The technique of field spinning Zeeman modulation in microwave spectroscopy has been extended to long cylindrical absorption cells by using orthogonal pairs of cosine distribution magnets. This magnet configuration permits economical application of the field spinning approach to rather long path length, large diameter cells with substantial homogeneity of the field. Fields adequate for microwave spectroscopy may be obtained even within a metallic (preferably austenitic stainless steel) cylindrical vacuum chamber. The solutions of Maxwell's equations for an idealization of the latter situation of an intervening conducting layer are presented, so that with the formulas given here, one may easily calculate available field as a function of geometry, amplifier power, modulation frequency, and circuit parameters. Two new microwave spectrometers have been constructed using such magnets, and our experiences with applying the field spinning technique to them will be discussed. Because the absorption cells are discharge tubes, we will consider the effects which the presence of the plasma has on the field spinning modulation method. While the plasma does give rise to the complication of a nonflat base line, it will be demonstrated that this can be held to quite manageable levels over a wide range of conditions. The spurious baseline fluctuation is likely to be observed in other configurations of Zeeman modulation of a plasma sample and appears to be related to a modulation of the plasma density and the resultant change in its refractive index.