Hyder (1968) has suggested that longitudinal magnetograph measurements of weak magnetic fields in prominences have underestimated field strengths as the result of zero-field levelcrossing interference (the Hanle effect). Hyder (1968) also suggested that resonance polarization effects have sometimes led to errors in measurements of the transverse component of magnetic fields. Stenflo (1969) has pointed out some errors in Hyder's paper, while contending that the Hanle effect is implicitly included in current theories of line formation in the presence of Zeeman splitting. In the present Note these questions are re-examined using the results of a density matrix treatment of absorption, emission, and scattering processes. The basic conclusions are as follows: (1) Longitudinal magnetograph measurements using optically thin lines are not influenced by the Hanle effect. (2) Although present theories of line formation in magnetic fields do not include the Hanle effect, this omission is generally unimportant for lines formed in the photosphere and lower chromosphere due to rapid collisional depolarization of atomic levels. (3) For the same reason, other resonance polarization effects are probably too small to cause significant errors in magnetograph measurements of all but the very weakest magnetic fields, when photospheric and lower chromospheric lines are used. (4) By contrast, the general phenomenon of atomic level polarization is quite important in most prominences. As emphasized by Hyder, extreme care must be used in selecting lines for magnetograph studies of solar magnetic fields.