Analytical Solution of Magnetic Declination Problem

The magnetic declination problem involves the determination of present magnetic bearings (or azimuths) of township surveys for the purpose of retracement, based on original survey data. This paper presents an analytical solution of a problem which has been solved only graphically. The analytical solution, which takes the form of simple formulas, gives the present magnetic azimuth of a line in terms of the original magnetic bearing, original and present declinations, and integer variables designating the directions of bearing and declinations. The formulas can be applied without the need for drawing sketches and are amenable to computation by calculators or computers. A calculator program for performing the computations is included. The analytical solution should save considerable time in preparing the retracement surveys, especially when they involve a large number of traverse lines.