The most widely used method for finding the number of unpaired electron spins in a sample is to compare the electron paramagnetic resonance signal of the sample with that for a standard sample containing a known number of spins (1, 2). When magnetic field modulation is employed, as is almost always the case, the signal is in the form of the derivative with respect to magnetic field of the resonance absorption curve. It is usual therefore to determine the number of spins, N, by comparison of these derivative spectra. The peak-to-peak height of the signal depends, among other factors, on the amplitudes H, and I$, of the microwave and modulation fields respectively and, in order to find N, the signal heights must be evaluated for the same II, and H, (H, refers to that component of the microwave field which induces transitions). This is trivial if both samples have the same size and shape and are placed at the same position within the microwave cavity. However, frequently this is not the case. One type of standard sample which is commercially available (for example, from Varian or Bruker) is “pitch in KCl”, which consists of fine particles of pitch dispersed in powdered KCI; this is contained in a thin-walled quartz tube with an outer diameter of about 4 mm. This tube is usually inserted so that the pitch extends the full length of the cavity. However, the sample with unknown number of spins may be nearly pointlike. In this case the nonun~brmity of both H, and H,,, must be taken into account when finding N. Poole ( 1) discusses the nonuniformity of H, and the need to take it into account when measuring relaxation times has been dealt with (3, 4) but we are unaware of any publication which considers the effect of the nonuniformity of H,. In this paper we present results for two X-band Bruker cavities-one rectangular . operating m the TEloz mode and the other the ER4108 TMH cylindrical cavity operating in the TM, ,0 mode. The internal dimensions of the rectangular cavity are 4.2 X 2.35 X 1.1 cm; it has sample access holes in the middle of the 4.2 X 1.1 cm faces. The cylindrical cavity has an internal diameter of 4 cm and has plastic inserts at both ends, on which are mounted the modulation coils. Two access holes on opposite “sides” of the cylinder allow the sample to be inserted along a diameter of the central circular cross section of the cylinder. The amplitude H, of the 100 kHz modulation field was measured as a function of position along the line joining the centers of the access holes-hereafter referred to as the sample axis-using a small pickup coil. The peak-to-peak height, h, of the EPR signal was also measured as a function of position along this axis using a small ( 1.3 X 1.5 X 1.9 mm) sample of MgO containing Pi