I finally found a reasonable description of the Zeeman effect.
b = zB cos θ , where z is the Zeeman splitting factor (Hz mG−1), B is the
magnetic field, and θ is the angle of the magnetic field to the line of sight (Crutcher et al.
1993).
This came from the paper "Detection of the Zeeman Effect in the 36 GHz Class I CH3OH maser line with the EVLA" by A. P. Sarma, E. Momjian
http://arxiv.org/PS_cache/arxiv/pdf/0910/0910.1081v1.pdf
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