Fitting Geomagnetic Fields before the Invention of Least Squares: I. Henry Bond's Predictions (1636, 1668) of the Change in Magnetic Declination in London

The London mathematical practitioner Henry Bond (c. 1600-78) correctly forecast in The Sea-Mans Kalendar for 1636 [?1638] that the then easterly magnetic declination in London would become zero in 1657 and would then increase westerly for 'at least 30 years'. In 1668, he published a table of predicted changes in annual declination for the years 1668-1716. Despite a detailed examination (in the 1670s) of his later claim to be able to determine longitude using a dip needle, the basis for his earlier forecasts was not examined and Bond himself appears never to have fully revealed his methods. It is demonstrated that Bond's predictions of 1636 and 1668 are consistent with the fitting of quadratic and cubic equations to existing observational data by means of the solution of simultaneous equations, and it is therefore argued that he anticipated 'Meyer's method' by over 100 years. Furthermore, Bond's forecast of 1668 made use of his discovery that the tangent of the angle of inclination is equal to twice the cotangent of the angle of magnetic latitude, thereby anticipating the findings of Biot and Krafft by c. 130 years.