New methods for interpolating and analyzing magnetic fields observed over the earth's surface are described and applied to the quiet-day magnetic daily variations during the sunspot minimum 1932-3. The methods avoid some of the disadvantages inherent in the use of spherical harmonic analysis. The field components are interpolated over the earth for selected instants of universal time. A potential is determined by numerical methods, the north and east components being used simultaneously. The potential is separated into parts of external and internal origin by the use of surface-integral formulae. The methods are described in part I, and tables required for their application are given. Part II deals with the results thus obtained for the Sq field for the combined months 1933 May to August. The definition of the Sq field and the reduction of the data to a standard form are also discussed.