Magnetometer observations on board the Polar spacecraft have been used to measure the magnetospheric response to rapid changes in the dynamic pressure of the solar wind. Over much of the magnetosphere the magnetic field increases when the solar wind dynamic pressure increases, roughly in proportion to the square root of the change of the solar wind dynamic pressure with a proportionality similar to that seen in ground-based data. Nevertheless, dynamic pressure increases can lead to reductions in the magnitude of the magnetic field. These reductions occur on the dayside polar field lines, where the magnetospheric field points southward while the perturbation field due to the magnetopause current is northward. Throughout most of the magnetosphere these changes occur slowly over ~5--10 min as the interplanetary shock envelopes the dayside magnetosphere and near tail. Compressions of the magnetosphere generally lead to increases in the intensity of the ULF waves along the field lines, but in one case the wave intensity decreased upon compression of the field. This decrease occurred in the predawn sector while the increases occurred in the noon to postdusk sector. ¿ 2001 American Geophysical Union