Spherical harmonic analysis of the earth's magnetic field is limited in the resolution that can be obtained. This limitation is caused by inadequacies of computers and of available data sets. The fundamental wavelength in spherical harmonic analysis is the circumference of the earth. To resolve wavelengths as short as 100 km would require a spherical harmonic analysis carried out to a degree and order 400 involving 160,800 coefficients. This is impractical even with modern computers. This limitation of spherical harmonic analysis can be overcome by using rectangular harmonic analysis in successively smaller areas so that the data are more fully utilized. Rectangular harmonic analysis is illustrated for data from Europe and then again for a subset of the data from a smaller area of Europe. The magnetic field at 15 observatories for the smaller area can be computed to an rms residual of only 7 nT for all three components using two sets of rectangular harmonic coefficients and the AWC/75 world chart model. Rectangular harmonic analysis and spherical harmonic analysis are complementary.