Earth's magnetic field has decayed by about 5% per century since measurements began in 1840. Directional measurements predate those of intensity by more than 250 years, and we combined the global model of directions with paleomagnetic intensity measurements to estimate the fall in strength for this earlier period (1590 to 1840 A.D.). We found that magnetic field strength was nearly constant throughout this time, in contrast to the later period. Extrapolating to the core surface showed that the fall in strength originated in patches of reverse magnetic flux in the Southern Hemisphere. These patches were detectable by directional data alone; the pre-1840 model showed little or no evidence of them, supporting the conclusion of a steady dipole up to 1840.