Fitting Geomagnetic Fields before the Invention of Least Squares: II. William Whiston's Isoclinic Maps of Southern England (1719 and 1721)

The English mathematical practitioner and theologian William Whiston (1667-1752) made the first known maps showing the direction of magnetic inclination (for south-eastern England) in 1719 and 1720. He also anticipated Graham's 1723 measurement of the ratio of horizontal and vertical magnetic intensities, and he understood their relationship to magnetic inclination. Whiston's work is examined to determine how he fitted the planar isoclinic surfaces. This is of interest because his study precedes the publication of 'Meyer's method' by thirty-one years and the Legendre-Gauss 'method of least squares' by eighty-six years. It is suggested that Whiston fitted the surfaces using observations of inclination at a chosen triplet of localities; and that he did this in order to use data from non-included localities as a check on his model. Best fits to his maps are given by inclinations based on Salisbury, Wiltshire, London, and Ainho [Aynho], Northamptonshire, in 1719, and on Wanstead, Essex, Ainho, and Saltfleet, Lincolnshire, in 1720. However, in both cases, the orientation of the isolines appears to be inconsistent with roughly contemporary data from Europe and Scandinavia, as well as a hindcast of the geomagnetic field in 1720, based on the modern Bloxham-Jackson global, time-dependent, spherical harmonic model.