Observations of variable broadband linear polarization in magnetic Ap stars (due to the transverse Zeeman effect), when combined with measurements of the mean longitudinal field Bɩ can in some cases allow one to determine the angles i and β (which describe the inclination of the stellar axis of rotation and the obliquity of the magnetic axis to the rotation axis) much more accurately than these angles can be determined from observations of Bɩ alone. Such variable intrinsic linear polarization has been observed for a number of stars; the effect is generally detectable only in cool Ap stars of unusually large field strength. We discuss the data and simple modelling for the stars HD 24712 = HR 1217, HD 137909 = β CrB, and HD 62140 = 49 Cam.