, to study ray propagation in the Earth's ionosphere in the late 1950s. Historically the best-known code applying Haselgrove's equations is the Jones-Stephenson codeJones, R. M. and Stephenson, J. J. A versatile three-dimensional ray tracing computer program for radio waves in the ionosphere, U. S. Department of Commerce, OT Report 75-76, 1975. which was developed in the 1970s and may be found at the US Department of Commerce website.
